#  The echo chamber effect resounds on financial markets: a social media alert
system for meme stocks

Ilaria Gianstefani  Institute for Advanced Studies Lucca, Piazza S.Francesco,
19, 55100 Lucca (LU)  Luigi Longo  Institute for Advanced Studies Lucca,
Piazza S.Francesco, 19, 55100 Lucca (LU)  Massimo Riccaboni  Institute for
Advanced Studies Lucca, Piazza S.Francesco, 19, 55100 Lucca (LU)

The short squeeze of Gamestop (GME) has revealed to the world how retail
investors pooling through social media can severely impact financial markets.
In this paper, we devise an early warning signal to detect suspicious users’
social network activity, which might affect the financial market stability. We
apply our approach to the subreddit r/WallStreetBets, selecting two meme
stocks (GME and AMC) and two non-meme stocks (AAPL and MSFT) as case studies.
The alert system is structured in two stpng; the first one is based on
extraordinary activity on the social network, while the second aims at
identifying whether the movement seeks to coordinate the users to a bulk
action. We run an event study analysis to see the reaction of the financial
markets when the alert system catches social network turmoil. A regression
analysis witnesses the discrepancy between the meme and non-meme stocks in how
the social networks might affect the trend on the financial market.
Keywords: Market manipulation, Social network analysis, Alert system, Event
study, Reddit.
JEL codes: G14; G18; G41; 039.

##  1 Introduction

Retail investors have always been considered as noise traders in the financial
and market microstructure literature: their choices are not driven by the
knowledge of the fundamentals of a stock or any sophisticated analysis of the
market, but they are guided mainly by their emotional and irrational beliefs.
Noise traders market impact has always been considered negligible compared to
the influence of large players (such as investment banks and hedge funds).
However, this picture of nonthreatening amateur investors seems outdated: the
progressive diffusion of social media combined with low cost trading platforms
are making investment strategies more and more widespread. The impact they
have on the financial market is anything but negligible. The most striking
episode is the short-squeeze that some retail investors triggered on GameStop
stock (ticker symbol on NYSE: GME) by coordinating themselves on Reddit, a
micro-blogging social network (Anand and Pathak, 2021).
Reddit is a website111In the top-10 of the most visited websites in the US
according to various websites such as
https://www.alexa.com/topsites/countries/US and
https://www.semrush.com/blog/most-visited-websites/ composed of user-generated
content and related discussions. The site’s content is divided into forums,
communities known as ”subreddits”, which deal with a specific topic. As a
network of communities, Reddit’s core content consists of posts (submissions)
from its users. Users can comment on others’ posts to continue the
conversation, and they can collect positive or negative votes (score). The
number of upvotes or downvotes determines the posts’ visibility on the site;
the more popular the content is, the higher the number of people it is
displayed.
One of the most popular and active subreddit is r/WallStreetBets, a community
focused on financial markets and stock trading. In this community, users boast
very aggressive trading strategies and what they did at the end of January
2021 with GameStop is no exception. GameStop (GME) is the world’s largest
American retailer of video games and accessories. The market for physical
video games started its decay in 2017 due to the downloadable version of many
games and services offered by the main consoles. GameStop started facing a
sharp decline in sales that determined a share-price dropping in the financial
market. The COVID-19 pandemic was a severe beating for the company, and its
fundamentals faced another shock. The stock price decline led many
institutional investors to sell the stock short. Conversely, some retail
investors, considering the stock undervalued, went against the trend of the
big players. In January 2021, a coordinated effort orchestrated by the
community of the subreddit
r/WallStreetBets surged the price of GME (US Securities and Exchange
Commission, 2021).
Apart from what happened on the financial market, the squeeze of the price and
the consequent losses faced by the short-sellers, the high volatility of
traded volumes and the liquidity issues, the most striking part of this
episode is to comprehend how an apparently harmless group of noise traders
were able to provoke such a substantial effect on a market usually dominated
by the big players.
Stylizing the phenomenon can be helpful to detect eventual anomalies based on
indicators of coordination. This is relevant in a perspective of policy-making
to prevent this kind of shock from happening or at least to tackle the harmful
effects.
Besides the specific case of GameStop, which is dramatic in terms of magnitude
and subsequent effects, the interest in how social media networks impact the
financial price formation of meme stocks is gaining growing attention
(Pedersen, 2021; Costola et al., 2021). Furthermore, an ever-increasing
decentralization of the financial system and the ease to access it via user-
friendly online trading platforms are potential destabilizers for the
financial ecosystem222See for example:
https://www.risk.net/investing/7810026/aqr-quant-on-the-network-effects-
behind-gamestop-frenzy. The fintech (r)evolution and the capillary diffusion
of the online social network, which allow us to receive the up-to-date
information as they happen, lay the foundations for a reinterpretation of
market manipulation steering through social networks. Hence, here is the
urgent need to create an alert system to pinpoint episodes of misconduct
behaviors in online social network that can result in potential market
manipulation. With misconduct behaviors, in this paper we refer to an
inappropriate activity at the social network level that might potentially
translate into market manipulation, a deliberate attempt to interfere with the
free and fair operation of the market.
Although there is no regulation legislating on the relationship between social
media coordination and the financial market, the U.S. securities and exchange
commission (SEC) defines as market
manipulation333https://www.investor.gov/introduction-investing/investing-
basics/glossary/market-manipulation all the actions where someone artificially
affects the supply or demand for a security.
Social network variables on mass coordination are valuable tools for building
nowcasting systems and scheduling real-time interventions to ensure stability.
Our paper contributes to the extant literature by designing an alert system to
detect potential misconducting behaviors or suspicious activity on the social
network to eventually prevent the harmful coordination from creating
instability in financial markets. The methodology relies on social listening
and social network analysis to identify the red light days to monitor. The
rest of the paper proceeds as follows: Section 2 reviews the literature on the
topic, Section 3 presents the data and their features, Section 4 describes the
alert system we develop, and Section 5 introduces the empirical results.
Finally, Section 6 concludes.

