Abstract - This paper investigates the long-term returns of firms after their stock experiences a short squeeze. It tests if the decrease in short interest after a short squeeze is accompanied by an increase in abnormal returns. This paper conducts an event study on cumulative average abnormal returns of a sample of 11 US-based firms. Following Kolari & Pynnönen’s (2010, 2011) methodology, parametric and non-parametric tests are performed on each firm’s return, as well as on the sample collectively. This paper studies three separate time windows, one three-day event window around the short squeeze and two post-event windows of medium- term and long-term scope. This paper finds statistical evidence that stocks, subjected to a short squeeze, experience significant positive abnormal returns in the short-term and medium-term.
However, the analysis rejects its initial hypothesis and finds no significant evidence in support of a long-term increase of stock returns after a short squeeze.
Keywords: event study, short squeeze, financial econometrics
Thesis M.Sc. Finance - Major Corporate Finance University of Amsterdam - Amsterdam Business School
Name of student : David Rossetti
Student number : 11662964
Supervisor : Dr. T. (Tolga) Caskurlu
Date of submission : 1st of December 2021
TERM RETURNS OF STOCKS
.
Statement of Originality
This document is written by David Rossetti who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Table of Contents
1. Introduction ... 4
2. Literature review ... 6
2.1. Event case studies ... 6
2.1.1 Assumptions ... 6
2.1.2. Conducting an event study ... 7
2.2. The event: short squeezes ... 16
2.2.1. Short selling ... 16
2.2.2. Borrowing shares and naked short selling ... 18
2.2.3. Short interest ... 19
2.2.4. Short squeeze ... 21
2.2.5. Long term effects of a short squeeze ... 23
2.3. Hypothesis... 24
3. Methodology ... 25
3.1. Assumptions ... 25
3.2. Defining the event date, estimation window, event window ... 26
3.2.1. Event date: the short squeeze... 26
3.2.2. Estimation window ... 27
3.2.3. Event windows ... 28
3.3. Estimated returns ... 29
3.4. Abnormal returns ... 30
3.5. Significance testing ... 30
3.5.1. KP-test ... 31
3.5.2. GRANK-test ... 32
4. Data and descriptive statistics ... 34
4.1. Data ... 35
4.2. Confirmation of short squeeze ... 36
4.3. Descriptive statistics ... 37
5. Results ... 39
5.1. Short squeeze ... 40
5.2. Medium term ... 42
5.3. Long term ... 44
6. Robustness of results ... 46
7. Conclusion ... 47
8. References ... 51
1. Introduction
This paper asks the following research question: What is the long-term impact of a short squeeze on a stock? This question is of most importance as predicting long term returns on risky assets is one of the long-standing interests of academia and practitioners (Keim &
Stambaugh, 1986).
Short squeezes are a controversial financial phenomenon, and their frequency seems to be on the rise (Dusaniwsky, 2021; Davis, 2021; Authers, 2021). In 2021, GameStop was the target of the first retail investment initiated short squeeze in US stock market history (Umar et al., 2021). AMC Entertainment Corp Inc followed shortly after (Fletcher & Darbyshire, 2021).
What used to be a rare event in modern stock markets could eventually become a more widely used trading strategy. Initiating short squeezes is no longer restricted to large institutional investors, such as hedge funds, with their enormous trading volume capacity. Instead, it is a tool used by regular individual investors who are part of ‘trading groups’ on social media sites.
A short squeeze is a market event, during which the short interest and price of a security spike and consequently diminish, as short investors clear their short positions (IHS Markit, 2015). Miller (1977) and Lecce et al. (2012) find that firms’ stock prices, attributed to high divergence of opinion and high levels of short-sales constraints, are biased downward. On the other hand, other papers find that negative returns increase with an increase in short interest, concluding that high levels of short interest are a strong bearish signal (Frino et al., 2011; Desai et al., 2002; Deshmukh et al., 2017). Additionally, the higher returns during the initial short squeeze can fundamentally change investors’ opinion of the stock, which in return should contribute to long-term positive returns (Long et al., 1991).
