# Labor Income Risk and the Cross-Section of Expected Returns

Mykola Pinchuk Simon Business School, University of Rochester. Email:
<EMAIL_ADDRESS>
I would like to thank Alan Moreira, Yixin Chen, Bill Schwert, Christian Opp,
Yukun Liu, Jerry Warner, Shuaiyu Chen, Pingle Wang, Yushan Zhuang, Xuyuanda
Qi, David Swanson and Robert Mann for helpful comments. All errors are my own.

(03 December 2020)

Abstract

This paper examines cross-industry dispersion (CID), defined as a mean
absolute deviation of returns of 49 industry portfolios. CID peaks during
periods of accelerated sectoral reallocation and heightened uncertainty. I
find that expected stock returns are related cross-sectionally to the
sensitivities of returns to innovations in CID. Annualized returns of the
stocks with high sensitivity to CID are 5.9% lower than the returns of the
stocks with low sensitivity. Abnormal returns with respect to the best factor
model are 3.5%, suggesting that common factors can not explain this return
spread. CID predicts unemployment through its long-term component, consistent
with the hypothesis that CID is a proxy for unemployment risk from sectoral
shifts.

##  1 Introduction

The economy is a dynamic system with permanently evolving structure. As some
industries are born, other industries lose their importance. Few people in
1970s could have predicted that within 20 years IT sector would capture the
largest share of the stock market. There is no reason to expect a constant
rate of this structural transformation. Naturally, accelerated structural
transformation increases aggregate economic uncertainty and labor income risk
for workers in underperforming industries. COVID-19 pandemic and resulting
reallocation of labor and capital across industries is the most recent example
of this transformation. This paper explores the asset pricing implications of
such sectoral reallocation and related labor risk.

####

The paper measures time-varying structural uncertainty using cross-industry
dispersion (CID), defined as the mean absolute deviation of the returns of 49
industry portfolios. I document a novel evidence that stock exposures to
cross-industry dispersion (CID) predict the cross section of expected returns.
The paper finds that the firms with large return sensitivity to CID deliver
smaller returns than the stocks with low sensitivity to CID. This finding
suggests that in equilibrium there exists an extra demand for stocks,
positively comoving with CID, implying low expected returns of these stocks.
The long-short value-weighted portfolio, formed on the sensitivity to CID,
delivers monthly return of 49 bps with abnormal returns of 29-60 bps. The
results are not explained by the other measures of volatility and uncertainty.
CID subsumes large fraction of cross-sectional return predictability of common
idiosyncratic volatility CIV (Herskovic, Kelly, Lustig, Van Niewerburgh 2016).

####

This evidence is consistent with several broad sources of risk, possibly
related to CID. Periods of highly nonhomogeneous performance across industries
(high CID) are likely to be periods of accelerated sectoral reallocation of
resources and increased economic uncertainty. Times with a large wedge between
winning and losing industries can proxy for the periods of rapid economic
transformation, when some industries become more important, while the others
lose relevance. High CID may indicate a temporary decrease in output and
efficiency as resources are reallocated across sectors (Lilien 1982).

####

More specifically, labor income risk can explain relevance of CID to asset
pricing. By construction, high CID means that some industries severely
underperform the market, while the others enjoy exceptionally high returns.
This pattern is likely to raise a concern that losing industry is under the
threat of dying. Naturally, this is a period of a negative shock to expected
lifetime labor income of the employees in underperforming industries. The fact
that there are both outperforming and underperforming industries with returns
sufficiently far from the market return implies even larger labor income risk
than the one during a recession. Within a recession, the common wisdom is that
most of lost jobs will be recovered at some point in the future, while a
disappearance of some industry means a loss of industry-specific jobs forever.

####

While many occupations are demanded across industries, they are usually low
skill occupations, less relevant to asset pricing. Losing high-wage job
constitutes larger negative shock to expected lifetime income. Moreover, high-
paid workers are likely to have more savings and produce larger effect on
financial market. High-skill jobs (e.g., aerospace engineer) are usually
confined to a few industries, implying very low across-industry labor
mobility. Thus, I expect that CID captures the asset pricing effect of Cross-
sectional Dispersion (CSD), consistent with labor income risk. According to
labor income risk explanation, stocks with negative covariance with CID are
more risky, since they tend to fall when the risk of losing high skill
industry-immobile jobs is large.

####

This paper draws upon the theoretical contribution of Duffie and
Constantinides (1996) to motivate CID as a state variable. Duffie and
Constantinides show that in a model with heterogeneous agents, subject to
uninsurable labor income shocks, cross-sectional variance of agents’
consumption growth becomes a state variable. As discussed above, severe
underperformance of their industry suggests a negative shock to expected
consumption growth of employees.

####

This article builds upon a body of work from macroeconomics. Lilien (1982)
reports that sectoral shifts and performance dispersion result in unemployment
shocks, caused by migration of employees between firms and sectors. Loungani,
Rush and Tave (1990) construct stock market dispersion index and document that
it predicts unemployment. Brainard and Cutler (1993) use similar measure to
assess the contribution of sectoral reallocation to unemployment. They find
that sectoral reallocation accounts for a large share of unemployment
fluctuations at long horizons. Multiple studies (Summers and Carrol 1991,
Blundell, Pistaferri and Preston 2008, Guvenen and Smith 2014, Heathcote,
Storesletten and Violante 2014) document that households do not completely
insure their consumption from persistent shocks to the labor income. These
findings highlight the importance of labor income risk for asset pricing.

####

The research on economic uncertainty frequently uses cross-sectional
dispersion of accounting variables as a measure of uncertainty. Bloom (2009)
documents a strong correlation between the indicators of macroeconomic
uncertainty, including time-series measures of market volatility, the cross-
sectional variance of firms‘ pretax profit growth and returns as well as a
dispersion across macroeconomic forecasts. He argues that all of these
variables proxy for financial and macroeconomic uncertainty. Sadka (2012)
finds that higher earnings dispersion is associated with higher expected
returns, suggesting that earnings dispersion is a state variable from an asset
pricing model. Jurado, Ludvigson and Ng (2015) use cross-sectional dispersion
of a profit growth in order to construct the index of macroeconomic
uncertainty.

####

This study contributes to several domains of literature. Different measures of
market volatility have traditionally been used as a proxy for economic and
financial uncertainty. Ang, Hodrick, Xing and Zhang (2006) empirically show
that exposure of stocks to VIX is priced in the cross-section of expected
stock returns. Herskovic, Kelly, Lustig and Van Nieuwerburgh (2016) report
that stocks with larger sensitivity to common idiosyncratic volatility (CIV)
earn lower expected returns. They argue that CIV proxies for idiosyncratic
risk faced by households and suggest labor income risk as a main channel.
Eiling (2013) uses industry-specific labor income growth rates to extend human
capital CAPM (Jagannathan and Wang 1996) and shows that her empirical model
can price 25 size and book-to-market portfolios. Eiling, Kan and Sharifkhani
(2018) use production-based asset pricing model to motivate the predictability
of market returns by sectoral labor reallocation shocks.

####

This paper is closely related to the literature on cross-sectional dispersion
(CSD), defined as a standard (mean absolute) deviation of the cross section of
stock returns. Bekaert and Harvey (1997, 2000) use CSD as a measure of
development and maturity of the stock market. Stivers (2003, 2006, 2010) finds
that CSD can predict idiosyncratic volatility as well as returns of value and
momentum premia. Maio (2013, 2016) reports that the cross-sectional standard
deviation of returns of the portfolios sorted on size and book-to-market can
predict market returns. The closest paper to this one is Verousis and
Voukelatos (2018). They find that the stocks with high sensitivity to CSD
offer lower returns in their 1996-2012 sample. Due to the more idiosyncratic
nature of CSD, the authors explain the findings by idiosyncratic risk without
elaborating on or providing evidence for their explanation.

####

This paper uses 1963-2019 sample and shows that high sensitivities to CID
predict lower expected returns. I argue that this predictability stems from
return dispersion across industries, proxying for labor income risk due to
sectoral shifts. These results suggest that only the cross-industry component
of CSD (i.e., CID) is priced. The long-short portfolio, formed on CID,
controlling for CSD, delivers 29 bps (t-statistic=2.1) monthly abnormal
returns, while the long-short portfolio, formed on CSD, controlling for CID,
produces 10 bps (t-statistic=0.5) returns. Therefore, these results suggest
that cross-sectional predictability of returns by CSD is not driven by
idiosyncratic risk, relevant for underdiverisified investors. CSD is a
manifestation of more fundamental economic force - labor income risk from
structural shifts, proxied by CID.

####

I show that industry returns predict industry employment growth. The
predictability is much stronger in the subsample with negative industry
returns, implying that this predictability reflects unemployment risk.
Consistent with sectoral shifts hypothesis, high CID predicts high aggregate
unemployment at the quarterly frequency. The results suggest that predictive
power of CID for unemployment growth is driven by the long-term component of
unemployment growth. Unlike aggregate demand shocks, sectoral reallocation
shocks are likely to have permanent effect on unemployment growth (Brainard
and Cutler 1993). Consistent with CID, proxying for labor income risk from
sectoral shifts, CID strongly predicts long-term unemployment, but has little
relation with its short-term component. Overall, these results support the
explanation of CID premium by industry-specific human capital risk from
sectoral shifts.

##  2 Data and Dispersion Measures

###  2.1 Sample

The paper uses stock price data from CRSP and accounting data from Compustat.
The sample encompasses 1963-2019. I download macroeconomic data from St. Louis
Federal Reserve Bank. Bureau of Labor Statistics (BLS) is the source of
unemployment data. I consider common stocks traded at NYSE, NASDAQ or AMEX and
perform the main asset pricing tests at the monthly frequency. The sample of
stock returns consists of 3058110 firm-month observations with nonmissing
returns. In order to exclude small and illiquid stocks from the analysis, I
restrict the sample to the stocks with price above $5 at the end of the
previous year and the stocks with market capitalization above $50 million in
2018 dollars. After this restriction the sample consists of 1841271 firm-month
observations. All the analysis below uses excess returns.