##  2 Literature Review

Digital and online social network revolutions are deeply affecting the
functioning of financial markets. One manifestation of this revolution is the
rising importance of retail traders. In the classical market microstructure
models (Glosten and Milgrom, 1985; Kyle, 1985), noise traders are considered
as a residual category because of their randomness in the trades and are
usually ignored in the price formation process because of their irrational
impact on the market (which temporary makes the price to diverge from the
fundamental value) is predominated and counterbalanced by rational agents on
the market.
One of the first models to recognize the relevance of noise traders in the
financial ecosystem is the one described by De Long et al. (1990) where the
authors model them as irrational traders with erroneous stochastic beliefs
whose unpredictability creates a risk in the price of an asset. As a result,
prices can diverge significantly from fundamental values even without
fundamental risk. This paper was highly enlightened and forward-looking as it
perceived how the agents, so far targeted as irrelevant, are effectively
impacting the asset price formation in certain circumstances.
Thanks to user-friendly, low-cost online trading platforms, the widespread
diffusion of social media and the easiness of accessing financial markets have
significantly transformed the market dynamics. As pointed out by Zheludev et
al. (2014), the proliferation of the internet has improved our ability to
access information in real-time, and in particular, the diffusion of social
media allows us to get in contact with the moods, thoughts, and opinions of a
large part of the world’s traders in an aggregated and real-time manner. Many
are the researches aim to analyze the impact of social media on the financial
markets both under a perspective of the volume of the social activity, the
search engine traffic, and the prevailing sentiment of the agents. A
consistent branch of the literature focuses, using various techniques, on the
impact of social media activity on the financial markets (Mao et al., 2012;
Bordino et al., 2012; Ruiz et al., 2012; Preis et al., 2013) . Most of the
results presented so far are based on empirical extrapolation.
In Renault (2018), the author focuses on a specific type of market
manipulation: the pump-and-dump scheme. He finds that an abnormal activity on
social media about a specific stock is associated with a sharp increase in
volume and price on the day of the event, while the price presents a reversal
over the following trading week. Pedersen (2021) proposes a new model that
revolutionizes the vision of the so-called noise traders. He describes how
investment strategies propagate in a social network and how they affect the
market. Four typologies of investors are considered: besides the classic
prototypes of rational short- (who tries to predict the sentiment changes
among naive investors based on social network dynamics) and long-term investor
(focused on the fundamental value of assets), it portrays two new types of
agents: the ’fanatics’ (investors with a stubborn view that can influence many
people thanks to their popularity on social media) and naive investors (agents
learning and relying on investment strategies proposed on social networks).
The model explains the belief formation process on the social network and how
it affects the fluctuations of prices and trading volumes on the financial
market. Modern social media, such as Reddit, allows envisioning (and
downloading) the data generating process that leads to the coordination of the
agents on the network and analyzes the underlying forces behind the event. To
the extent of our knowledge, there are no works devoted to studying the
network evolution and consequent market impact. Suppose social network
activity does generate a force that drives the financial market dynamics. In
such a case, the GameStop saga can be an exciting case study to understand the
network indicators to monitor to prevent extreme phenomena like the one that
happened at the end of January 2021. Hence, as recommended by Pedersen (2021)
in the conclusion of his paper, the availability of data from social media
might open ’new research possibilities to test model’s prediction using data
on networks and market behaviors’.
Dim (2021) analyzes the implications on the financial markets of non-
preofessional social media investment analysts that publish investment
strategies shaping the views and actions of many retail investors. This study
highlights how the interplay of social media and retail trading poses new
challenges for financial markets and regulators, which requires a deeper
understanding of belief formation on social media.
Our paper works towards defining some indicators and parameters to monitor on
the social network to detect extreme situations that might affects the
financial market stability. Inspired by the setting proposed in Costola et al.
(2021), our alert system has two consecutive red flags: if the first one,
based on extraordinary activity on the social network, activates, we start
monitoring the structure of the user social network.
In the network analysis, distinguishing the various roles the users can play
is crucial. Many works are devoted to this categorization (Ríos et al., 2019;
Choi et al., 2015; Thukral et al., 2018). A special role is played by the
influencers, aka the leaders, or to use a term proposed Pedersen (2021), the
”fanatics”. We track the users’ activity within the network, catch the agents
distinguishing for their ability to be central and vocal in the network by
proposing relevant contributions.
Before delving into the core of our paper, we cross-reference all the works
dealing with the GameStop case, the triggering factor of this piece of
literature devoted to creating an alert system to prevent the dysfunctional
social network activity destabilizing the financial market. Investment
recommendation (Bradley et al., 2021), social network activity volume and tone
(obtained with sentiment analysis) (Long et al., 2021; Umar et al., 2021)
influence the GME returns and traded volume on the financial market. Also, the
Google trend researches with keywords related to the event are positively
correlated with the financial GameStop performance (Klein, 2021; Vasileiou et
al., 2021). Hasso et al. (2021) profile the agents participating in the frenzy
and describe their average performance; they have proven to be relatively
inexperienced and unsophisticated (Eaton et al., 2021). Eaton et al. (2021)
also infers that a large portion of agents acting on the subreddit
r/WallStreetBets uses Robinhood as a trading app. Robinhood is a zero
commission, no account minimum, and an easy-to-use interface trading app
widely used among young investors. During the most turbulent period of GME
frenzy, the trading app went down or malfunctioned several times, avoiding
investors from acting on the financial market and loosing the best moments to
trade. Many were the complains about this malfunction reported on a website
DownDetector.com444https://downdetector.com/, an online platform that provides
users with information about the status of various websites and services based
upon user outage reports.
The disruptive effect would have been milder if only the financial market
presented more substantial barriers to entry. Finally, in Fusari et al.
(2021), they report as a case study the extreme event of GME, demonstrating
that they can predict the bubble using a model based on options.

##  3 Data

Our analysis is run on four NYSE-listed stocks in the period October 2020 -
June 2021 for the following stocks (NYSE ticker is reported in parenthesis):
GameStop (GME), American Multi-Cinema Entertainment (AMC), Apple Inc. (AAPL)
and Microsoft Corporation (MSFT). For each stock, we download the financial
daily data on price and trading volume and all the post on the social network
Reddit containing the ticker. GME and AMC are two examples of meme stocks,
meaning stock that gains popularity among retail investors through social
media. As reported in US Securities and Exchange Commission (2021), a meme
stock is characterized by a confluence of all these factors: large price
moves, large volume changes, large short interest, frequent mentions on social
media and significant coverage in the mainstream media. At the contrary, AAPL
and MSFT are two non-meme stock to use as controls.

###  3.1 Market data

We download the time series with daily resolution of price and traded number
of share (volume) from October 1st 2020 to June 30th 2021\. For each stock we
compute the daily returns:

$R_{t,s}=\frac{P_{t,s}-P_{t-1,s}}{P_{t-1,s}}$ (3.1)

where $P_{t,s}$ is the closing price of stock $s$ on day $t$. The daily
trading volume is denoted as $Vol_{t,s}$.

###  3.2 Reddit data

Rooting our analysis in the theoretical framework proposed by Pedersen (2021),
we design a model to study the interaction of agents on the social platform,
evaluate their coordination effort and quantify the impact of their action on
the financial market. Modern social media contain an outstanding informative
potential related to the users’ sentiment evolution and opinion formation. If
properly squeezed, the confidential information can be a forerunner for
upcoming events.
Relying on the informative power of the social network and with the help of
PRAW (an acronym for ’Python Reddit API Wrapper’, a Python package that allows
accessing Reddit’s API), we downloaded all the posts containing as keyword the
ticker of the stock to investigate. We limit the data download to the
subreddit r/WallStreetBets in the period from October 2020 to June 2021. For
each post we obtained the related comment forests and attributes. We
downloaded the data and run the analysis for the following keywords, standing
for the stock tickers: GME, AMC, AAPL, and MSFT. Precisely, we extracted every
post (in Reddit jargon ’Submission’) satisfying the conditions above and the
related comment tree.555See the Appendix A for more details of downloaded
data.

We are interested in the emerging collective phenomena when the retail
investors cooperate to determine a significant effect on the financial market.
We exclude from our analysis the messages generated automatically from the
bots (that in our dataset are denoted with the tag ’moderator’ in the variable
distinguished). A conversation thread can be modeled as a directed tree
$T_{t,s}^{k}=(M_{t,s}^{k},C_{t,s}^{k})$. $M_{t,s}^{k}$ the set of nodes
represented by the messages in the tree $k$ (where the initial submission
represents the root of the tree and the comments are the following-up
branching) and $C_{t,s}^{k}$ is the set of edges, each of them connecting two
messages linked by commenting activity. The direction of the edge points to
the parent node to which the comment is addressed.
Figure 1 reports the number of daily posts (i.e. the number of trees)
containing as keyword the ticker in the title of each subgraph and related
comments (i.e. the number of nodes excluding the initial submission). Each
subgraph has a double scale y-axis; on the left in red is the scale measuring
the absolute value of daily submissions, on the right in blue is the
corresponding measure for the number of related comments. We note that for the
meme stocks (GME and AMC), the activity on the social network is massive
compared to other well-known but not meme stocks (like AAPL and MSFT).
Furthermore, when the social network is active on a specific topic, the
correlation between creating new content and commenting activity is high.

Figure 1: Time series of the daily number of post (submission) containing the
word reported in the title of each subgraph (GME, AMC, AAPL, MSFT) and related
comments on the subreddit r/Wallstreetbets in the period October 2020 - June
2021. The post y-axis scale measure is on the left in red, while the
corresponding scale for the comments is on the right of each graph and in
blue.

Similarly, Figure 2 shows the time series of the daily number of users who
write content containing the ticker in the title of each subgraph and the
daily number of users who take part in the conversation threads. In red on the
left is the y-axis for the submitters; in blue on the right side is the
corresponding one for commenters. The analysis is ideally in line with the one
done for Figure 1.
The social network data informativeness is not limited to its extent over
time. It can be further squeezed by analyzing the interaction among users to
identify their roles within the network.

Figure 2: Time series of the daily number of submitters citing the word
reported in the title of each subgraph (GME, AMC, AAPL, MSFT) and related
comments by the users on the subreddit r/Wallstreetbets in the period October
2020 - June 2021. The submitter y-axis scale measure is on the left in red,
while the corresponding scale for the commenters is on the right of each graph
and in blue.