This paper concludes from the existing literature that a stock should experience medium- term to long-term positive abnormal returns after a short squeeze. The periodic decrease in short interest after a short squeeze is identified as the main driver. This paper presents the following two hypotheses:
1. After a short squeeze, a stock experiences medium-term positive abnormal returns.
with null hypothesis CAAR=0, and alternative hypothesis CAAR>0
2. After a short squeeze, a stock experiences long-term positive abnormal returns.
with null hypothesis CAAR=0, and alternative hypothesis CAAR>0
The implications of predicting a long-term increase in stock price and returns are significant for market participants. Stocks affected by a surge in stock price can utilise this positive price movement to acquire more capital when they issue equity after a short squeeze. AMC Entertainment Corp Inc tried to do exactly that in June 2021 but had to retract its shareholder proposal after heavy backlash by a substantial part of its shareholders (Gilblom, 2021; Graffeo, 2021). Additionally, market regulators might wish to intervene if the risk exposure of retail investors becomes too high. In contrast, all investors would benefit from more empirical data surrounding the subject to make informed investment decisions accordingly.
This paper uses event study methodology, setting short squeezes as event dates, to answer the aforementioned research question. It uses a sample of 11 US stocks and their price data, acquired through the CSRP Daily Stock database, to compute daily returns. These daily returns are used to determine the estimated returns of each stock, which give insight into what return the stock would have experienced if the short squeeze had not happened. Estimated returns are based on an estimation window lasting 101 trading days. They are computed using three different estimation models, the Historical Mean Model (HMM), the market model and the Fama French 3-Factor model (FF3F) (Sharpe, 1964; Fama, 1993). The additional data for these estimation models is sourced from the NASDAQ website and the Kenneth R. French database.
Next, the actual returns are used in combination with the estimated returns to compute each stock’s cumulative average abnormal return (CAAR). The CAAR is calculated for each stock over the medium-term and long-term. This paper defines the medium-term post-event window as spanning from the first trading day after the short squeeze until the sixth. The long-term post-event window spans from the sixth trading day until the 106th trading day after a stock’s short squeeze, mirroring the length of the estimation window. Finally, following Kolari and Pynnönen’s (2011) advice, the parametric KP-test and a non-parametric GRANK test are performed on the abnormal returns of each firm and the sample collectively.
Following the described methodology, this paper finds mixed results regarding its hypotheses. It concludes that the initial significant increase in returns over the short term, caused by the event, decreases strongly over a 6-trading day post-event window. However, medium-term returns are still significantly above pre-event levels, with a 5% significance level;
as such, the medium-term null hypothesis is rejected. No significant statistical evidence is found regarding long-term returns, and thus the analysis fails to reject the null hypothesis in the long term.
The paper follows up this introduction, with Section 2, the literature review. Next are Section 3 and 4, which respectively provide the data overview and methodology section.
Section 5 presents the results of the statistical analysis and presents the implications for the hypotheses. Section 6 presents robustness checks, while Section 7 consists of the conclusion of this paper and puts forward the limitation of this thesis and the recommendations for future research. Finally, Section 8 and 9 will provide the reference list and appendix.
2. Literature review
The literature review will explore academia and other literature surrounding the subjects of event studies (2.1.) and short squeezes (2.2.). Combining findings will enable this paper to conduct an event study on stocks affected by short squeezes and gain new empirical insight regarding their long-term effect on stock prices. The final section (2.3) will present the main conclusion drawn from the literature review and present the study’s hypotheses.
2.1. Event case studies
The following section will cover the relevant literature around event studies, focussing on the field of finance. It will start with the general assumptions, laying out the four main steps of conducting an event study. These four main steps will then be described in detail in sub- sections.
2.1.1 Assumptions
Event studies have been used in various domains, e.g., accounting, finance, social studies, law. In the field of finance, they have been used to study earning announcements, issuance of debt/equity, the announcement of government policies or statistics, and mergers and acquisitions (M&A) effects, to name some (MacKinlay, 1997). Some critical assumptions are necessary to ensure that an event study’s findings hold external validity. In financial econometrics, three essential assumptions are consistent within the literature when conducting event studies on stock returns.