####

Kenneth French‘s website is a source of data on stock market factors as well
as industry classifications and returns of industry portfolios. I download
uncertainty indices, constructed by Jurado, Ludvigson and Ng (2015) from
Sydney Ludvigson‘s website.

###  2.2 Construction of Dispersion Measures

The paper defines cross-industry dispersion as the mean absolute deviation of
returns across 49 industry portfolios at any given period.

$CID_{t}=\frac{1}{N}\sum^{N}_{i=1}{|R_{it}-R_{MKT,t}|}.$ (1)

I use monthly value-weighted returns of Fama-French 49 industry portfolios. I
compute CID every month during the period, spanning 1927-2020. Since some
industries have few firms at the beginning of the sample, the paper computes
CID across the industries with at least 10 firms. I proxy for the market
return with the value-weighted market return across all firms from CRSP
(vwretd). I use the similar approach to calculate Cross-Sectional Dispersion
(CSD) and Within-Industry Dispersion (WID).

####

The Figure 1 plots the time series of CID. To be consistent with asset pricing
literature, I focus on CID after 1963. The time series of CID exhibits two
large secular increases. The first long-term spike took place within 1998-2003
and is likely associated with the dotcom boom and the following decline. The
second spike was recorded during 2007-2009, coinciding with the recent
financial crisis. Both events are consistent with the hypothesis that CID
proxies for some dimension of uncertainty and is related to the rate of
sectoral shifts in the economy. Intuitively, CSD is a sum of CID and WID, so
Figure 1 facilitates comparison between these variables. Notice large spike in
CID during March-April 2020. This jump in CID reflects heterogeneous impact of
COVID-19 pandemic and related mitigation measures on different industries.

####

The next step of the analysis will be to estimate sensitivities of the stocks
to fluctuations in CID. To facilitate the interpretation of CID as a state
variable from consumption-based asset pricing model and avoid econometric
issues, I difference CID, using the same specification as in Pastor and
Stambaugh (2003). That is, I calculate first difference of CID and estimate
its residuals from AR(1) model:

$\Delta(CID_{t})=\gamma_{0}+\gamma_{1}\Delta(CID_{t-1})+\gamma_{2}CID_{t-1}+u_{t}.$
(2)

Abusing notation, I refer to the residual $\hat{u}_{t}$ as $CID_{t}$ in the
rest of the paper. 1-lag autocorrelation of CID is -0.05, implying very low
persistence. Thus, I can use $CID_{t}$ as an explanatory variable in
predictive regressions without spurious regression issues (Novy-Marx 2013).

####

Table 1 reports correlations of CID with other measures of uncertainty and
volatility. Since all time series are differenced according to Pastor and
Stambaugh (2003) specification, the correlations are relatively low. CID has
positive correlation with all the variables, ranging from 0.07 to 0.30. The
results suggest that CID is distinct from, though positively related to
frequently used uncertainty and volatility measures.

##  3 Asset Pricing Results

This section documents and discusses the main results of the paper. First, I
explain how I estimate the sensitivity of stock returns to CID. Then, I form
decile portfolios on $\beta_{CID}$ and compute their returns. Finally, the
section discusses the asset pricing performance of different measures of
cross-sectional dispersion.

###  3.1 Estimation of $\beta_{CID}$

I use monthly stocks returns in order to obtain estimates of their
sensitivities to CID. While using daily returns produces more precise
estimates, it hampers interpretation of CID as labor income risk. The paper
uses two years of monthly excess returns to estimate betas from the following
time series regression:

$R_{it}=\alpha+\beta CID_{t}+\epsilon_{t}.$ (3)

Since controlling for market returns has little effect on the results, I use
simpler specification (3). I estimate betas over the period 1963-2018. To
compensate for the extreme values of $\hat{\beta}_{CID}$, possibly resulting
from imprecise estimation, I winsorize $\hat{\beta}_{CID}$ at 1% and 99%
percentiles. Section 5.3 verifies that the results are not due to factors,
omitted during estimation of $\beta_{CID}$.

###  3.2 Portfolios, formed on $\beta_{CID}$

Every month, I sort the stocks into quintile portfolios based on their
$\beta_{CID}$. I update estimates of $\beta_{CID}$ and rebalance portfolios
every month. Table 2 reports mean values of characteristics of decile
$\beta_{CID}$-sorted value-weighted portfolios. Stocks in the highest quintile
are somewhat larger, more liquid, have faster asset growth and higher past
returns.

####

Table 3 describes excess returns of value-weighted portfolios, formed on
$\beta_{CID}$. Returns of value-weighted portfolios, sorted on $\beta_{CID}$,
decrease monotonically. The long-short value-weighted portfolio generates 49
bps average monthly returns with t-statistic of 3.19.

####

Table 4 presents abnormal returns of the value-weighted long-short quintile
portfolio with respect to most frequently used factor models. Controlling for
market beta does not have significant effect on the CID premium. T-statistic
of these abnormal returns stays comfortably below -3, meeting the challenge of
Harvey et al. (2016). Fama-French 5 factor model, augmented with momentum and
short-term reversal factors, leaves abnormal returns of 50 bps (t-statistics =
-3.26). While the loadings on size, vale and profitability factors can explain
a fraction of returns of this trading strategy, the loadings on market and
momentum factors make these returns even more anomalous (Table 5).
Profitability is the only factor, which can explain large part of CID premium.
The results are consistent with the idea that CID premium is the price of some
risk, unexplained by commonly used factor models. The next section empirically
shows that high CID is associated with larger unemployment risk for workers
with industry-specific human capital. High $\beta_{CID}$ stocks are natural
hedges against such labor risk from sectoral shifts.

####

Table 6 reports the returns of long-short portfolios, double-sorted on size
and CID. Even controlling for size, the long-short portfolio from tercile
sorts on CID delivers statistically significant abnormal returns of 17-40 bps.
Somewhat weaker results are likely driven by both size effect and a low
precision of $\beta_{CID}$ estimates, combined with very coarse sorts.

####

Monthly frequency, used to estimate $\beta_{CID}$, raises the question of the
trade-off between economic intuition and statistical precision. While labor
risk story is more intuitive at monthly CID frequency, the estimates of
sensitivity of returns to other variables at monthly frequency are notoriously
imprecise. In unreported results, $\beta_{CID}$, estimated at daily frequency,
produces larger return spreads and strong positive relationship between pre-
ranking betas and post-ranking betas.

###  3.3 Cross-sectional Results

To check a robustness of the cross-sectional predictability of returns by
$\beta_{CID}$, I employ Fama-MacBeth regressions. Table 7 reports the results
of Fama-MacBeth regressions across decile $\beta_{CID}$-sorted portfolios.
Controlling for stock characteristics, $\beta_{CID}$ is a significant negative
determinant of excess returns. Its coefficient varies between -0.08 and -0.12,
corresponding to 1.0% to 1.5% smaller annualized returns. Since the standard
deviation of $\beta_{CID}$ is 3.22, the results suggest that 1 standard
deviation increase in $\beta_{CID}$ is associated with 3.2%-4.6% smaller
annualized returns. These numbers suggest economically significant price of
risk, associated with CID. These estimates of the price of risk are very
similar to the estimates from nonparametric analysis using time-series
regressions.

###  3.4 Performance of other dispersion measures

Verousis and Voukelatos (2018) find that in 1996-2012 sample lower CSD is
associated with high excess returns. The obvious question is whether CSD
premium is driven by its across-industry component (CID) or within-industry
component (WID). To answer this question, I perform double sorts on WID and
CID. Table 8 reports the results with value-weighted portfolios from 5x5
double sorts. I construct the long-short portfolio from the sort on CID,
controlling for WID, and vice versa. Except the case of CAPM, the long-short
portfolio from WID sorts delivers abnormal returns between 21 and -15 bps, not
significantly different from zero. The long-short portfolio from CID sorts
produces abnormal returns between 30 and 14 bps, which are significant in
three cases. These results imply that CID is better than WID in capturing a
priced dimension of cross-sectional dispersion.

####

Table 9 reports the similar results from 5x5 double sorts on $\beta_{CID}$ and
$\beta_{CSD}$. The long-short portfolio from CSD sorts produces negative
abnormal returns with respect to Fama-French 5 factor model, augmented with
momentum factors. Since these returns have the sign, inconsistent with the
idiosyncratic risk explanation of Verousis and Voukelatos, the results clearly
suggest that CSD predicts the cross section of expected returns only through
CID. Controlling for CSD, CID long-short portfolio generates abnormal returns
between 12 and 30 bps. Overall, the results suggest that CID reflects a priced
component of cross-sectional volatility.

###  3.5 CID and idiosyncratic volatility

As Table 1 suggest, sensitivity of stocks to CID is likely to be strongly
correlated with the sensitivity to other volatility measures, such as market
volatility and CIV (Herskovic, Kelly, Lustig and Van Nieuwerburgh 2016). Since
Herskovic et al. (2016) argue that CIV captures household labor risk, it is
important to compare asset pricing relevance of CID and CIV.

####

Table 11 reports the results of double-sorts on $\beta_{CID}$ and
$\beta_{CIV}$. 5x5 independent double sort allows to form long-short
portfolios on $\beta_{CID}$, controlling for $\beta_{CIV}$ and vice versa.
While long-short portfolio, formed on $\beta_{CID}$ generates economically and
statistically significant return of 40 bps, the long-short portfolio, formed
on $\beta_{CIV}$, has only 8 bps returns and fails to consistently produce
abnormal returns. Its abnormal returns range between -5 and 5 bps and are not
statistically significant. On the other hand, the long-short portfolio, formed
on $\beta_{CID}$, delivers abnormal returns between 20 and 54 bps with
t-statistics above 2 with respect to most factor models. Overall, the results
suggest that CID mostly subsumes abnormal component of CIV premium.

####

In order to obtain further evidence on asset pricing performance of CID and
CIV, I employ spanning tests. Tables 12 and 13 document their results using
CID and CIV factors, constructed as the long-short quintile portfolios from
univariate sorts on these variables. Controlling for CIV factor decreases
abnormal returns of CID factor from 50 to 47 bps with t-statistic of 3. On the
other hand, CID factor weakens performance of CIV factor from 15 to 5 bps
abnormal returns (t-statistic of 0.3).