####  3.2.1 Social network analysis

We extrapolate the daily agent interplay from the tree-level raw data by
reconstructing their discussing interchanges. We define a network where the
nodes represent the active users on the day $t$, and the edges are users’
interactions through the comments: the network structure is outlined by
$G_{t,s}=(N_{t,s},E_{t,s})$. The set of active users on the day $t$ for ticker
$s$, $N_{t,s}$, represents the graph’s nodes. The commenting activity
establishes the links among them: $E_{t,s}$ is the set of directed edges from
the user writing the comment to the author of the initial submission.
Following Ríos et al. (2019), we adopt a simplification in the user-network
reconstruction (see Figure 3): the links always point to the author of the
initial submission even if the comment is a reply to a second or higher-order
comment. The ratio underlying this network reduction is due to the need to
identify the users acting like hubs, gaining popularity, consensus, and
driving a potentially impactful movement with their contents. In addition, the
stylization is still a realistic representation of the social dynamic: when
scrolling the blog, the user first reads the main submission; then, if
attracted by the topic, she opens the cascade of comments. Our reduction
considers all the comments as first-level comments. This structure emphasizes
the submitter that becomes the central actor of a thread and, eventually, the
driver of a particular message or idea. Figure 4 depicts an example of
interaction among users. The network represents the interaction on Reddit on
January 14st, 2021, based on submissions containing the ticker GME. There are
6,465 users (represented by the nodes) interacting on the platform throughout
commenting activity (the 8,741 edges connecting them). The social network has
a hub-and-spoke structure, with the colored users representing the hubs (i.e.,
central nodes in the network). In Appendix B we report similar examples of
networks for AMC, AAPL and MSFT.

Figure 3: Example of user network reconstruction from two conversation
threads. Starting from two conversation threads
$T_{t,s}^{k}=(M_{t,s}^{k},C_{t,s}^{k}),k=1,2$ stylized as a comment trees
(left-hand panel), we reconstruct the interaction among users
$G_{t,s}=(N_{t,s},E_{t,s})$ by reducing the density and the level of detail.
We consider all the comments to be addressed to the submission creators (in
the example the users labeled with 0 and 6), as all the comments were at the
first level of the tree. We do not consider how many times a user interacts
with another one: we consider whether a user comments to the submitter to
streamline the social network.  Figure 4: The Figure shows the network of
users interacting on Reddit on January 14st, 2021. The network reports the
interactions of users posting a submission containing the wording ’GME’. The
network has 6,465 nodes and 8,741 edges. The top 10 nodes with the highest in-
degree centrality are colored in blue.

##  4 Methodology

This section presents the backbone of our analysis. We describe the design and
the functioning of the alert system to detect situations of misconducting
behavior at social network level. Subsequently, we illustrate how we structure
an event study analysis to check whether the alert system is capable of
anticipating potential attempts of market manipulation.

###  4.1 Alert system

We devise an alert system based on social-network-retrieved information.
Cooperation among users can translate into a dangerous impact on financial
market stability. Detecting potential misconduct behaviors and anticipating a
coordinated action concocted on social media might be beneficial for the
financial market well-functioning. The alert system is query-dependent,
meaning that we have to instruct the system on which keyword we want to
monitor. For the sake of practical usability, two consecutive stpng compose
the structure.

####  4.1.1 First stage

The first stage of the alert system consists of a screening of the days where
the ticker-related activity on the social network is extensive compared to the
previous days. We use the volume-related metrics to implement the first stage:
we skim the days, identifying when ticker-related activity is extraordinary.
Technically speaking, for every day and each ticker, we determine:

  * •

The number of submissions citing the ticker in their content;

  * •

The number of active users discussing that ticker;

  * •

The overall666Meaning the whole activity during the day on the subreddit
r/WallStreetBets, not specifically related to a ticker. activity on the
subreddit, both in terms of submissions and users.

And construct the following variables:

  1. (1)

Relative number of daily submission: the ratio between the submissions citing
ticker and the total submissions on the subreddit, to identify the portion of
the activity on that topic during the day;

  2. (2)

Absolute number of daily submission: the total number of daily submissions
about that ticker, to identify the magnitude of the movement in absolute
terms;

  3. (3)

Relative percentage change in the number of daily submissions: the percentage
variation of number of ticker-related submissions with respect to the previous
day;

  4. (4)

Relative number of daily users: the ratio between the number of users citing
ticker and total users on the subreddit, to identify the portion of the
community discussing that topic during the day;

  5. (5)

Absolute number of daily users: computed as the total number of daily users
citing that ticker, to identify the magnitude of the user-trend in absolute
terms;

  6. (6)

Relative percentage change in the number of daily users: the percentage
variation of number of ticker-related users with respect to the previous day;

The first stage of the alert system switches on when at least four variables
exceed their threshold. For the relative and the absolute number of daily
submissions (users), variables (1), (2), (4), (5), the threshold for the day
$t$ is the mean value of the variable over the previous ten days plus one mean
absolute deviation computed over the same period. We define the mean value of
the variable as

$\bar{V}_{t,s}^{(v)}=\frac{1}{I}\sum_{i=1}^{I}V_{t-i,s}^{(v)}$ (4.1)

The mean absolute deviation as

$MAD({V}_{t,s}^{(v)})=\frac{1}{I}\sum_{i=1}^{I}\left(V_{t-i,s}^{(v)}-\bar{V}_{t,s}^{(v)}\right)$
(4.2)

Hence, the threshold is defined as

$T_{t,s}^{(v)}=\bar{V}_{t,s}^{(v)}+MAD({V}_{t,s}^{(v)})$ (4.3)

where $v$ refers to the variables $j=1,2,4,5$, $t$ indicates the day, $s$ the
ticker $s=GME,AMC,AAPL,MSFT$ and $I$ is the length of the window over which we
compute the threshold, in our case $I=10$. For the relative percentage change
in the number of daily submissions (users), variables (3) and (6), the
threshold to overcome is $100\%$, hence when on the day $t$ they double the
value with respect to the previous day $t-1$.
When the social network conditions determine the activation of the alert, we
approach the situation in a prudential and conservative way: we keep
monitoring the stock until the average number of active indicators over the
previous three days is below three. In this way, we keep controlling the
situation even if it is not exceptional compared to the earlier days, but it
is still turbulent.
A single indicator (or variable) switches on when it overcomes its critical
threshold defined in (4.3):

$I_{V_{t,s}^{(v)}}=\begin{cases}1,&\mbox{if }V_{t,s}^{(v)}>T_{t,s}^{(v)}\\\
0,&\mbox{otherwise}\end{cases}$ (4.4)

The minimum alert-activation condition is:

$\sum_{v=1}^{6}I_{V_{t,s}^{(v)}}\geq 4$ (4.5)

The alert remains on until the following condition verifies:

$\frac{1}{3}\sum_{i=1}^{3}\sum_{v=1}^{6}I_{V_{t-i,s}^{(v)}}\leq 3$ (4.6)

Step one of the alert system detects the days when the activity is
exceptional, calling for further controls on the network structure.

####  4.1.2 Second stage

The second stage of the alert system activates only for those days recognized
as an alert state by the first one.
For each day selected by the first step, we reconstruct the network structure
to model the interaction among the agents, $G_{t,s}=(N_{t,s},E_{t,s})$ in the
manners set in the previous paragraph: the links always point to the author of
the initial submission even if the comment is a reply to a second or higher-
order comment.
We also implement other filters in the network modeling: creating a nowcasting
alert system requires the tool to be quick and smartly devised, beyond the
fact that it has to detect the bigwigs. Hence, the network reconstruction is
made of only the users whose submission obtained a score above the median and
with a cascade of at least ten comments.
We now move to the detection of the users acting like leaders, able to gain
trustworthiness, popularity, prestige, leadership, and authority, essential
features for a virtual user to lead a movement that can translate its effects
on the real economy.
We rank the users according to their in-degree centrality (fraction of nodes
its incoming edges are connected to) for each day in the subset of first-
stage-detected days:

$C_{D}(n_{t,s}^{(i)})=\frac{\sum_{j}a_{t,s}^{ij}}{N_{t,s}}$ (4.7)

The indicator identifies the ten authors with the highest relative incoming
links: users able to attract a vast portion of the community. To test whether
the detected authors are trending and critically acclaimed, for each day $t$,
we define a set of the most critical users according to the algorithm of
PageRank (Page et al., 1999). We consider the network in the window
$[t-20,t-1]$ and identify the users who were standing out for the published
content. According to the ranking, the first twenty users belong to the set of
influencers at time $t$. We finally check whether some of the top in-degree
centrality authors on the day $t$ belong to the influencers set over the past
twenty days777We do some robustness checks by changing the number of users
with the highest in-degree centrality, and also modifying the parameters of
the influencer set (window length and number of critical users identified by
the PageRank algorithm). The results are unaffected. . If the intersection
between the two sets is not empty, the second stage of the alert system
switches on.
The methodology narrows down the set of agents we monitor to avoid
misconducting behaviors on the online social network and prevent repercussions
on the financial stability. The method aims at pin down the users who might
manage suspicious movements by promoting extreme investment strategies masked
by financial pieces of advice. In a perspective of macroprudential stability,
a regulatory authority using the tool can quickly pinpoint the users to check
to analyze their contents throughout textual analysis tools and eventually ban
the profiles.