The impact of an event on company value can be measured through financial data, specifically by analysing the return on its stock price (Fama, 1970). This return is known as Rit, with i connotating a specific company and t the date. Fama (1970) presents the efficient market hypothesis (EMH), which states that financial markets are efficient. According to him, prices on financial markets ‘fully reflect’ the information surrounding a stock, even if the
information itself is not revealed to all market participants. He finds that said information is indirectly and instantaneously revealed through the price mechanism; this is known as the strong form of the EMH. Malkiel (1973) lays out two additional types of the EMH. The weak form of EMH, also known as the random walk theory, states that security prices are unaffected by their past and future. In such a scenario, stock prices reflect only recent information. The semi-strong form of the EMH assumes that current stock prices adjust rapidly to the release of novel public information. Most event studies, as well as this paper assume the latter, the semi- strong form, to be true.
In order to be able to interpret that the change in company value is in response to a specified event, one must assume that the event is unforeseen by the market (MacKinlay, 1997).
Otherwise, it would already be priced in before the event itself occurred. It is thus essential to correctly date the time of the event, focusing on when the market became aware of it.
Lastly, we assume that no confounding effects are statistically significantly influencing our abnormal returns during the respective estimation and event windows. This assumption is necessary to interpret that the price change is correlated to the specified event and not to another event. Using an estimation model that incorporates market risk can help reinforce this assumption, as does choosing a shorter event window.
To sum up, this paper assumes for its methodology (Section 3.1.):
1. The semi-strong form of the EMH.
2. The event’s effect is not already pre-priced into the stock.
3. No significant confounding effects are present in the estimation window.
2.1.2. Conducting an event study
MacKinlay (1997) and Benninga (2008) explain the exact procedure to perform an event study on stock returns and provide the following steps as a guide: First, one must define the event date and event window. Secondly, one should estimate the expected returns by determining an estimation window and choosing a form of conditioning, also called the estimation model. Next, the abnormal returns are computed, and finally, the significance of these abnormal returns is statistically estimated.
2.1.2.1. Defining the event and event window(-s)
First, the researcher must identify the event of interest specified according to the phenomenon the researcher wishes to study. An event can take on many specifications, such as but not limited to; earnings announcements, the announcement of issuing new debt/equity, the announcement of government policies or statistics or announcements of mergers and acquisitions (MacKinlay, 1997). Next, one must describe under which criteria the securities in the sample have been selected. One should provide a summary of the critical characteristics of the sample, pointing out possible biases that the selection could have induced.
Next, the researcher must define the event window(-s). One must determine the period(-s) over which the investigated event is theorised to influence the price of the sample. This is commonly called the event window(-s). The start of this event window is defined as T1, and it ends at T2 with the event date, time point 0, between or consisting of one of the two.
Event windows can take on many different lengths. There is no established standard, but there are some generally agreed-upon characteristics; event dates should be centred around the event and at least cover one day before and one day after the event. Allen et al. (2007) performed a meta-study on event studies and found that the most common specification is six days long and constitutes 76.3% of their sample. MacKinlay (1997) presents similar findings, stating that the typical event study window spans one to 11 days and is centred around the event date. It is generally agreed upon that event windows shorter than one day are problematic and should be avoided (Litzenberger, 1988; MacKinlay, 1997).
Multiple papers conclude that longer event windows are advantageous as they are more likely to capture the event date in case of misidentification of the exact time of the event (Campbell et al., 2010; MacKinlay, 1997; Ball & Torous, 1988). They also state that one can capture volatility induced by information leakages by including the day before the event date.
It is to be noted that event windows and estimation windows should not overlap. Similarly, they note that including the day after the event captures delayed market reactions.