####

CID can explain significant fraction of CIV premium, while the results from
spanning tests suggest that CID factor mostly subsumes CIV factor. Overall,
CID and CIV appear to share significant common component, which is better
explained by CID. The remaining asset pricing power of these two measures
seems to come from different sources. As a measure of time-series volatility,
CIV additionally proxies for some form of time-varying uncertainty, while CID
measures cross-section dispersion and is likely to proxy for the rate of
sectoral transformation of the economy.

##  4 Economic Channel: Labor Income Risk

###  4.1 Economic Mechanism

Constantinides and Duffie (1996) develop the model with agents, subject to
heterogeneous uninsurable income shocks. They show that the cross-sectional
variance of individual consumption growth enters Euler equation. While the
model analytically proves the relevance of the cross-sectional variance of
consumption growth for asset pricing, it remains silent on its economic
channels and meaning. This story naturally fits macrolabor literature which
uses different measures of dispersion of stock returns to proxy for
unemployment shocks, resulting from structural shifts.

####

Fluctuations in individual labor income can arise from two channels: a change
in wage and a change in employment. Larger magnitude of labor income shocks
from employment loss as well as downward wage rigidity suggests that
unemployment risk is the most important component of labor income fluctuations
for asset pricing. Macroeconomic literature views the changes in aggregate
employment as the result of two forces: aggregate shocks and reallocation
shocks. Lilien (1982) introduces the sectoral shifts hypothesis entailing that
higher magnitude of sectoral shifts leads to higher unemployment by increasing
amount of labor reallocation. While Lilien uses the variance of employment
growth across sectors to measure the reallocation, Loungani, Rush and Tave
(1990) argue that the variance of stock returns across sectors is more precise
and forward-looking measure.

####

This paper uses CID to capture a divergence in performance across industries,
indicative of a change in sectoral composition of the economy. Therefore,
periods of high CID are indicators of increased risk of losing lobs in
underperforming industries. While many occupations are not industry-specific
(e.g., janitor), the others are closely related to few industries (e.g.,
aerospace engineer). A potential disappearance of underperforming industry
constitutes large labor income risk for such high-skill industry-specific
occupations. Addison and Portugal (1989) as well as Jacobson, LaLonde and
Sullivan (1993) document that workers experience large wage decrease after
switching industry.

####

According to this story, changes in CID should have positive relationship with
both contemporaneous and future unemployment growth. Since a positive shock to
CID reflects an increase in the rate of sectoral reallocation of resources and
labor, it should be associated with layoffs. Therefore, I expect a positive
relationship between CID changes and unemployment changes. Since stock prices
have more forward-looking nature and move faster than measures of real
economic activity, the firm’s employment decisions will respond to stock
returns with some lag. Thus, we should expect positive predictability of
unemployment growth by CID changes.

###  4.2 Results

Table 13 shows that CID predicts unemployment at the quarterly frequency,
controlling for other stock market-based predictors of business cycles. Using
the sample of 1948-2019, I regress unemployment growth on the changes in CID
in the previous quarter. The first two columns report positive and
statistically significant coefficients (t-statistic of 2.77 and 2.59),
suggesting that the results are robust to known stock market predictors of
business cycle. These results are consistent with the findings of Loungani,
Rush, Tave (1990) and Brainard, Cutler (1993) and suggest that CID can
forecast unemployment growth.

####

Labor risk explanation of CID premium is based on the idea that CID is a proxy
for more permanent component of unemployment risk, arising from sectoral
shifts as opposed to aggregate shocks. Macroeconomic literature (Lilien 1982,
Loungani et al. 1990) argues that while unemployment from aggregate shocks
have transitory nature, sectoral shifts have more long-term effects on
unemployment. For example, if small short-term aggregate shock hits the
economy, then struggling firms in different industries are likely to fire
workers to cut the costs. As long as there are no industries,
disproportionally affected by this shock, it will not cause sectoral
reallocation of labor. Successful firms are likely to hire workers, fired from
struggling firms in the same industries. Therefore, such short-term aggregate
shocks are unlikely to have a major effect on long-term unemployment.

####

The last four columns of Table 13 show that the predictability of unemployment
growth by CID changes is mostly driven by long-term component of unemployment
growth. CID predicts growth in long-term unemployment (t-statistics 2.24), but
can not predict growth in short-term unemployment. Adjusted $R^{2}$ of these
regressions provide even stronger results. While CID explains 4% of the
variation in future long-term unemployment growth, adding aggregate market
predictors (first and second moments of market returns) increases this
fraction only to 6%. On the other hand, CID has no explanatory power for the
variation in future short-term unemployment growth as evidenced by negative
adjusted $R^{2}$. However, adding aggregate market controls increases the
fraction of explained variation to 12%. These results suggest that CID is more
important predictor of long-term unemployment than aggregate stock market
variables are, while these aggregate variables are much better predictors of
short-term unemployment growth. These findings are consistent with CID
reflecting sectoral shifts and aggregate stock market variables accounting for
aggregate short-term shocks. Thus, the evidence supports the explanation of
CID premium by long-term unemployment risk from sectoral shifts.

##  5 Further results

###  5.1 Robustness to other industry classifications

Since Fama-French (FF) 49 industry classification is arbitrary, I explore the
robustness of the findings to industry definitions at the varying levels of
coarseness. I compute CID using FF30, FF17, FF10 and FF5 industry definitions.
Figure 3 reports CID premium at the different levels of industry aggregation.
The results change a little as industry coarseness increases. Surprisingly, we
observe large CID premium even as the paper computes CID across 5 industry
portfolios. The results suggest that CID premium reflects the variation of
returns between few broad industries.

####

Figure 3 reports that the results are robust to finer industry
classifications, such as the first 2, 3, 4 digits of company SIC code. Since
in such fine classifications often there are very few firms in a particular
industry group, I compute CID using only industries, containing at least 5
firms. The median number of such industries are 63, 174 and 212 for SIC 2, SIC
3 and SIC 4 classifications respectively. The Figure 3 shows that mean returns
of $\beta_{CID}$-sorted quintile long-short portfolios continue increasing as
we use finer industry classifications. This is consistent with table 8,
indicating small return spread in WID dimension using FF49 industries. As we
refine the industry sorts, this variation gets reflected into CID. However,
consistent with the fact that WID dimension from FF49 industries does not
generate large abnormal returns, using very fine industry classifications to
estimate CID does not increase abnormal returns.

####

Table 14 reports the returns of long-short portfolios, double-sorted on CID
and WID using FF5 industry classification. Now CID dimension is associated
with smaller return spread, ranging between -0.01 and 0.27. This spread is
statistically significant only with respect to two factor models. These
results are consistent with our intuition and show that the use of very coarse
industry classification leads to a loss of information, contained in CID.
Since dividing firms into 5 sectors leaves relatively heterogeneous firms
within each sector, a part of the variation, previously attributed to CID, is
now reflected in WID. These findings are different from Table 8, which reports
that CID from FF49 classification is much more relevant for asset pricing than
WID.

###  5.2 Robustness to other uncertainty measures

Table 1 reports the correlations between CID and other measures of
uncertainty: VIX, market volatility, financial uncertainty (Jurado, Ludvigson
and Ng 2015), macroeconomic uncertainty (Jurado, Ludvigson and Ng 2015) and
common idiosyncratic volatility (Herskovic, Kelly, Lustig and Van Nieuwerburgh
2016). Consistent with the hypothesis that all these variables capture
financial uncertainty, CID has a positive correlations with all of them.
However, the largest correlation of CID with these variables is 30%, implying
that CID is not just a noisy proxy for these uncertainty measures.

####

Table 10 reports the relationship between CID premium and aforementioned
uncertainty variables. I use 5x5 double sorts to control for sensitivities to
these uncertainty measures. Double sorts on $\beta_{CID}$ and $\beta_{Vol}$
indicate that CID is associated with large risk premium, robust to controlling
for asset pricing factors. The long-short portfolio, constructed on
$\beta_{CID}$ sorts, produces abnormal returns between 34 and 60 bps and
t-statistics above 2.4. While sorts on $\beta_{Vol}$ produce return spread, it
does not seem robust to different factor models. Panels B and C show that
$\beta_{CID}$ subsumes the relationship between stock sensitivities to
financial and macroeconomic uncertainty (Ludvigson 2015) and expected returns.
After controlling for $\beta_{CID}$, these uncertainty measures fail to
generate return spread of correct sign. On the other hand, in 11 out of 12
specifications, CID spread is highly significant, ranging between 28 and 67
bps. $\beta_{VIX}$ is the only variable, controlling for which eliminates
statistical significance of the CID premium. Controlling for VIX exposure,
long-short portfolios, formed on $\beta_{CID}$, deliver abnormal returns
between -11 and +28 bps.

###  5.3 Common factors in industry portfolios

One possible explanation of documented results is the difference in loadings
on common factors across industries. According to this hypothesis, the time-
series variation in CID merely reflects the variation in asset pricing
factors. For example, if there is a large heterogeneity in loadings on the
profitability factor across industries, then periods of very large or very low
returns of the RMW factor will mechanically generate large CID.

####

To test this explanation, I use abnormal returns of industry portfolios with
respect to Fama-French 5 factor model to calculate CID. Tables 15 reports that
hedging factor exposures has no effect on quintile returns. Similarly, Table
16 suggests that controlling for factor loadings across industries has small
effect on a magnitude of abnormal returns. Abnormal returns range between 22
and 57 bps.

###  5.4 $\beta_{CID}$ at daily, monthly and quarterly frequency

Labor risk explanation of CID premium crucially depends on our ability to ex
ante identify stocks, which hedge unemployment shocks, driven by sectoral
shifts. In other words, the necessary condition for this explanation is a
positive relationship between pre-ranking and post-ranking $\beta_{CID}$.

####

Decades of asset pricing research show that it is very hard to obtain accurate
estimates of covariances between individual stocks and a proxy for some state
variable at monthly frequency. Estimating betas at daily frequency is
increasingly common. Thus this subsection explores covariance between CID and
stock returns at different frequencies.