###  4.2 Analysis of abnormal returns

We finally check whether the algorithm based on social network analysis can
adequately detect the financially unstable days. In order to evaluate the
accuracy of our algorithm, we develop an event study analysis following
MacKinlay (1997). We measure whether abnormal returns occur for the stock
discussed in the Reddit community right after the alert turns on.
The abnormal returns are constructed by defining an estimation window that
goes from $T_{0}$ to $T_{1}$, and an event date $\tau$. The event window goes
from $T_{1}$ to $T_{2}=$. $L_{1}=T_{1}-T_{0}$ and $L_{2}=T_{2}-T_{1}$ are
respectively the length of the estimation and the event window. The abnormal
returns are defined with the specification of the market model, to purge it by
the market fluctuations:

$AR_{\tau,s}=R_{\tau,s}-\hat{\alpha}_{s}-\hat{\beta}_{s}R_{\tau,m}$ (4.8)

where $R_{\tau,s}$ is the return for security $s$ at time $\tau$, while
$R_{\tau,m}$ is the market return. The parameters of the model are estimated
via OLS over the estimation window $[T_{0}:T_{1}]$. Under the null hypothesis,
the abnormal returns, $AR_{\tau,s}$, are normally distributed with zero
conditional mean and conditional variance $\sigma^{2}\left(AR_{\tau,s}\right)$
is set to be the variance of the OLS residuals $\sigma_{\varepsilon_{t}}^{2}$.

Under the null hypothesis, that event has no impact on the returns, the
distribution of the abnormal returns in the event window is:

$AR_{\tau,s}\sim N\left(0,\sigma^{2}\left(AR_{\tau,s}\right)\right)$ (4.9)

The significance of the abnormal returns is tested via the non-parametric rank
test by Corrado (1989). The abnormal returns are standardized as a ranked
descending variable defined by:

$K_{\tau,s}=\frac{\operatorname{rank}\left(AR_{\tau,s}\right)}{1+M_{s}}$
(4.10)

where $M_{s}$ are the the number of observations in the sample for security
$s$. The ranked variable is uniformly distributed in a [0,1] interval.
The variance computed across all the stock $s$ observations is:

$S_{\bar{K}}^{2}=\frac{1}{M_{s}}\sum_{t=0}^{T}\left({K}_{s,t}-0.5\right)^{2}$
(4.11)

where 0 and T stand for the first and last date of the sample. The
significance is computed as a t-rank statistic for a standard uniform
distribution with expected value of 0.5:

$t_{\text{rank }}=\left(\frac{{K}_{s,\tau}-0.5}{S_{{K}}}\right)$ (4.12)

These results can be used to make inference on the absolute returns for every
security in the event window.
We also test the impact of the detected events on the trading volume.
Specifically, we consider the abnormal trading volume computed as the volume
traded on a given day divided by the average volume traded on the estimation
window [$T_{0}:T_{1}$]. For each day $\tau$, the abnormal trading volume is
defined as:

$AVol_{\tau,s}=\frac{Vol_{\tau,s}}{\frac{1}{L_{1}}\sum_{t=T_{0}}^{T_{1}}Vol_{t,s}}$
(4.13)

##  5 Results

This section consists of an empirical application of the methodology we design
in the previous section. We present the days spotted by the alert tool and
evaluate the associated abnormal returns with an event study analysis.
Subsequently, we provide a regression analysis to understand the main drivers
of abnormal returns and how they differ between the meme and non-meme stocks.
We find that social networks-related variables significantly explain the meme
stock performance, while market-related variables primarily drive non-meme
stocks.

###  5.1 Event detection

In Figures 5, 6, 7, and 8 we report the daily time series of price and traded
volume for the stocks under analysis, together with the the days the alert
system detects extraordinary activity and cooperation on the social network.
The alert tool identifies 21 suspicious movements on the social network for
GME, 4 for AMC, 2 for AAPL, and 1 for MSFT.
GME is the stock facing the most incredible attention and chattering on social
media. Let us consider the short squeeze that happened at the end of January
2020 as the most striking episode of social network cooperation impacting the
financial economy. We appreciate that our alert tool can detect abnormal and
suspecting movements on the network many days before the social coordination
affects the financial market. In addition, the tool can narrow down the few
users that drive the movement, simplifying the eventual inspection by a
surveillance authority. In Table 1, we report all the dates and the users
noticed by the alert system. The tool can trace the user acting like leaders
for the movement. In Appendix B, we show a user network to highlight how
agents interacts on the social network.
Despite the lower media frenzy compared to GME, AMC experiences considerable
attention on social media. Retail investors attempt a pump-and-dump scheme
during the same days of the GME frenzy, but they create actual instability on
the second mid of May 2021 when they considerably purge the price. The price
has risen about seven times in ten days since the warning first lit on May
19th, 2021.
Unlike GME and AMC, the financial performance of prices and volumes of non-
meme-stocks (AAPL and MSFT) is entirely unaffected by social media activity.
Leading users (’fanatics’) on social networks are aware that stocks with such
high capitalization are challenging to implement pump-and-dump schemes or
drive the price away from fundamental value. For this reason, the alert is
rarely triggered and the identified alerting events are insignificant compared
to those of meme-stocks.

Figure 5: The figure shows financial data together with the alert days for the stock GME over the period October 2020 - June 2021. The above panel of the figure presents the time series of the daily price with a candlestick chart and the vertical blue lines are the days when the alert system turns on; in the bottom panel, the daily traded volume over the corresponding period. Figure 6: The figure shows financial data together with the alert days for the stock AMC over the period October 2020 - June 2021. The above panel of the figure presents the time series of the daily price with a candlestick chart and the vertical blue lines are the days when the alert system turns on; in the bottom panel, the daily traded volume over the corresponding period. Figure 7: The figure shows financial data together with the alert days for the stock AAPL over the period October 2020 - June 2021. The above panel of the figure presents the time series of the daily price with a candlestick chart and the vertical blue lines are the days when the alert system turns on; in the bottom panel, the daily traded volume over the corresponding period. Figure 8: The figure shows financial data together with the alert days for the stock MSFT over the period October 2020 - June 2021. The above panel of the figure presents the time series of the daily price with a candlestick chart and the vertical blue lines are the days when the alert system turns on; in the bottom panel, the daily traded volume over the corresponding period. GME |  | AMC
---|---|---
Alert date ($\tau$) | Influencer(s) |  |  Alert date ($\tau$) | Influencer(s)
09/11/2020 | DeNovaCain |  | 09/11/2020 | Killtrend
10/11/2020 | Veryforestgreen |  | 31/01/2021 |  | dhiral1994
---
BrandinoGames
20/11/2020 |  | Neothedreamer
---
Imboredsoyh
| 19/05/2021 | Realplayer16
21/11/2021 | Ackilles |  | 01/06/2021 | Nobjos
22/11/2021 | Ackilles |  |  |
25//11/2021 | Ackilles |  |  |
27/11/2020 | SIR_JACK_A_LOT |  |  |
26/12/2020 | Uberkikz11 |  |  |
03/01/2021 | Uberkikz11 |  |  |
14/01/2021 | DeepFuckingValue |  |  |
18/01/2021 | Its-Loki |  |  |
19/01/2021 |  | Gardeeon
---
DeepFuckingValue
|  |
21/01/2021 | Unlucky-Prize |  |  |
23/01/2021 | Unlucky-Prize |  |  |
25/01/2021 | DeepFuckingValue |  |  |
28/01/2021 | DeepFuckingValue |  |  |
29/01/2021 | DeepFuckingValue |  |  |
09/03/2021 | dumbledoreRothIRA |  |  |
15/04/2021 | OPINION_IS_UNPOPULAR |  |  |
16/04/2021 | DeepFuckingValue |  |  |
25/06/2021 | Chillznday |  |  |
# events = 21 |  | # events = 4
AAPL |  | MSFT
Alert date ($\tau$) | Influencer(s) |  |  Alert date ($\tau$) | Influencer(s)
24/12/2020 | Nafizzaki |  | 20/05/2021 |  | Mysterious—-
---
EmphasisOk3036
22/06/2021 | Tilthefatladysings |  |  |
# events = 2 |  | # events = 1
Table 1: The Table reports for each stock under analysis the events spotted by
the alert system. For each detected event, it indicates the date and the and
the user(s) under investigation.