A less common use of event studies in financial academia is to examine the long-term effects of an event without including the initial market reaction. One can add post-event dates in the analysis (Benninga, 2008, Dutta et al., 2018). This type of event window does not include the event date and is thus strictly positioned after the event date. It spans from T2 until T3. Post- event windows can be as short as 30 trading days, up to multiple years (Benninga, 2008, 333).
2.1.2.2. Estimating expected returns
The next step is estimating each security’s expected returns, often noted as E(Rit|Xt). The expected return represents a security’s predicted return as if the event had not happened. It is based on the normal return (Rit), which is the return of security (i) throughout the estimation window (T0 to T1), which takes place before the event. Multiple estimation models (Xt), also called conditioning, are available to compute the expected return. The most commonly sued ones will be presented in this section.
To compute the expected returns, one must define an estimation window and feed the security price data within this estimation window into one or more chosen estimation models.
In addition to the literature surrounding estimation windows, this paper will present five commonly used estimation models and their strengths and weaknesses. The following models will be explained in detail: The historical mean model (HMM), the market-adjusted model, the market model, the CAPM-adjusted model, and finally, the Fama French 3-factor adjusted model (FF3F-model).
There is no standardised estimation window length in the existing literature, but it is agreed upon to use estimation windows longer than 100 days and to exclude the event date. The estimation window starts at the earliest data point, T0 and typically ends at T1. Meta-research analysing the methodology of 400 event studies finds that the estimation window lengths used span from 30 to 750 days (Holler, 2014). Researchers studying the sensitivity of results, how well a given estimation window length predicts the actual return on the event date find that results are not particularly sensitive to changes in length (Armitage, 1995, Park, 2004). They note that a minimum threshold of 100 days should be exceeded to produce reliable results.
Some authors recommend cutting off the estimation window earlier than T1 and estimating the normal returns until the 30th trading day before the event date to avoid overlapping the estimation and the event windows (Pacicco et al., 2018).
Figure 1.
Structure of an event study
The following Figure is adapted from Benninga (2008). It illustrates the sequential structure of an event study and lays out the roles of the event date, estimation window, event window and post-event window in respect to the event of interest.
Adapted from Benninga (2008, p. 332)
One of the most established estimation models is the historical mean model (HMM). The HMM, also called the mean-adjusted model, takes a security's average returns over the defined estimation window. This model is easy to interpret and compute but also has clear pitfalls. Most importantly, the HMM does not correct for any systematic risk, thus ignores any market movement over the estimation period (Dyckman et al., 1984). The following formula (1) can be used to estimate the expected return with the historical mean model:
E(R
𝑖𝑡) =
∑ (𝑅𝑖𝑡)𝑇2𝑘=𝑇1
𝑁
(1)
With E(Rit) being the expected return of stock i at time t, ∑𝑇𝑘=𝑇2 (𝑅𝑖𝑡)
1 being the sum of the stocks return over estimation period, T1 to T2 being the start and end of the estimation period and N being the duration of the estimation window.
The market-adjusted model aims to rectify the faults of the HMM and incorporates market movement by defining the expected return of a stock as the market return. It assumes a stable linear relationship between market return and the security’s return, with a sensitivity of +1 between both. Generally, a relevant benchmark index is used to proxy for the market return.
This model incorporates systematic risk in the model, but it does not capture a firm’s individual systematic risk profile. As a result, it does not provide reliable results, especially if the event window is characterised by high market volatility (Dyckman et al., 1984). Similarly to the
HMM, it holds the advantage of being simple to calculate and interpret. The following formula (2) can be used to estimate the expected return with the market-adjusted model:
E(R
𝑖𝑡) = 𝑅
𝑚𝑡(2)
With E(Rit) being the expected return of stock i at time t, and Rmt being the market’s/benchmark’s return at time t.