####

According to labor risk explanation, investors exhibit hedging demand for the
stocks, which tend to appreciate in value during periods of accelerated
sectoral reallocation of labor and capital. Therefore, this story is the most
consistent with monthly or quarterly $\beta_{CID}$ being priced in the cross-
section of expected stock returns. Figure 4 reports the relationship between
pre-ranking and post-ranking $\beta_{CID}$, estimated at monthly frequency. I
estimate pre-ranking betas using rolling 24-months window and use full sample
to estimate post-ranking betas of quintile portfolios. Post-ranking betas seem
to be flat. Using different window lengths does not achieve positive
relationship between pre- and post-ranking betas.

####

Tables 24 and 25 show the returns of quintile portfolios, formed on
$\beta_{CID}$, estimated at quarterly frequency. While returns of long/short
portfolio decrease in magnitude, alphas with respect to 3 out of 6 factor
models remain statistically significant at 5% significance level. Figure 5
shows slightly negative relationship between pre-ranking and post-ranking
betas, estimated at quarterly frequency.

####

Alternatively, I used 2 years of the recent daily returns to estimate
$\beta_{CID}$. Table 26 documents that returns of long-short portfolio remain
significant at 31 bps per month. Abnormal returns of this trading strategy are
significant with respect to 4 models out of 6. Most importantly, Figure 6
shows that pre-ranking $\beta_{CID}$ perfectly predicts post-ranking
$\beta_{CID}$, when estimated at daily frequency.

####

Table 28 explores possibility to use daily $\beta_{CID}$ as more accurate
proxy for monthly $\beta_{CID}$. Surprisingly, long-short portfolios, built
using the two betas, exhibit slightly negative correlation. Since it is
unlikely that unemployment risk from sectoral shifts varies a lot at daily
frequency, it is possible that the two trading strategies are driven by
different economic forces. Uncertainty is one of the possible explanation of
CID premium, when measured at daily frequency.

####

Lack of positive relationship between pre-ranking and post-ranking
$\beta_{CID}$ poses a challenge to rational explanation of CID premium by
unemployment risk. One possible explanation is investors‘ errors in predicting
$\beta_{CID}$. This story, in which investors require premium for holding the
stocks which appear though are not risky, violates rational expectations.

###  5.5 Variation in employment across industries and CID [Under
construction]

According to the explanation of CID premium by unemployment risk from sectoral
shifts, periods of increased CID precede times of accelerated sectoral
reallocation. We can use employment across industries to measure such sectoral
shifts.

####

Bureau of Labor Statistics (BLS) conducts Current Population Survey (CPS) at
monthly frequency. CPS contains information on employment across industries,
defined by their NAICS codes. Before 1989 CPS has very coarse sectoral
classification with 16 industries. After 1990 CPS contains employment data at
much finer level of NAICS classification, allowing to match them with returns
of FF49 industries.

####

The necessary condition for labor risk hypothesis is that returns of industry
portfolios are leading indicators of employment within these industries.
Therefore, risk of sectoral shifts increases when returns across industry
portfolios start diverging and not necessarily when employees lose jobs in
underperforming industries.

####

We can test this hypothesis by using returns of industry portfolios to predict
employment growth in those industries. The following two paragraphs will
discuss predictability of employment growth in 14 industries by their returns.
Since CPS is based on NAICS industry classification and this classification is
very inconvenient to import, for now I precisely match 14 industries from CPS
to respective FF49 industries. These 14 FF49 industries account for 49% - 53%
of total employment in my sample.

####

Figure 7 reports t-statistics of coefficients on lagged industry returns in
monthly-frequency predictive panel regressions. Both employment growth and
return of each industry are in excess of respective aggregate variables. While
there is no contemporaneous relation between return and employment growth,
there is significant predictability using returns for up to 3 lags. This is
consistent with economic intuition: firms in industries, underperforming in
the current month, do not start firing employees immediately. Industry returns
seem to lead industry employment growth by 2-3 months. This result is
consistent with CID predicting unemployment at quarterly frequency. It appears
that quarterly frequency is the optimal frequency to capture fluctuations in
unemployment risk due to sectoral shifts.

####

Table 29 documents results of predictive panel regressions at quarterly
frequency. The first columns shows that in 1990-2019 sample, industry return
over the last quarter is significant predictor of employment growth in the
current quarter. The next two columns report the results in subsamples with
quarters, where industry returns are negative(positive). Most of this
predictability comes from the subsample with negative stock returns. This
result implies that while underperforming industries significantly cut labor
force, winner industries increase number of employees to a smaller degree.
Therefore, industry returns contain more information about firing rather than
hiring decisions of firms within an industry.

##  6 Conclusion

This paper introduces CID as a measure of labor income risk from sectoral
shifts and explores its asset pricing implications. Stocks with low
$\beta_{CID}$ are more risky, since they decline precisely when investors are
subject to increased labor income risk. Consistent with this idea, these
stocks produce higher returns. The value-weighted long-short portfolio, formed
on $\beta_{CID}$, delivers 49 bps monthly returns. Abnormal returns range
between 29 and 63 bps. A heterogeneity in factor loadings across industry
portfolios does not explain these findings. The results are not explained by
known measures of uncertainty and labor income risk, such as volatility and
VIX (Ang, Hodrick, Xing and Zhang 2006), macroecocnomic and financial
uncertainty (Jurado, Ludvigson and Ng 2015) or common idiosyncratic volatility
(Herskovic, Kelly, Lustig and Van Nieuwerburgh 2016). I show that the
previously documented cross-sectional predictability of returns by cross-
sectional dispersion (CSD, Verousis and Voukelatos 2018) is a manifestation of
the CID premium. Controlling for CID, CSD loses its asset pricing relevance,
implying that CID reflects a priced component of CSD.

####

These findings are consistent with the hypothesis that CID premium arises due
to labor income risk from sectoral shifts. This paper uses CID as a proxy for
a rate of sectoral shifts, leading to unemployment risk in underperforming
industries. I show that industry returns predict industry employment growth.
The predictability is much stronger in the subsample with negative industry
returns, implying that this predictability reflects unemployment risk.
Consistent with macroeconomic literature, I find that CID predicts
unemployment. This predictability is mostly driven by medium-term and long-
term unemployment, in line with more permanent effect of sectoral reallocation
shocks on unemployment. These results support the idea that CID premium is
driven by industry-specific human capital risk due to sectoral shifts.

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## Appendix

Figure 1: Dispersion Measures

The plot describes the time series of cross-industry dispersion (CID) and
within-industry dispersion (WID). All the measures are calculated as the mean
absolute deviation of returns at the monthly frequency. Industries are defined
according to Fama-French 49 industry classification. The paper uses value-
weighted industry returns to calculate CID.

Figure 2: Performance of $1 (log scale)

The plot describes the growth of $1, invested in the long-short unisorted
quintile value-weighted portfolio, formed on $\beta_{CID}$.

Figure 3: Returns of quintile L/S portfolio using different Fama-French
industry partitions

The plot describes monthly returns and abnormal returns of quintile L/S
portfolios, formed on $\beta_{CID}$. X axis corresponds to the number of
industries in industry classification. I use Fama-French industry definitions
with different coarseness: 49, 30, 17, 10 and 5 industries to compute CID. To
obtain finer sorts, I use SIC 2, 3 and 4 digits to classify the firms into
industries. I compute CID only using the industries with at least 5 firms for
every period. The median number of industries with at least 5 firms for SIC
2-4 classifications are 63, 174 and 212. In the case of SIC classifications,
these numbers are depicted at x axis. Abnormal returns are calculated with
respect to Fama-French 5 factor model, augmented with Momentum and Short-term
Reversal factors.

Figure 4: Post-ranking betas vs pre-ranking betas using monthly returns

The plot describes realized full-sample $\beta_{CID}$ of quintile portfolios
compared to ex-ante rolling betas $\hat{\beta}_{CID}$ of these portfolios.

Figure 5: Post-ranking betas vs pre-ranking betas using quarterly returns

The plot describes realized full-sample $\beta_{CID}$ of quintile portfolios
compared to ex-ante rolling betas $\hat{\beta}_{CID}$ of these portfolios.

Figure 6: Postranking daily $\beta_{CID}$

The plot describes the relationship between postranking and preranking
$\beta_{CID}$ of decile portfolios, sorted on $\beta_{CID}$. Preranking betas
are estimated from regression (3) using 504 most recent days. To calculate
postranking betas, I run the regression (3) for each decile portfolio.

Figure 7: Predictability of industry employment using industry returns

The plot shows coefficient estimates from predictive panel regression for
industry employment growth using lagged industry returns. Industry employment
growth and return are normalized by aggregate employment growth and market
return. Sample covers 1990-2019.

Table 1: Correlations of differences in CID with differences in other
variables

The table reports correlations between differences in CID and changes in other
variables at the monthly frequency. VIX is implied volatility, available
starting from 1990. FU and MU are financial and macroeconomic uncertainty from
Sydney Ludvigson website. VOL is the volatility of monthly value-weighted
market index over the recent 24 months. CIV is common idosyncratic volatility
(Kelly et al., 2016).

| CID | FU | MU | VOL | CIV | VIX
---|---|---|---|---|---|---
CID | $1$ | $0.24$ | $0.07$ | $0.30$ | $0.29$ | $0.11$
FU | $0.24$ | $1$ | $0.44$ | $0.30$ | $0.39$ | $0.40$
MU | $0.07$ | $0.44$ | $1$ | $0.11$ | $0.24$ | $0.36$
VOL | $0.30$ | $0.30$ | $0.11$ | $1$ | $0.27$ | $0.34$
CIV | $0.29$ | $0.39$ | $0.24$ | $0.27$ | $1$ | $0.50$
VIX | $0.11$ | $0.40$ | $0.36$ | $0.34$ | $0.50$ | $1$

Table 2: Characteristics of quintile $\beta_{CID}$-sorted vw portfolios

The table reports mean values of characteristics of quintile portfolios,
sorted on $\beta_{CID}$. Size is log of market equity in the previous month.
B/M is Book-to-Market. OP is operating profitability. BA spread is the average
bid-ask spread as a percentage of average price over the previous month.