###  5.2 Analysis of the abnormal returns

The submissions from the influencers during the days of unusual activity,
detected by the two stpng of the alert system, are considered as events
potentially triggering a response in the financial market. We analyze abnormal
returns constructed with a market model to evaluate whether the submission
from the influencers triggers a reaction in the financial markets. For each
detected event, i.e., when the alert system turns on ($\tau=0$), we compute
the abnormal return on the estimation window [-21:-11], $L_{1}=10$ and we
consider as event window the period [-10:10], $L_{2}=21$ trading days. The
abnormal return is defined with a market model, specified in (4.8), with the
CRSP index as a proxy for the market returns. We impose a minimum of 10 days
between two events to avoid contagion on the event window and consider the
events independent. If an event happens on a non-trading day, we consider the
next trading day as the event date.
Under these conditions, we end up with eight events for GME, four events for
AMC, two events for AAPL, and one for MSFT over the sample period. It is clear
that influencers driving unusual activity on social are more present for memes
than non-meme stocks.
Considering that Reddit users are mostly inexperienced retail investors, we
assume they primarily trade with a long position on the stock. Indeed, their
primary concern is to move the price up by massively buying the stock. For
this reason, we report and evaluate the significance of the event that
generates the highest positive abnormal returns in the ten days after. Results
are reported only for the case of meme stock. The event for the non-meme stock
does not generate a clear upward trend after the submission, although some
abnormal returns are significant. The events reported for GME and AMC are
respectively submissions by u/DeepFuckingValue on January 14th, 2021 and by
u/realplayer16 on May 19th, 2021.

Day ($\tau$) | $AR_{GME,t}$ | $CAR_{GME,t}$ | $AVol_{GME,t}$
---|---|---|---
-10 | 0.012 | 0.012 | 0.464
-9 | -0.009 | 0.004 | 0.651
-8 | -0.075 | -0.072 | 1.001
-7 | 0.013 | -0.057 | 0.494
-6 | $0.057$ | -0.0009 | 0.551
-5 | -0.011 | -0.011 | 0.554
-4 | -0.043 | -0.054 | 0.492
-3 | $0.104$ | 0.049 | 1.060
-2 | -0.038 | 0.011 | 0.568
-1 | $0.534^{**}$ | 0.545 | 11.521
0 | $0.233^{*}$ | 0.778 | 7.379
+1 | -0.152 | 0.626 | 3.801
+2 | $0.078$ | 0.704 | 6.117
+3 | -0.030 | 0.674 | 2.657
+4 | $0.082$ | 0.756 | 4.571
+5 | $0.493^{*}$ | 1.249 | 17.338
+6 | $0.164^{*}$ | 1.412 | 16.173
+7 | $0.935^{**}$ | 2.347 | 20.292
+8 | 1.349∗∗ | 3.697 | 11.961
+9 | -0.443∗∗ | 3.253 | 7.463
+10 | $0.630^{**}$ | 3.883 | 2.503
Table 2: Event study for GME on the event date January 14th, 2021 ($\tau=0$). This table shows the abnormal returns, the cumulative abnormal returns and the abnormal volumes on a [-10:+10] days event window around the event day. ∗∗∗, ∗∗, ∗ represents significance at 1%, 5% and 10% for the abnormal returns only. The highest value for each column in bold. Day ($\tau$) | $AR_{AMC,t}$ | $CAR_{AMC,t}$ | $AVol_{AMC,t}$
---|---|---|---
-10 | -0.012 | -0.012 | 0.710
-9 | -0.016 | -0.028 | 1.069
-8 | $0.054^{*}$ | 0.026 | 0.982
-7 | 0.020 | 0.045 | 1.067
-6 | 0.012 | 0.057 | 1.156
-5 | -0.0005 | 0.057 | 1.267
-4 | $0.217^{**}$ | 0.274 | 6.972
-3 | 0.007 | 0.281 | 5.024
-2 | $0.072^{*}$ | 0.353 | 4.001
-1 | 0.0007 | 0.354 | 4.438
0 | $-0.098$ | 0.256 | 2.277
+1 | -0.007 | 0.248 | 1.569
+2 | -0.031 | 0.217 | 1.329
+3 | $0.135^{**}$ | 0.353 | 2.866
+4 | $0.202^{**}$ | 0.555 | 5.241
+5 | $0.203^{**}$ | 0.758 | 9.941
+6 | $0.365^{**}$ | 1.123 | 18.382
+7 | -0.033 | 1.090 | 10.702
+8 | 0.202∗∗ | 1.293 | 6.592
+9 | 0.919∗∗ | 2.212 | 8.603
+10 | -0.215 | 1.996 | 5.868
Table 3: Event study for AMC on the event date May 19th, 2021 ($\tau=0$). This
table shows the abnormal returns, the cumulative abnormal returns and the
abnormal volumes on a [-10:+10] days event window around the event day. ∗∗∗,
∗∗, ∗ represents significance at 1%, 5% and 10% for the abnormal returns only.
The highest value for each column in bold.

Table 2 and 3 represents the abnormal returns, the cumulative abnormal returns
and the abnormal volumes for the stocks GME and AMC over the event window
[-10:10]. The event window presents significant abnormal returns for both
stocks, but the significance is generally higher for GME and more concentrated
after the event. Interestingly, in both stocks, we find a clear upward trend
of the abnormal returns after the event, perfectly in line with the
assumptions that users are coordinated on the Reddit community to buy the
stock massively. Figure 9 corroborates the claim.

Figure 9: The figure shows the abnormal returns and the cumulative abnormal
returns on a [-10:10] days event window centered in $\tau=0$ that corresponds
to the event date, marked with the red vertical line. The event date for GME
is January 14th, 2021. The event date for AMC is May 19th, 2021. The
horizontal dashed line indicates when the (cumulative) abnormal return equals
0. $AR_{t}$ and $CAR_{t}$ plot for GME and AMC single event triggering the
highest (cumulative) abnormal returns in the following 10 days.

In Figure 10 we report the graphical representation of the event analysis for
the abnormal volume (last column of Tables 2 and 3). In line with the analysis
of (cumulative) abnormal returns, the abnormal volume has a similar reaction
after the event happens. It presents a significant upward trend after
detecting unusual and cooperative activity on the social network.

Figure 10: The figure shows the abnormal volume on a [-10:10] days event
window centered in $\tau=0$ that corresponds to the event date, marked with
the red vertical dashed line. The event date for GME is January 14th, 2021.
The event date for AMC is May 19th, 2021. The horizontal dashed line indicates
when the abnormal volume equals 1.

Overall, the event analysis suggests significant abnormal returns following
the alert dates for the meme-stock only, GME and AMC. The alert for non-meme
stocks (AAPL and MSFT) turns on rarely and without generating abnormal
returns. The alert results mark significant differences between the meme and
non-meme stocks. When the alert system turns on for the meme stocks, it is
related to an attempt by retail traders to coordinate an action to drive the
stock market price up. The alert system on the non-meme stock detects agents
on the social network discussing the stock’s performance without necessarily
coordinating moves onto the market.