| Q1 | Q2 | Q3 | Q4 | Q5 | L/S
---|---|---|---|---|---|---
Return | $0.79$ | $0.63$ | $0.58$ | $0.45$ | $0.30$ | -$0.49$
T-stat (Return) | $3.83$ | $3.51$ | $3.55$ | $2.59$ | $1.40$ | -$3.19$
Prebeta | -$3.25$ | -$1.08$ | $0.27$ | $1.66$ | $4.12$ | $7.37$
Size | $8.12$ | $8.76$ | $8.96$ | $8.87$ | $8.40$ | $0.28$
log(B/M) | -$0.78$ | -$0.77$ | -$0.78$ | -$0.80$ | -$0.84$ | -$0.07$
OP | $0.16$ | $0.17$ | $0.17$ | $0.17$ | $0.17$ | $0.01$
Investment | $0.19$ | $0.15$ | $0.14$ | $0.15$ | $0.22$ | $0.03$
Beta | $1.04$ | $0.98$ | $0.99$ | $1.03$ | $1.14$ | $0.11$
BA Spread | $0.31$ | $0.23$ | $0.20$ | $0.19$ | $0.21$ | -$0.10$
Momentum 12-2 | $0.12$ | $0.09$ | $0.10$ | $0.12$ | $0.19$ | $0.07$
Volatility (1m) | $2.01$ | $1.68$ | $1.61$ | $1.69$ | $2.07$ | $0.06$
Volatility (12m) | $2.13$ | $1.75$ | $1.69$ | $1.79$ | $2.21$ | $0.08$

Table 3: Returns of quintile $\beta_{CID}$-sorted portfolios

The table reports mean monthly excess returns of quintile portfolios, sorted
on $\beta_{CID}$. Q1 is the quintile portfolio with the lowest $\beta_{CID}$
and Q5 contains the highest $\beta_{CID}$ stocks. L/S is the long-short
portfolio, formed by buying Q5 and selling Q1. Value-weighted portfolios are
constructed using as weights the market capitalization from the previous
month. The returns are calculated at the monthly frequency over 1963-2018.

| Q1 | Q2 | Q3 | Q4 | Q5 | L/S
---|---|---|---|---|---|---
Mean ew | 0.81 | 0.79∗∗∗ | 0.73∗∗∗ | 0.65∗∗∗ | 0.50∗∗ | -0.31∗∗
T-stat ew | 3.56 | 4.09 | 3.96 | 3.42 | 2.09 | -2.47
Mean vw | 0.79 | 0.63∗∗∗ | 0.58∗∗∗ | 0.45∗∗∗ | 0.30 | -0.49∗∗∗
T-stat vw | 3.83 | 3.51 | 3.55 | 2.59 | 1.40 | -3.19

Table 4: Abnormal returns of quintile $\beta_{CID}$-sorted vw portfolios

The table reports abnormal monthly returns of the long-short value-weighted
quintile portfolio, formed from sorts on $\beta_{CID}$. The last column
contains the abnormal returns with respect to Fama-French 5 factor model,
augmented with momentum and short-term reversal factors. The returns are
calculated at the monthly frequency over 1963-2018.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
LS | -0.49∗∗∗ | -0.52∗∗∗ | -0.40∗∗∗ | -0.63∗∗∗ | -0.29∗ | -0.50∗∗∗
| [ -3.19] | [ -3.42] | [ -2.64] | [ -4.22] | [ -1.87] | [ -3.26]

Table 5: Factor loadings of quintile $\beta_{CID}$-sorted vw portfolios

The table reports factor loadings of value-weighted portfolios, sorted on
$\beta_{CID}$, on Fama-French 5 factor model, augmented with momentum and
short-term reversal factors. The returns are calculated at the monthly
frequency over 1963-2018.

Quintile | Ret | Alpha | EMKT | HML | SMB | RMW | CMA | MOM | STR | adjR2
---|---|---|---|---|---|---|---|---|---|---
1 | 0.79 | 0.27 | 1.07 | 0.10 | 0.17 | 0.06 | -0.01 | -0.16 | -0.01 | 0.85
| [ 3.83] | [ 3.07] | [ 49.36] | [ 2.34] | [ 5.78] | [ 1.50] | [ -0.16] | [ -7.44] | [ -0.29] |
2 | 0.63 | 0.07 | 1.02 | 0.13 | -0.01 | 0.19 | 0.08 | -0.12 | 0.02 | 0.90
| [ 3.51] | [ 1.08] | [ 67.00] | [ 4.46] | [ -0.49] | [ 6.32] | [ 1.89] | [ -8.30] | [ 0.86] |
3 | 0.58 | 0.03 | 0.97 | 0.05 | -0.07 | 0.18 | 0.11 | -0.05 | 0.01 | 0.94
| [ 3.55] | [ 0.64] | [ 91.19] | [ 2.27] | [ -4.64] | [ 8.87] | [ 3.79] | [ -5.02] | [ 0.87] |
4 | 0.45 | -0.09 | 0.99 | -0.04 | -0.05 | 0.06 | 0.04 | 0.02 | 0.03 | 0.92
| [ 2.59] | [ -1.72] | [ 78.18] | [ -1.47] | [ -2.82] | [ 2.32] | [ 1.00] | [ 1.47] | [ 1.77] |
5 | 0.30 | -0.23 | 1.11 | -0.04 | 0.08 | -0.28 | -0.18 | 0.13 | 0.00 | 0.87
| [ 1.40] | [ -2.72] | [ 53.56] | [ -0.95] | [ 2.70] | [ -7.08] | [ -3.09] | [ 6.54] | [ -0.11] |
LS | -0.49 | -0.50 | 0.04 | -0.14 | -0.10 | -0.35 | -0.17 | 0.29 | 0.01 | 0.14
| [ -3.19] | [ -3.26] | [ 0.93] | [ -1.87] | [ -1.85] | [ -4.75] | [ -1.60] | [ 7.88] | [ 0.11] |

Table 6: Abnormal returns of 2x3 double-sorted portfolios on size and
$\beta_{CID}$

The table reports abnormal monthly returns of long-short value-weighted
portfolios, formed from independent 2 by 3 double sorts on size and
$\beta_{CID}$. By convention, in tercile sort I use 30 and 70 percentiles. The
long-short portfolios are formed in the following way:
$L/SSize=\frac{1}{3}(SmallLow+SmallMedium+SmallHigh)-\frac{1}{3}(BigLow+BigMedium+BigHigh)$,
$L/SCID=\frac{1}{2}(SmallLow+BigLow)-\frac{1}{2}(SmallHigh+BigHigh)$.
The last column contains the abnormal returns with respect to Fama-French 5
factor model, augmented with momentum and short-term reversal factors. The
returns are calculated at the monthly frequency over 1963-2018.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
L/S Size | 0.21∗∗ | 0.14 | -0.04 | 0.01 | -0.07∗∗ | -0.05∗
T-stat | [ 2.11] | [ 1.45] | [ -1.15] | [ 0.36] | [ -2.24] | [ -1.66]
L/S CID | 0.28∗∗∗ | 0.30∗∗∗ | 0.20∗∗ | 0.40∗∗∗ | 0.17∗ | 0.33∗∗∗
T-stat | [ 2.72] | [ 2.94] | [ 2.05] | [ 4.16] | [ 1.68] | [ 3.40]

Table 7: Fama-MacBeth regression

The table reports the results of Fama-MacBeth regression of excess returns on
characteristics of decile $\beta_{CID}$-sorted portfolios. Size is log(ME) in
the previous month. Momentum is the return over the past year, excluding the
most recent month. Investment is defined as the growth in total assets over
the recent year. $\beta_{VOL}$ is the sensitivity to the volatility of monthly
market returns over the recent 2 years. The returns are calculated at the
monthly frequency over 1963-2018.

| Dependent variable: Return
---|---
| (1) | (2) | (3) | (4) | (5)
$\beta_{CID}$ |  $-$0.12∗∗∗ |  $-$0.09∗∗∗ |  $-$0.09∗∗∗ |  $-$0.08∗∗ |  $-$0.10∗∗
| [$-$3.99] | [$-$3.43] | [$-$3.46] | [$-$2.54] | [$-$2.05]
$\beta$ |  | 0.44∗∗ | 0.28 |  $-$0.38 |  $-$0.60
|  | [2.18] | [0.62] | [$-$0.74] | [$-$0.84]
size |  |  | 0.01 | 0.06 | 0.01
|  |  | [0.30] | [1.19] | [0.14]
logbm |  |  | 0.03 | 0.12 | 0.18
|  |  | [0.16] | [0.62] | [0.61]
mom122 |  |  |  | 1.24∗ | 1.50
|  |  |  | [1.69] | [1.52]
op |  |  |  |  | 3.19
|  |  |  |  | [1.38]
inv |  |  |  |  |  $-$1.12
|  |  |  |  | [$-$0.74]
Constant | 0.52∗∗∗ | 0.09 | 0.10∗ | 0.09∗ | 0.08∗∗
| [3.22] | [1.19] | [1.80] | [1.96] | [2.47]
Observations | 10 | 10 | 10 | 10 | 10
Adjusted R2 | 0.38 | 0.58 | 0.75 | 0.80 | 0.89
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

Table 8: Abnormal returns of 5x5 portfolios, double-sorted on within-industry
dispersion $\beta_{WID}$ and $\beta_{CID}$

The table reports abnormal monthly returns of long-short value-weighted
portfolios, formed from independent 5 by 5 double sorts on $\beta_{WID}$ and
$\beta_{CID}$. WID (within-industry dispersion) is a mean absolute deviation
of returns of the stocks within each industry, averaged across 49 industries.
The long-short portfolios are formed in the following way:
$L/SWID=\frac{1}{5}(LowWIDLowCID+LowWIDCID2+LowWIDCID3+LowWIDCID4+LowWIDHighCID)-\frac{1}{5}(HighWIDLowCID+HighWIDCID2+HighWIDCID3+HighWIDCID4+HighWIDHighCID)$,
$L/SCID=\frac{1}{5}(LowCIDLowWID+LowCIDWID2+LowCIDWID3+LowCIDWID4+LowCIDHighWID)-\frac{1}{5}(HighCIDLowWID+HighCIDWID2+HighCIDWID3+HighCIDWID4+HighCIDHighWID)$.
The last column contains the abnormal returns with respect to Fama-French 5
factor model, augmented with momentum and short-term reversal factors. The
returns are calculated at the monthly frequency over 1963-2018.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
L/S WID | 0.07 | 0.32∗ | 0.20 | 0.21 | -0.15 | -0.10
T-stat | [ 0.40] | [ 1.74] | [ 1.22] | [ 1.28] | [ -0.97] | [ -0.63]
L/S CID | 0.30∗∗ | 0.23 | 0.14 | 0.27∗ | 0.20 | 0.28∗∗
T-stat | [ 2.22] | [ 1.58] | [ 1.02] | [ 1.91] | [ 1.42] | [ 1.97]

Table 9: Abnormal returns of 5x5 portfolios, double-sorted on cross-sectional
dispersion $\beta_{CSD}$ and $\beta_{CID}$

The table reports abnormal monthly returns of long-short value-weighted
portfolios, formed from independent 5 by 5 double sorts on $\beta_{CSD}$ and
$\beta_{CID}$. CSD (cross-sectional dispersion) is a mean absolute deviation
of returns of all stocks. The long-short portfolios are formed in the
following way:
$L/SCSD=\frac{1}{5}(LowCSDLowCID+LowCSDCID2+LowCSDCID3+LowCSDCID4+LowCSDHighCID)-\frac{1}{5}(HighCSDLowCID+HighCSDCID2+HighCSDCID3+HighCSDCID4+HighCSDHighCID)$,
$L/SCID=\frac{1}{5}(LowCIDLowCSD+LowCIDCSD2+LowCIDCSD3+LowCIDCSD4+LowCIDHighCSD)-\frac{1}{5}(HighCIDLowCSD+HighCIDCSD2+HighCIDCSD3+HighCIDCSD4+HighCIDHighCSD)$.
The last column contains the abnormal returns with respect to Fama-French 5
factor model, augmented with momentum and short-term reversal factors. The
returns are calculated at the monthly frequency over 1963-2018.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
L/S CSD | 0.10 | 0.35∗ | 0.21 | 0.23 | -0.21 | -0.17
T-stat | [ 0.50] | [ 1.80] | [ 1.23] | [ 1.30] | [ -1.28] | [ -1.03]
L/S CID | 0.29∗∗ | 0.21 | 0.12 | 0.26∗ | 0.22 | 0.30∗∗
T-stat | [ 2.11] | [ 1.46] | [ 0.87] | [ 1.82] | [ 1.50] | [ 2.09]

Table 10: Abnormal returns of 5x5 portfolios, double-sorted on $\beta_{CID}$
and other variables

Construction procedure is equivalent to the one used in the previous tables.
MU and FU are macroeconomic and financial uncertainty indices from Ludvigson
et al. (2015). Market volatility is a standard deviation of monthly value-
weighted market returns over the last 24 months.

Panel A: Market volatility vs CID
---
|  |  |  |  |  |
Statistic |  Ret |  $\alpha_{CAPM}$ |  $\alpha_{FF3}$ |  $\alpha_{Carhart}$ |  $\alpha_{FF5}$ |  $\alpha_{FF5+UMD+STR}$
L/S VOL |  0.26∗ |  0.14 |  0.19 |  0.22 |  0.38∗∗∗ |  0.36∗∗∗
T-stat |  [ 1.87] |  [ 1.06] |  [ 1.42] |  [ 1.61] |  [ 2.80] |  [ 2.61]
L/S CID |  0.42∗∗∗ |  0.47∗∗∗ |  0.38∗∗∗ |  0.60∗∗∗ |  0.34∗∗ |  0.52∗∗∗
T-stat |  [ 3.09] |  [ 3.43] |  [ 2.82] |  [ 4.55] |  [ 2.41] |  [ 3.81]

Panel B: Macroeconomic uncertainty (Ludvigson 2015) vs CID
---
|  |  |  |  |  |
Statistic |  Ret |  $\alpha_{CAPM}$ |  $\alpha_{FF3}$ |  $\alpha_{Carhart}$ |  $\alpha_{FF5}$ |  $\alpha_{FF5+UMD+STR}$
L/S MU |  -0.16 |  -0.26∗ |  -0.22 |  -0.17 |  0.00 |  -0.07
T-stat |  [ -1.09] |  [ -1.83] |  [ -1.58] |  [ -1.25] |  [ 0.02] |  [ -0.51]
L/S CID |  0.41∗∗∗ |  0.43∗∗∗ |  0.28∗∗ |  0.54∗∗∗ |  0.18 |  0.41∗∗∗
T-stat |  [ 2.83] |  [ 2.97] |  [ 1.96] |  [ 3.98] |  [ 1.24] |  [ 3.00]

Panel C: Financial uncertainty (Ludvigson 2015) vs CID
---
|  |  |  |  |  |
Statistic |  Ret |  $\alpha_{CAPM}$ |  $\alpha_{FF3}$ |  $\alpha_{Carhart}$ |  $\alpha_{FF5}$ |  $\alpha_{FF5+UMD+STR}$
L/S FU |  -0.04 |  -0.16 |  -0.29∗∗ |  -0.40∗∗∗ |  -0.41∗∗∗ |  -0.48∗∗∗
T-stat |  [ -0.30] |  [ -1.10] |  [ -2.07] |  [ -2.89] |  [ -2.91] |  [ -3.33]
L/S CID |  0.44∗∗∗ |  0.49∗∗∗ |  0.39∗∗∗ |  0.67∗∗∗ |  0.41∗∗∗ |  0.65∗∗∗
T-stat |  [ 3.33] |  [ 3.66] |  [ 2.97] |  [ 5.34] |  [ 3.02] |  [ 5.08]

Panel D: VIX vs CID
---
|  |  |  |  |  |
Statistic |  Ret |  $\alpha_{CAPM}$ |  $\alpha_{FF3}$ |  $\alpha_{Carhart}$ |  $\alpha_{FF5}$ |  $\alpha_{FF5+UMD+STR}$
L/S VIX |  -0.09 |  -0.50∗∗ |  -0.47∗∗ |  -0.34∗ |  -0.15 |  -0.07
T-stat |  [ -0.36] |  [ -2.54] |  [ -2.46] |  [ -1.80] |  [ -0.80] |  [ -0.38]
L/S CID |  0.13 |  0.17 |  0.05 |  0.28 |  -0.11 |  0.07
T-stat |  [ 0.64] |  [ 0.83] |  [ 0.24] |  [ 1.55] |  [ -0.57] |  [ 0.40]

Table 11: Abnormal returns of 5x5 portfolios, double-sorted on $\beta_{CID}$
and $\beta_{CIV}$

The table reports abnormal monthly returns of long-short value-weighted
portfolios, formed from independent 5 by 5 double sorts on $\beta_{CID}$ and
$\beta_{CIV}$. CIV is common idiosyncratic volatility from Herskovic, Kelly,
Lustig and Van Nieuwerburgh (2016). The long-short portfolios are formed in
the following way:
$L/SCIV=\frac{1}{5}(LowCIVLowCID+LowCIVCID2+LowCIVCID3+LowCIVCID4+LowCIVHighCID)-\frac{1}{5}(HighCIVLowCID+HighCIVCID2+HighCIVCID3+HighCIVCID4+HighCIVHighCID)$,
$L/SCID=\frac{1}{5}(LowCIDLowCIV+LowCIDCIV2+LowCIDCIV3+LowCIDCIV4+LowCIDHighCIV)-\frac{1}{5}(HighCIDLowCIV+HighCIDCIV2+HighCIDCIV3+HighCIDCIV4+HighCIDHighCIV)$.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
L/S CIV | 0.08 | -0.01 | -0.01 | -0.05 | 0.05 | 0.01
T-stat | [ 0.57] | [ -0.07] | [ -0.10] | [ -0.37] | [ 0.39] | [ 0.04]
L/S CID | 0.40∗∗∗ | 0.43∗∗∗ | 0.28∗∗ | 0.54∗∗∗ | 0.20 | 0.43∗∗∗
T-stat | [ 2.78] | [ 2.94] | [ 2.02] | [ 4.02] | [ 1.40] | [ 3.16]

Table 12: Spanning tests between CID factor and CIV factor

The table reports the results of spanning tests between CID factor and CIV
factor. Both factors are constructed as the long-short quintile portfolios
from the sorts on $\beta_{CID}$ and $\beta_{CIV}$ respectively. The both
factors are long stocks with high sensitivity to non-traded factor and short
stocks with low sensitivity. $\beta_{CIV}$ is the sensitivity to the common
idiosyncratic volatility CIV (Herskovic et al., 2016), estimated over the
recent 5 years. The returns are calculated at the monthly frequency over
1963-2018.

| Dependent variable:
---|---
| CID factor | CIV factor
| (1) | (2) | (3) | (4)
EMKT | 0.033 | 0.066∗ |  $-$0.154∗∗∗ |  $-$0.160∗∗∗
| [0.926] | [1.865] | [$-$4.354] | [$-$4.651]
SMB |  $-$0.076 |  $-$0.027 |  $-$0.231∗∗∗ |  $-$0.215∗∗∗
| [$-$1.479] | [$-$0.519] | [$-$4.520] | [$-$4.292]
HML |  $-$0.191∗∗∗ |  $-$0.164∗∗ |  $-$0.129∗ |  $-$0.088
| [$-$2.667] | [$-$2.328] | [$-$1.805] | [$-$1.258]
RMW |  $-$0.227∗∗∗ |  $-$0.205∗∗∗ |  $-$0.102 |  $-$0.054
| [$-$3.206] | [$-$2.957] | [$-$1.453] | [$-$0.780]
CMA |  $-$0.131 |  $-$0.157 | 0.117 | 0.145
| [$-$1.243] | [$-$1.513] | [1.119] | [1.413]
MOM | 0.284∗∗∗ | 0.270∗∗∗ | 0.067∗∗ | 0.007
| [8.289] | [8.020] | [1.977] | [0.205]
CIVf |  | 0.215∗∗∗ |  |
|  | [5.326] |  |
CIDf |  |  |  | 0.211∗∗∗
|  |  |  | [5.326]
Constant |  $-$0.501∗∗∗ |  $-$0.468∗∗∗ |  $-$0.152 |  $-$0.046
| [$-$3.392] | [$-$3.239] | [$-$1.040] | [$-$0.321]
Observations | 605 | 605 | 605 | 605
R2 | 0.174 | 0.212 | 0.102 | 0.143
Adjusted R2 | 0.166 | 0.202 | 0.093 | 0.133
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