###  5.3 Regression analysis

In this section we focus on the differences between the meme and non-meme
stocks’ abnormal returns. In particular, we assess the dependence between
abnormal returns and social network-retrieved information, finding different
patterns for the two stocks’ categories. We run a time-series regression of
abnormal stock returns on social network-related variables, controlling for
market-related and stock-specific variables.
The contemporaneous regression is estimated via OLS with HAC estimator for the
variance by Newey and West (1987) for each stock $s$:

$AR_{t,s}=\alpha_{s}+Vol_{t,s}+P^{O}_{t,s}+AR_{t-1,s}+Rep_{t}+SubRank_{t}+ABN_{t,s}+O_{t,RH}+ABN_{t,s}\times
O_{t,RH}+\varepsilon_{t,s}$ (5.1)

Stock-specific financial variables are the transaction volume $Vol_{t,s}$ and
the stock open-price $P^{O}_{t,s}$; they enter the regression in the first
difference to mitigate non-stationarity and trends. The lagged term for the
abnormal returns $AR_{t-1,s}$ is included.
We also include some subreddit specific variables: the variable $Rep_{t}$ is
the daily number of reports of non-functioning of the RobinHood trading
application, which is very popular among young retail investors. The data is
downloaded from DownDetector.com, an online platform that provides users with
real-time information on various websites and services.
$SubRank_{t}$ is a metric computed internally by Reddit to compare the
popularity across the various communities as a function of its users. For each
community, they compute the number of subscribers and their popularity
(according to the karma, the number of upvotes,..) and they rank the
subreddits according to this indicator. Hence, the lower the metric, the
higher is the popularity of the subreddit. See Appendix C.
$O_{t,RH}$ is a dummy assuming a value of 1 when the website DownDetector.com
reports the presence of malfunctioning of RobinHood. According to
DownDetector.com, malfunctioning is related to the platform’s outages or
generic problems in the service (like Robinhood being slow in placing trades’
orders)888$O_{t,RH}$ assumes value of 1 when the variable $Rep_{t}$ is
different from 0..
The stock-specific social-network-related variable $ABN_{t,s}$ is the average
branching number, a proxy of the daily virality of the comment-trees. The
proxy of virality is inspired by Choi et al. (2015) where conversations’
thread are defined as tree $T^{k}_{t,s}$. The average branching number
(virality) quantifies on average how many comments a node generates. It is
computed as the average number of children at each (non-leaf) node: number of
non-root nodes (the volume of the tree minus one $M^{k}_{t,s}-1$, namely the
number of edges) divided by the number of non-leaf nodes (the number of nodes
with children). In the equation (5.1) the average branching number interacts
with the dummy $O_{t,RH}$.

| Meme stock |  | Non meme stock
---|---|---|---
| GME | AMC |  | AAPL | MSFT
$\alpha_{t,s}$ | 0.0262 | -0.0267 |  | 0.0021 | 0.0007
| (0.657) | (-1.559 ) |  | (1.464) | (0.485)
Volt,s | 0.0609∗∗∗ | 0.1791∗∗∗ |  | -0.0033∗∗ | -0.0041∗∗∗
| (3.026) | (4.358) |  | (-1.976) | (-3.573)
$P^{O}_{t,s}$ | 0.1162∗∗∗ | 0.0469∗ |  | 0.0099∗∗∗ | 0.0066∗∗∗
| (5.254) | (1.878) |  | (6.361) | (3.408)
$AR_{t-1,s}$ | -0.0597 | 0.0600 |  | -0.3247∗∗∗ | -0.2589∗∗
| (-0.551) | (0.878) |  | (-3.320) | (-2.126)
$Rep_{t}$ | 0.5224∗∗ | 0.5826∗∗∗ |  | 0.0026 | 0.0135∗∗∗
| (2.260) | (2.659) |  | (0.363) | (2.718)
$SubRank_{t}$ | 0.0168∗∗ | 0.0204∗∗ |  | -0.0019 | -0.0019∗
| (2.121) | (2.009) |  | (-1.493) | (-1.860)
$ABN_{t,s}$ | -0.0161 | 0.0026 |  | -0.0002 | 0.0008
| (-1.067) | (0.423) |  | (-0.268) | (0.674)
$O_{t,RH}$ | -0.2097∗∗ | -0.0815 |  | -0.0164∗∗∗ | -0.0003
| (-2.171) | (-1.648) |  | (-3.834) | (-0.099)
$ABN_{t,s}\times O_{t,RH}$ | 0.0738∗∗ | 0.0632∗∗ |  | -0.0513∗∗∗ | -0.0013
| (2.000) | (2.333) |  | (-3.313) | (-0.791)
Observations: | 166 | 166 |  | 166 | 166
Adjusted $R^{2}$: | 0.459 | 0.618 |  | 0.192 | 0.190
AIC: | -118.5 | -92.07 |  | -884.6 | -947.6
t statistics in parentheses |  |
* $p<0.05$, ** $p<0.01$, *** $p<0.001$ |  |
Table 4: Contemporaneous regression of daily abnormal return. In each column
the dependent variable is the abnormal return $AR_{t,s}$ and the independent
variables are stock or subreddit specific characteristics. The regression is
estimated via OLS with HAC estimator for the standard errors.

Table 4 summarizes regression results. The variable $Subrank_{t}$ presents
significant and positive coefficients for the meme-stock, while it is negative
and significant only for MSFT. An increase in the average rank of users on the
Wallstreetbets community positively impacts the abnormal returns, meaning that
the prestige of the users relates to a positive increase in the abnormal
returns of the meme-stocks. The same does not happen for the non-meme stocks.
The number of Robinhood outage reports has a positive and significant effect
on the abnormal returns for the meme-stock. The effect of reports for AAPL is
not significant, while for MSFT is still positive and significant, but lower
in magnitude than the meme-stocks. The increase in the number of reports may
be related to high activity in the stock market for buying stock discussed on
the Wallstreetbets community. This effect is associated with an increase in
abnormal returns, and it is even more marked for the meme-stock.
Interestingly, the daily virality of the comment trees positively impacts the
abnormal returns during the day of outages of the Robinhood platform. While
interacting the average branching number with outages positively impacts
abnormal returns for GME, the dummy outages alone is associated with negative
abnormal returns. Intuitively, this might be related to big players’ moves on
the GME stock. During the Robinhood outages, banks and hedge funds operated in
the market without the noisy traders that usually invest through the Robinhood
platform. Their action is associated with a fall in price. Indeed, during the
day of the GME squeeze - where the price peaked and started to fall
vertiginously - the Robinhood platform was shut down. As the average branching
number (virality) is related to the higher activity of the users on the
Wallstreetbets community, considering it during the platform outages, may
disentangle the effect of noisy traders rather than big corporations on the
stock. The price of the stock increase during days of high virality and
platform outages, which might be related to the noisy traders’ action. The
coefficient on the transaction volume is negative for the non-meme stock, and
in line with the standard liquidity theory999Liquidity is the ease of trading
securities. It is the degree to which a significant quantity of an asset can
be traded within a short time frame without incurring a significant
transaction cost or adverse price impact.: a higher trading volume commands a
lower expected stock return because liquidity is a desired stock feature for a
risk-averse agent101010Numerous works are confirming this evidence. For
instance, Acharya and Pedersen (2005) and Chordia et al. (2001). . For the
meme-stock case, the transaction volume has an unexpected significant positive
effect on abnormal returns111111We run a predictive regression on the abnormal
returns, presenting the results in the appendix. The purpose of the predictive
regression is to evaluate whether social network-retrieved information adds
information when market-related variables, such as transaction volume and
price, are included in the regression..
To evaluate the echo chamber effects from Reddit to the stock market, we run a
regression with the abnormal volume as a dependent variable: To evaluate the
role of users in trading the meme and non-meme stocks, we run a regression
where the dependent variable is the abnormal volume:

$AV_{t,s}=\alpha_{s}+Vol_{t,s}+P^{C}_{t,s}+AV_{t-1,s}+Sub_{t}+O_{t,RH}+Sub_{t}\times
O_{t,RH}$ (5.2)

The close price $P^{C}_{t,s}$ is used as a regressor. The variable $Sub_{t}$
represents the total number of subscribers to the Wallstreetbets community
each day, and interacts with the dummy outages.