Table 13: Predictive regressions for unemployment

The table reports the results of the regression, predicting seasonally-
adjusted unemployment at the quarterly frequency. Mkt and Vol correspond to
the value-weighted market return and monthly volatility of value-weighted
market returns over most recent 24 months. All dependent variables are
differenced using the specification from Pastor and Stambaugh (2003). Long-
term (LT) unemployment is defined as unemployment for more than 15 weeks.
Short-term (ST) unemployment is unemployment for less than 5 weeks. The sample
is restricted to 1948-2019 due to availability of unemployment data. I use
Newey-West standard errors with 4 lags.

| Dependent variable:
---|---
| Unemployment | LT Unemployment | ST Unemployment
| (1) | (2) | (3) | (4) | (5) | (6)
CID | 4.02∗∗∗ | 3.62∗∗∗ | 2.65∗∗ | 2.39∗∗ | 0.24 | 0.16
| [2.77] | [2.59] | [2.15] | [2.24] | [0.53] | [0.42]
Mkt |  |  $-$1.07∗∗∗ |  |  $-$0.12 |  |  $-$0.45∗∗∗
|  | [$-$3.35] |  | [$-$0.52] |  | [$-$4.78]
Vol |  | 0.17∗∗ |  | 0.08∗∗ |  | 0.05∗
|  | [2.27] |  | [2.02] |  | [1.88]
Constant | 0.005 | 0.01 | 0.01 | 0.01 |  $-$0.003 |  $-$0.002
| [0.10] | [0.20] | [0.19] | [0.29] | [$-$0.31] | [$-$0.23]
Observations | 284 | 284 | 284 | 284 | 284 | 284
R2 | 0.03 | 0.13 | 0.05 | 0.07 | 0.001 | 0.13
Adjusted R2 | 0.03 | 0.12 | 0.04 | 0.06 |  $-$0.002 | 0.12
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

Table 14: Abnormal returns of 5x5 portfolios, double-sorted on within-industry
dispersion $\beta_{WID}$ and $\beta_{CID}$ using FF5 industry classification

The table reports abnormal monthly returns of long-short value-weighted
portfolios, formed from independent 5 by 5 double sorts on $\beta_{WID}$ and
$\beta_{CID}$. WID (within-industry dispersion) is a mean absolute deviation
of returns of the stocks within each industry, averaged across 5 industries.
The long-short portfolios are formed in the following way:
$L/SWID=\frac{1}{5}(LowWIDLowCID+LowWIDCID2+LowWIDCID3+LowWIDCID4+LowWIDHighCID)-\frac{1}{5}(HighWIDLowCID+HighWIDCID2+HighWIDCID3+HighWIDCID4+HighWIDHighCID)$,
$L/SCID=\frac{1}{5}(LowCIDLowWID+LowCIDWID2+LowCIDWID3+LowCIDWID4+LowCIDHighWID)-\frac{1}{5}(HighCIDLowWID+HighCIDWID2+HighCIDWID3+HighCIDWID4+HighCIDHighWID)$.
The last column contains the abnormal returns with respect to Fama-French 5
factor model, augmented with momentum and short-term reversal factors. The
returns are calculated at the monthly frequency over 1963-2018.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
L/S WID | 0.10 | 0.30∗∗ | 0.23∗ | 0.16 | -0.02 | -0.05
T-stat | [ 0.61] | [ 2.03] | [ 1.72] | [ 1.20] | [ -0.13] | [ -0.39]
L/S CID | 0.17 | 0.13 | -0.01 | 0.27∗∗∗ | 0.09 | 0.27∗∗
T-stat | [ 1.44] | [ 1.14] | [ -0.08] | [ 2.63] | [ 0.77] | [ 2.54]

Table 15: Returns of the quintile portfolios, formed on $\beta_{CID}$,
calculated from abnormal returns of FF49 industry portfolios

The table reports mean monthly excess returns of quintile portfolios, sorted
on $\beta_{CID}$. Q1 is the quintile portfolio with the lowest $\beta_{CID}$
and Q5 contains the highest $\beta_{CID}$ stocks. LS is the long-short
portfolio, formed by buying Q5 and selling Q1. Value-weighted portfolios use
market capitalization as of the previous month. The returns are calculated at
the monthly frequency over 1963-2018. I calculate $\beta_{CID}$ from abnormal
returns of FF49 industries with respect to FF3 model.

| Q1 | Q2 | Q3 | Q4 | Q5 | LS
---|---|---|---|---|---|---
Mean ew | 0.76∗∗∗ | 0.79∗∗∗ | 0.72∗∗∗ | 0.68∗∗∗ | 0.52∗∗ | -0.24∗∗
T-stat ew | [3.45] | [4.20] | [3.96] | [3.51] | [2.15] | [-2.17]
Mean vw | 0.78∗∗∗ | 0.63∗∗∗ | 0.51∗∗∗ | 0.53∗∗∗ | 0.31 | -0.48∗∗∗
T-stat vw | [3.94] | [3.70] | [3.15] | [3.10] | [1.37] | [-3.20]

Table 16: Abnormal returns of the long-short portfolio, formed on
$\beta_{CID}$, calculated from abnormal returns of FF49 industry portfolios

The table reports abnormal monthly returns of the long-short value-weighted
quintile portfolio, formed from sorts on $\beta_{CID}$. The last column
contains the abnormal returns with respect to Fama-French 5 factor model,
augmented with momentum and short-term reversal factors. The returns are
calculated at the monthly frequency over 1963-2018. I calculate $\beta_{CID}$
from abnormal returns of FF49 industries with respect to FF3 model.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
LS | -0.48∗∗∗ | -0.55∗∗∗ | -0.44∗∗∗ | -0.57∗∗∗ | -0.22 | -0.30∗∗
| [-3.20] | [-3.69] | [-2.97] | [-3.84] | [-1.47] | [-2.04]

Table 17: Fama-MacBeth regression

The table reports the results of Fama-MacBeth regression of excess returns on
characteristics of the stocks. Size is log(ME) in the previous month. Momentum
is the return over the past year, excluding the most recent month. Investment
is defined as the growth in total assets over the recent year. MAX stands for
the largest daily return over the previous month. All independent variables
are winsorized at 10% and 90%. The returns are calculated at the monthly
frequency over 1963-2018.

| Dependent variable: Return
---|---
| (1) | (2) | (3) | (4) | (5) | (6) | (7)
$\beta_{CID}$ |  $-$0.05∗∗ |  $-$0.03∗ |  $-$0.02∗ |  $-$0.02∗ |  $-$0.02∗∗ |  $-$0.02∗∗ |  $-$0.02∗∗
| [$-$2.29] | [$-$1.87] | [$-$1.80] | [$-$1.72] | [$-$2.02] | [$-$2.00] | [$-$2.09]
$\beta$ |  |  $-$0.21 |  $-$0.20 |  $-$0.07 |  $-$0.29 |  $-$0.23 | 0.13
|  | [$-$0.75] | [$-$0.63] | [$-$0.25] | [$-$1.00] | [$-$0.78] | [0.46]
size |  |  |  $-$0.05 |  $-$0.03 |  $-$0.02 |  $-$0.03 |  $-$0.09∗∗
|  |  | [$-$1.15] | [$-$0.71] | [$-$0.51] | [$-$0.68] | [$-$2.38]
logbm |  |  |  | 0.22∗∗∗ | 0.22∗∗∗ | 0.15∗∗∗ | 0.11∗∗
|  |  |  | [3.83] | [3.93] | [2.68] | [2.12]
mom122 |  |  |  |  | 1.33∗∗∗ | 1.26∗∗∗ | 1.13∗∗∗
|  |  |  |  | [7.08] | [6.63] | [6.06]
inv |  |  |  |  |  |  $-$0.94∗∗∗ |  $-$0.93∗∗∗
|  |  |  |  |  | [$-$6.79] | [$-$6.76]
MAX |  |  |  |  |  |  |  $-$0.08∗∗∗
|  |  |  |  |  |  | [$-$12.34]
Constant | 0.66∗∗∗ | 0.84∗∗∗ | 1.05∗∗∗ | 2.44∗∗∗ | 2.44∗∗∗ | 2.01∗∗∗ | 2.20∗∗∗
| [3.49] | [4.80] | [4.30] | [5.51] | [5.57] | [4.63] | [5.05]
Observations | 653 | 653 | 653 | 653 | 653 | 653 | 653
R2 | 0.0001 | 0.0003 | 0.0003 | 0.001 | 0.001 | 0.001 | 0.002
Adjusted R2 | 0.0001 | 0.0003 | 0.0003 | 0.001 | 0.001 | 0.001 | 0.002
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

Table 18: Average returns of quintile $\beta_{CID}$-sorted portfolios, formed
from 49 industry portfolios

The table reports mean monthly excess returns of quintile portfolios, sorted
on $\beta_{CID}$ from original 49 industry portfolios. Q1 is the quintile
portfolio of industry portfolios with the lowest $\beta_{CID}$ and Q5 contains
the highest $\beta_{CID}$ industry portfolios. L/S is the long-short
portfolio, formed by buying Q5 and selling Q1. Value-weighted portfolios are
constructed using as weights the market capitalization from the previous
month. The returns are calculated at the monthly frequency over 1963-2018.

| Q1 | Q2 | Q3 | Q4 | Q5 | L/S
---|---|---|---|---|---|---
Mean ew | 0.98∗∗∗ | 0.91∗∗∗ | 0.96∗∗∗ | 0.92∗∗∗ | 0.84∗∗∗ | -0.14
T-stat ew | [4.87] | [4.79] | [5.12] | [4.74] | [4.07] | [-1.06]
Mean vw | 1.09∗∗∗ | 0.86∗∗∗ | 1.04∗∗∗ | 0.85∗∗∗ | 0.78∗∗∗ | -0.31∗
T-stat vw | [5.62] | [4.65] | [5.65] | [4.54] | [3.78] | [-1.90]

Table 19: Abnormal returns of quintile $\beta_{CID}$-sorted portfolios, formed
from 49 industry portfolios

The table reports abnormal monthly returns of the long-short value-weighted
quintile portfolio, formed from sorts on $\beta_{CID}$ across original 49
industry portfolios. The last column contains the abnormal returns with
respect to Fama-French 5 factor model, augmented with momentum and short-term
reversal factors. The returns are calculated at the monthly frequency over
1963-2018.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
L/S | -0.31∗ | -0.36∗∗ | -0.20 | -0.43∗∗∗ | -0.09 | -0.31∗∗
| [-1.92] | [-2.21] | [-1.32] | [-2.82] | [-0.57] | [-1.98]

Table 20: Predictive regressions for unemployment | Dependent variable: Unemployment growth
---|---
| (1) | (2) | (3)
CIV | 4.02∗∗∗ | 3.97∗∗∗ | 3.69∗∗∗
| [2.77] | [2.90] | [2.85]
Mkt |  |  $-$0.80∗∗ |  $-$0.71∗∗
|  | [$-$2.53] | [$-$2.34]
Vol |  | 0.17∗∗ | 0.17∗∗
|  | [2.37] | [2.51]
FU |  |  | 0.83
|  |  | [0.60]
CIV |  |  | 0.02
|  |  | [0.37]
Constant | 0.005 |  $-$0.01 |  $-$0.01
| [0.10] | [$-$0.27] | [$-$0.27]
Observations | 284 | 220 | 220
R2 | 0.03 | 0.19 | 0.19
Adjusted R2 | 0.03 | 0.18 | 0.17
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 21: Predictive regressions for long-term unemployment | Dependent variable: Unemployment growth
---|---
| (1) | (2) | (3)
CID | 2.65∗∗ | 2.88∗∗∗ | 3.22∗∗∗
| [2.15] | [2.62] | [3.14]
Mkt |  |  $-$0.03 |  $-$0.12
|  | [$-$0.14] | [$-$0.56]
Vol |  | 0.10∗∗ | 0.11∗∗
|  | [2.16] | [2.34]
FU |  |  |  $-$0.21
|  |  | [$-$0.25]
CIV |  |  |  $-$0.04
|  |  | [$-$0.91]
Constant | 0.01 |  $-$0.002 |  $-$0.002
| [0.19] | [$-$0.07] | [$-$0.08]
Observations | 284 | 220 | 220
R2 | 0.05 | 0.14 | 0.14
Adjusted R2 | 0.04 | 0.13 | 0.13
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 22: Predictive regressions for short-term unemployment | Dependent variable: Unemployment growth
---|---
| (1) | (2) | (3)
CID | 0.24 | 0.08 |  $-$0.25
| [0.53] | [0.22] | [$-$0.58]
Mkt |  |  $-$0.36∗∗∗ |  $-$0.24∗∗∗
|  | [$-$3.54] | [$-$2.67]
Vol |  | 0.03 | 0.02
|  | [1.41] | [1.31]
FU |  |  | 1.03∗∗
|  |  | [2.28]
CIV |  |  | 0.03
|  |  | [1.62]
Constant |  $-$0.003 |  $-$0.01 |  $-$0.005
| [$-$0.31] | [$-$0.85] | [$-$0.81]
Observations | 284 | 220 | 220
R2 | 0.001 | 0.13 | 0.16
Adjusted R2 |  $-$0.002 | 0.11 | 0.14
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 23: Returns of portfolios, double-sorted on $\beta_{CID}$ and
$\beta_{NVIX}$

The table reports monthly returns of long-short value-weighted quintile
portfolios, formed from independent sorts on $\beta_{CID}$ and $\beta_{NVIX}$.
NVIX is news-implied volatility (Manela and Moreira, 2017.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
L/S NVIX | 0.04 | -0.10 | -0.03 | 0.06 | 0.25∗ | 0.36∗∗∗
T-stat | [ 0.26] | [ -0.72] | [ -0.19] | [ 0.42] | [ 1.88] | [ 2.63]
L/S CID | 0.45∗∗∗ | 0.49∗∗∗ | 0.33∗∗ | 0.55∗∗∗ | 0.23 | 0.43∗∗∗
T-stat | [ 2.99] | [ 3.26] | [ 2.28] | [ 3.82] | [ 1.54] | [ 2.94]

Table 24: Quintile returns using quarterly $\beta_{CID}$

The table reports mean monthly excess returns of quintile portfolios, sorted
on $\beta_{CID}$. Q1 is the quintile portfolio with the lowest $\beta_{CID}$.
The returns are calculated at the monthly frequency over 1963-2019.

| Q1 | Q2 | Q3 | Q4 | Q5 | LS
---|---|---|---|---|---|---
Mean ew | 0.82∗∗∗ | 0.77∗∗∗ | 0.76∗∗∗ | 0.73∗∗∗ | 0.63∗∗∗ | -0.19∗
T-stat ew | [4.23] | [4.43] | [4.24] | [3.91] | [2.79] | [-1.90]
Mean vw | 0.66∗∗∗ | 0.57∗∗∗ | 0.51∗∗∗ | 0.48∗∗∗ | 0.45∗∗ | -0.22
T-stat vw | [3.57] | [3.59] | [3.07] | [2.74] | [2.21] | [-1.51]

Table 25: Quintile abnormal returns using quarterly $\beta_{CID}$

The table reports abnormal monthly returns of the long-short value-weighted
quintile portfolio, formed from sorts on $\beta_{CID}$. The last column
contains the abnormal returns with respect to Fama-French 5 factor model,
augmented with momentum and short-term reversal factors. The returns are
calculated at the monthly frequency over 1963-2019.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
LS | -0.22 | -0.29∗∗ | -0.19 | -0.38∗∗∗ | -0.24∗ | -0.40∗∗∗
| [-1.51] | [-2.06] | [-1.38] | [-2.86] | [-1.69] | [-2.90]

Table 26: Quintile return using daily $\beta_{CID}$

The table reports mean monthly excess returns of quintile portfolios, sorted
on $\beta_{CID}$. Q1 is the quintile portfolio with the lowest $\beta_{CID}$.
The returns are calculated at the monthly frequency over 1963-2019.

| Q1 | Q2 | Q3 | Q4 | Q5 | LS
---|---|---|---|---|---|---
Mean ew | 0.70∗∗∗ | 0.79∗∗∗ | 0.78∗∗∗ | 0.66∗∗∗ | 0.54∗∗ | -0.17
T-stat ew | [3.15] | [4.20] | [4.13] | [3.33] | [2.27] | [-1.56]
Mean vw | 0.69∗∗∗ | 0.65∗∗∗ | 0.58∗∗∗ | 0.54∗∗∗ | 0.38∗ | -0.31∗∗
T-stat vw | [3.43] | [3.86] | [3.55] | [3.29] | [1.92] | [-2.29]

Table 27: Quintile abnormal returns using daily $\beta_{CID}$

The table reports abnormal monthly returns of the long-short value-weighted
quintile portfolio, formed from sorts on $\beta_{CID}$. The last column
contains the abnormal returns with respect to Fama-French 5 factor model,
augmented with momentum and short-term reversal factors. The returns are
calculated at the monthly frequency over 1963-2019.

Statistic | Ret | $\alpha_{CAPM}$ | $\alpha_{FF3}$ | $\alpha_{Carhart}$ | $\alpha_{FF5}$ | $\alpha_{FF5+UMD+STR}$
---|---|---|---|---|---|---
LS | -0.31∗∗ | -0.31∗∗ | -0.35∗∗∗ | -0.19 | -0.34∗∗∗ | -0.13
| [-2.29] | [-2.34] | [-2.75] | [-1.51] | [-2.61] | [-0.96]

Table 28: Correlations between L/S portfolios, formed on $\beta_{CID}$ at
varying frequencies

The table reports abnormal monthly returns of the long-short value-weighted
quintile portfolio, formed from sorts on $\beta_{CID}$. The last column
contains the abnormal returns with respect to Fama-French 5 factor model,
augmented with momentum and short-term reversal factors. The returns are
calculated at the monthly frequency over 1963-2019.

Quarterly_LS | Monthly_LS | Daily_LS
---|---|---
$1$ | $0.26$ | -$0.04$
$0.26$ | $1$ | $0.06$
-$0.04$ | $0.06$ | $1$

Table 29: Predictability of industry employment by industry returns at
quarterly frequency

The table reports results of predictive panel regressions employment growth of
14 industries using their lagged returns. Employment growths and returns are
normalized by aggregate employment growth and market return. The variables are
calculated at the quarterly frequency over 1990-2019.

| Dependent variable: Employment growth
---|---
Return_t-1 | 0.013∗∗∗ | 0.020∗∗∗ | 0.007∗
| (0.002) | (0.006) | (0.004)
Constant |  $-$0.107∗∗∗ |  $-$0.073∗ |  $-$0.070∗∗
| (0.018) | (0.041) | (0.034)
Sample | Full | Negative R_t-1 | Positive R_t-1
Observations | 1,680 | 842 | 838
Adjusted R2 | 0.018 | 0.014 | 0.002
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

Table 30: Predictability of industry employment by industry returns at
semiannually frequency

The table reports results of predictive panel regressions employment growth of
14 industries using their lagged returns. Employment growths and returns are
normalized by aggregate employment growth and market return. The variables are
calculated at the semiannual frequency over 1990-2019.

| Dependent variable: Employment growth
---|---
| (1) | (2) | (3)
Return_t-1 | 0.026∗∗∗ | 0.051∗∗∗ | 0.014∗∗
| (0.004) | (0.010) | (0.007)
Constant |  $-$0.210∗∗∗ |  $-$0.008 |  $-$0.126
| (0.046) | (0.102) | (0.087)
Sample | Full | Negative R_t-1 | Positive R_t-1
Observations | 826 | 419 | 407
Adjusted R2 | 0.046 | 0.055 | 0.007
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01


* Zhang et al. (2018) Y. Zhang, R. Chandra, and J. Gao.  Cyclone track prediction with matrix neural networks.  In _2018 International Joint Conference on Neural Networks (IJCNN)_ , pages 1–8, 2018.  doi: 10.1109/IJCNN.2018.8489077.