| Meme stock |  | Non-meme stock
---|---|---|---
| GME | AMC |  | AAPL | MSFT
$\alpha_{t,s}$ | 0.1862∗∗ | 0.3565∗∗∗ |  | 0.0321∗∗∗ | 0.0373∗∗∗
| (2.539) | (3.058) |  | (2.926) | (2.661)
Volt,s | 1.0646∗∗∗ | 0.2971∗∗∗ |  | -0.0033∗∗ | 0.2858∗∗∗
| (4.1555) | (8.350) |  | (45.209) | (63.264)
$P^{C}_{t,s}$ | 0.0806 | -0.1437∗ |  | 0.0038 | -0.0004
| (1.412) | (-1.879) |  | (0.956) | (-0.137)
$AV_{t-1,s}$ | 0.7315∗∗∗ | 0.0600 |  | 0.9596∗∗∗ | 0.9618∗∗∗
| (12.025) | (9.396) |  | (73.303) | (63.706)
$Sub_{t}$ | 0.0219 | -0.0109 |  | -0.0023 | -0.0010
| (0.464) | (-0.120) |  | (-0.618) | (-0.345)
$O_{t,RH}$ | 0.4222∗ | 0.1663 |  | 0.0062 | 0.0028
| (1.875) | (1.016) |  | (0.906) | (0.422)
$Sub_{t}\times O_{t,RH}$ | -0.3487∗ | -0.2621 |  | 0.0038 | -0.0001
| (-1.908) | (-1.483) |  | (0.542) | (-0.017)
Observations: | 166 | 166 |  | 166 | 166
Adjusted $R^{2}$: | 0.759 | 0.731 |  | 0.977 | 0.989
t statistics in parentheses |  |
* $p<0.05$, ** $p<0.01$, *** $p<0.001$ |  |
Table 5: Contemporaneous regression of daily abnormal volume. In each column
the dependent variable is the abnormal volume $AV_{t,s}$ and the independent
variables are stock or subreddit specific characteristics. The regression is
estimated via OLS with HAC estimator for the standard errors.

Interestingly, the market variables are highly significant for the non-meme
stock (mainly because they are less volatile and less driven by social
networks-related variables), pushing towards the adjusted $R^{2}$. The
striking part of Table 4 is the first column, where the dependent variable is
the abnormal volume for GME. The coefficient on outages is positive: this
means that big corporations invested in the stock during the Robinhood
shutdown. The effect on the price was negative (Table 3): this led us to think
that noisy traders on Reddit essentially move the price forward by massively
buying the stock. At the same time, big banks and hedge funds drove the fall
in price on January 29th (short-squeeze) when the platform was shut down. The
number of subscribers during the Robinhood outages negatively impacts the
abnormal volume; therefore, higher activity on the Wallstreetbets community is
not associated with higher transaction volumes when Robinhood is shut down.
This confirms that investors are inexperienced and noisy traders who mainly
use the platform Robinhood to buy the stock.

##  6 Final discussion

Social media are a powerful and impacting tool to disseminate information and
stir a vast mass of people. This paper provides empirical evidence of the echo
chamber effect on the financial market from the social network, a form of
market manipulation (albeit indirect). Reddit and, in general, social media
are great places to share advice and manipulate poorly-informed,
unsophisticated, and prone to be convinced investors.
We provide evidence that the manipulators, or to use a word a là Pedersen, the
fanatics can coordinate many naive investors to provoke the desired stock
price movement. The fanatics can effectively undermine the financial market
stability by persuading inexperienced and easily reachable people.
We design an alert system to detect abnormal movement related to a specific
stock on social media based on the extraordinary activity in terms of volume
and the detection of a potential manipulator that coordinates the mass
movement.
While it is far from our duty to evaluate whether the promotion and persuasion
practice falls within the boundaries of the law, our consideration concerns
the market microstructure models. In front of these episodes, the retail
investors can no longer be relegated to a residual category of ’noise
traders’, but models should consider that many small and apparently harmless
investors if aggregated and coordinated, can generate a disruptive effect on
the financial market.
In the end, the entire analysis spots significant differences between the meme
and non-meme stocks. The detection system finds alerts for both categories.
Still, they never turn into abnormal returns for the non-meme stocks,
suggesting fewer chances of suspicious trading activity or market manipulation
in those cases. Moreover, the regression analysis indicates that social
network-retrieved information is significant for meme stock abnormal returns
only, resulting in structural differences between the price formation of the
two categories. Indeed, noisy traders may determine the price of meme stocks
through social activity and potential coordination.

##  Appendix A Data download

For each tree, we have as many rows in the data frame as the number of
comments, and each row contains the following information:

  * •

title: the textual content of the initial submission;

  * •

body: the textual content of the comment;

  * •

name: the id of the author of the comment (each id is prefixed by ’t1_’ to
specify the author made a comment activity);

  * •

parent_id: the author of the parent comment to which the comment in question
refers to (the parent_id can be prefixed by ’t1_’ if the author of the comment
replies to an other comment or it can be prefixed by ’t3_’ if the author of
the comment replies to the top-level post, i.e. the submission);

  * •

author_name: the name of the author who post the initial submission;

  * •

depth: the level of the comment tree at which the comment in question is
located (if a tree is composed by the initial submission only, the depth is 0;
if the comment refers to the initial submission the depth is 1; if the comment
refers to a comment in the first level, the depth is 2; and so on);

  * •

score: the number of up-votes minus the number of down-votes obtained by the
comment;

  * •

score_submission: the number of up-votes minus the number of down-votes
obtained by the initial submission;

  * •

upvote_ratio: the percentage of upvotes on the total votes received by a
submission;

  * •

time_submission: date and time at which the initial submission is published;

  * •

time_comment: date and time at which the comment is published;

  * •

num_comment: number of comments below the initial submission that compose the
tree;

  * •

flair: a tag used to categorize the post according to the topic it deals with;
they are subreddit specific and in the case of the subreddit r/WallStreetBets
the users can select among the following ones:

    * –

YOLO, the acronym for ’You Only Live Once, it can be used for posts presenting
extremely aggressive investment strategies with a consistent value at risk;

    * –

DD, the acronym for Due Diligence, must be applied to post presenting research
on a specific company/sector/trade. It should include sources and citations;

    * –

Discussion, an idea or article that you would like to talk about;

    * –

Gain, to show off a solid winning trade;

    * –

Loss, to show off a brutal, crushing loss;

    * –

Earnings Thread, weekly earnings discussion thread or a specific earnings
event;

    * –

Daily Discussion, daily catch-all thread for discussions;

    * –

Mods, only for official business.

  * •

distinguished: if a bot automatically performs the commenting activity, the
variable reports the wording ’Moderator’, none otherwise, when a non-automatic
user adds the comment.

Note that in the case of submission without comments below, the data frame has
a single row with empty values for the comments-related variables.

##  Appendix B The Social Network of Reddit users

In Figure 11, we present an example of network user graph on January 31st,
2021, where the main submissions contain the ticker AMC. There are 15.534
users (represented by the nodes) interacting among them on the platform
throughout commenting activity (the 21.032 edges connecting them).
The directed edges point from the comment’s author to the author of the main
submission. The peripheral nodes in the graph are the less connected users; in
the central part of the network, the most connected and central users: the
colored ones are the users with the highest in-degree centrality.
Figure 12 presents the network graph for AAPL a and MSFT on two alert dates,
respectively June 22nd, 2021 for AAPL and on May 20th, 2021 for MSFT. Compared
to the meme-stock case, the non-meme-stocks present a feeble activity on the
social network even in extraordinary occasions that determine the alert
activation.

Figure 11: The Figure shows the network of users interacting on Reddit on
January 31st, 2021. The network reports the interactions of users posting a
submission containing the wording ’AMC’. The graph contains 15.534 nodes and
21.032 edges. The colored part of the network is the nodes involved in the net
of the 10 users with the highest in-degree centrality.

Figure 12: The Figure shows the network of users interacting on Reddit on June
22nd, 2021 for AAPL and on May 20th, 2021 for MSFT. The network shows the
interactions of users posting a submission containing the wording ’AAPL’ and
’MSFT’ respectively.

##  Appendix C Subscriber rank

In Figure 13 we represent how the Reddit indicator ’Subscriber rank’ varies
over time, in the period 2013-2022.

Figure 13: The figure shows the time series of the indicator subscriber rank
in the period 2013-2022.

##  Appendix D Predictive regression

This section aims at understanding whether social network information enhances
the predictability of abnormal returns. We run a regression where future
abnormal returns depend on market-related variables and variables from the
social network.

$AR_{t,s}=\alpha_{s}+Vol_{t-1,s}+Vol_{t-2,s}+P^{O}_{t-1,s}+P^{O}_{t-2,s}+rank_{t-1}+rank_{t-2}+Rep_{t}+\varepsilon_{t,s}$
(D.1)

The variable $rank_{t}$ represents the daily average rank between subscribers
and users commenting on submissions.

| Meme stock |  |
---|---|---|---
| GME | AMC |  |
$\alpha_{t,s}$ | -0.0825∗ | -0.0942∗∗ |  |
| (-1.705) | (-2.602) |  |
Volt-1,s | 0.0350∗∗∗ | -0.0401 |  |
| (2.828) | (-1.063) |  |
Volt-2,s | 0.0157 | 0.0038 |  |
| (1.004) | (0.168) |  |
$P^{O}_{t-1,s}$ | -0.0341 | -0.0274 |  |
| (-1.321) | (-1.293) |  |
$P^{O}_{t-2,s}$ | 0.0467∗∗ | 0.0212 |  |
| (2.529) | (0.645) |  |
$rank_{t-1,s}$ | 0.0199∗∗ | 0.0252∗ |  |
| (2.042) | (1.663) |  |
$rank_{t-2,s}$ | 0.0040 | 0.0019 |  |
| (0.445) | (0.140) |  |
$Rep_{t,s}$ | 0.6684∗∗ | 0.9110∗ |  |
| (2.290) | (1.697) |  |
Observations: | 164 | 164 |  |
Adjusted $R^{2}$: | 0.243 | 0.211 |  |
t statistics in parentheses |  |  |
* $p<0.05$, ** $p<0.01$, *** $p<0.001$ |  |  |
Table 6: Predictive regression of daily abnormal return. In each column the
dependent variable is the abnormal return $AR_{t,s}$ and the independent
variables are the lagged stock or subreddit specific characteristics. The
regression is estimated via OLS with HAC estimator for the standard errors.

We do not include non-meme stock results because they are not significant. The
1-day lagged volume is significant in predicting the abnormal returns of GME,
while the 1-day lagged rank well predicts both GME and AMC abnormal returns.
The number of reports remains significant when included in the regression with
a positive coefficient. This regression shows how social network-retrieved
information to standard market variables such as volume and stock price when
predicting abnormal returns.

## References

  * Acharya and Pedersen (2005) Acharya, V., Pedersen, L., 2005\.  Asset pricing with liquidity risk.  Journal of Financial Economics 77, 375–410.
  * Anand and Pathak (2021) Anand, A., Pathak, J., 2021\.  The role of reddit in the gamestop short squeeze.  Economics Letters , 110249.
  * Bordino et al. (2012) Bordino, I., Battiston, S., Caldarelli, G., Cristelli, M., Ukkonen, A., Weber, I., 2012\.  Web search queries can predict stock market volumes.  PloS One 7, e40014.
  * Bradley et al. (2021) Bradley, D., Hanousekb, J., Jamed, R., Xiaoe, Z., 2021\.  Place your bets? the market consequences of investment advice on reddit’s wallstreetbets.  \- .
  * Choi et al. (2015) Choi, D., Han, J., Chung, T., Ahn, Y., Chun, B., Kwon, T., 2015.  Characterizing conversation patterns in reddit: From the perspectives of content properties and user participation behaviors, in: COSN ’15: Proceedings of the 2015 ACM on Conference on Online Social Networks, pp. 233–243.  doi:10.1145/2817946.2817959.
  * Chordia et al. (2001) Chordia, T., Subrahmanyam, A., Anshuman, V., 2001.  Trading activity and expected stock returns.  Journal of Financial Economics 59, 3–32.
  * Corrado (1989) Corrado, C.J., 1989.  A nonparametric test for abnormal security-price performance in event studies.  Journal of financial economics 23, 385–395.
  * Costola et al. (2021) Costola, M., Iacopini, M., Santagiustina, C.R., 2021.  On the “mementum” of meme stocks.  Economics Letters 207, 110021\.
  * De Long et al. (1990) De Long, J., Shleifer, A., Summers, L., Waldmann, R., 1990\.  Noise trader risk in financial markets.  Journal of Political Economy 98, 703––738.
  * Dim (2021) Dim, C., 2021.  Should retail investors listen to social media analysts? evidence from text-implied beliefs.  \- .
  * Eaton et al. (2021) Eaton, G., Green, T., Roseman, B., Wu, Y., 2021\.  Zero-commission individual investors, high frequency traders, and stock market quality.  \- .
  * Fusari et al. (2021) Fusari, N., Jarrow, R., Lamichhane, S., 2021.  Testing for asset price bubbles using options data.  Johns Hopkins Carey Business School Research Paper 20-12.
  * Glosten and Milgrom (1985) Glosten, L., Milgrom, P., 1985\.  Bid, ask and transaction prices in a specialist market with heterogeneously informed traders.  Journal of Financial Economics 14, 71––100.
  * Hasso et al. (2021) Hasso, T., Müller, D., Pelster, M., Warkulat, S., 2021\.  A note on gamestop, short squeezes, and autodidactic herding: An evolution in financial literacy?  Finance Research Letters In press.
  * Klein (2021) Klein, T., 2021.  A note on gamestop, short squeezes, and autodidactic herding: An evolution in financial literacy?  Finance Research Letters In press.
  * Kyle (1985) Kyle, A., 1985.  Continuous auctions and insider trading.  Economatrica 53, 1315––1336.
  * Long et al. (2021) Long, C., Lucey, B., Yarovaya, L., 2021.  ”i just like the stock” versus ”fear and loathing on main street”: The role of reddit sentiment in the gamestop short squeeze.  Social Science Research Network preprint.
  * MacKinlay (1997) MacKinlay, A.C., 1997.  Event studies in economics and finance.  Journal of economic literature 35, 13–39.
  * Mao et al. (2012) Mao, Y.and Wei, W., Wang, B., Liu, B., 2012.  Correlating s&p500 stocks with twitter data.  \- , –.
  * Newey and West (1987) Newey, W.K., West, K.D., 1987\.  Hypothesis testing with efficient method of moments estimation.  International Economic Review , 777–787.
  * Page et al. (1999) Page, L., Brin, S., Motwani, R., Winograd, T., 1999\.  The PageRank Citation Ranking: Bringing Order to the Web.  Technical Report 1999-66. Stanford InfoLab.  URL: http://ilpubs.stanford.edu:8090/422/. previous number = SIDL-WP-1999-0120.
  * Pedersen (2021) Pedersen, L., 2021.  Game on: Social networks and markets.  NYU Stern School of Business Forthcoming .
  * Preis et al. (2013) Preis, T., Susannah Moat, H., Stanley, E., 2013.  Quantifying trading behavior in financial markets using google trends.  Scientific Reports 3, 1684\.
  * Renault (2018) Renault, T., 2018.  Market manipulation and suspicious stock recommendations on social media.  (Forthcoming) .
  * Ruiz et al. (2012) Ruiz, E., Hristidis, V., Castillo, C., Gionis, A., Jaimes, A., 2012.  Correlating financial time series with micro-blogging activity.  \- .
  * Ríos et al. (2019) Ríos, S., Aguilera, F., Nuñez-Gonzalez, J., Graña, M., 2019\.  Semantically enhanced network analysis for influencer identification in online social networks.  Neurocomputing 326, 71–81.
  * Thukral et al. (2018) Thukral, S., Meisheri, H., Kataria, T., Agarwal, A., Verma, I., Chatterjee, A., Dey, L., 2018.  Analyzing behavioral trends in community driven discussion platforms like reddit, in: 2018 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), pp. 662–669.  doi:10.1109/ASONAM.2018.8508687.
  * Umar et al. (2021) Umar, Z., Gubareva, M., Yousaf, I., Ali, S., 2021\.  A tale of company fundamentals vs sentiment driven pricing: The case of gamestop.  Journal of Behavioral and Experimental Finance 30, 2214–6350.
  * US Securities and Exchange Commission (2021) US Securities and Exchange Commission, 2021\.  Staff report on equity and options market structure conditions in early 2021.  \- .
  * Vasileiou et al. (2021) Vasileiou, E., Bartzou, E., Tzanakis, P., 2021.  Explaining gamestop short squeeze using Ιntraday data and google searches.  \- .
  * Zheludev et al. (2014) Zheludev, I., Smith, R., Aste, T., 2014.  When can social media lead financial markets?  Scientific Reports 4, 4213\.