The market model, similarly to the market-adjusted model, makes use of the market return to correct for systematic risk. It improves on the adjusted-market model by estimating a stocks sensitivity to the market return, noted
β
𝑖, instead of assuming a universally and stable coefficient of +1. The stock return is regressed on the benchmark index's return, using ordinary least squares regression (OLS) (Sharpe, 1964). As such, the market model incorporates the stocks specific systematic risk with the market. The following formula (3) can be used to estimate the expected return with the market model:E(R
𝑖𝑡) = α
𝑖+ β
iR
𝑚𝑡(3)
With E(Rit) being the expected return of stock i at time t, α𝑖 being the stocks excess return over the index and βi be the stock’s sensitivity with the market return, R𝑚𝑡.
The CAPM-adjusted return is based on Sharpe (1966) & Jensen (1968) work, which built on the traditional market model, creating the capital asset pricing model (CAPM). They argue that the market model mistakenly assumes that the risk-free rate, which is incorporated in the α𝑖 factor, is constant. They added precision to the market model by adding the risk-free rate factor,
𝑅
𝑓𝑡, to the model. The CAPM-adjusted model estimates the expected return with the return of a benchmark while respecting the stocks specific systematic risk towards the benchmark (Sharpe, 1970; Sharpe et al., 1998). The following formula (4) can be used to estimate the expected return with the CAPM-adjusted model:E(R
𝑖𝑡) = R
𝑓𝑡+ β
i(R
𝑚𝑡− 𝑅
𝑓𝑡)
(4)With E(Rit) being the expected return of stock i at time t, R𝑓𝑡 being the Risk-free interest rate at time t and βi being the stocks sensitivity with the market return, R𝑚𝑡− 𝑅𝑓𝑡).
Fama and French (1993) developed the 3 Factor Fama French model, referred to in event study academia as a multi-factor model. It builds on the Jensen’s alpha (Jensen, 1968) to predict excess market return and adds two additional factors, the small minus big factor (SMB) and
the high minus low factor (HML). SMB accounts for the difference in returns between small- cap and large-cap firms, incorporated due to small firms historically outperforming larger ones.
HML, also called the value premium, accounts for the difference in returns between value stocks, stocks with a high book-to-market ratio, and so-called growth stocks, stocks with a low book-to-market ratio. Fama and French (1993) note that their model is highly reliable, explaining over 90% of the diversified portfolio’s returns in their US sample ranging from 1963 to 1991. The following formula (5) can be used to estimate the expected return with the FF3F- adjusted model:
E(R
𝑖𝑡) = R
𝑓𝑡+ β
i(R
𝑚𝑡− 𝑅
𝑓𝑡) + 𝑆
𝑖∗ 𝑆𝑀𝐵
𝑡+𝐻
𝑖∗ 𝐻𝑀𝐿
𝑡(5)
With E(Rit) being the expected return of stock i at time t, R𝑓𝑡 being the Risk-free interest rate at time t and βi being the stocks sensitivity with the market return, R𝑚𝑡− 𝑅𝑓𝑡). Si denominates the stocks sensitivity to the SMBt factor at time t. Hi denominates the stocks sensitivity to the HMLt factor at time t.
2.1.2.3. Abnormal returns
The following section covers how to compute the abnormal return of a single firm or a sample of firms, panel data, and at one point in time or throughout time, time series.
In order to estimate the effect of a given event, one must separate overall stock market movement from the individual stock’s price movement (Schweitzer, 1989). To do so, one computes the abnormal return realized over the event window based on two variables. First, one measures the realized return, also called actual return, of the security over the event window. Second one determines the estimated normal return, which we expect over the event window, based on a form of conditioning (choice of estimation model, see section 2.2.2.2.).
By deducting the expected return from the realized return, we find the abnormal return:
𝐴𝑅
𝑖𝑡= 𝑅
𝑖𝑡− 𝐸(𝑅
𝑖𝑡|X
𝑡) (
6)
With 𝐴𝑅𝑖𝑡 being the abnormal return of security I at time t, 𝑅𝑖𝑡 being the actual return of security I at time t, and 𝐸(𝑅𝑖𝑡|X𝑡) being the expected return of security I at time t, using estimation model X for time t.
When one is interested in investigating the effect of an event over a multi-day period then the AR must be structured in a time series aggregation form, as such converted to cumulative
abnormal returns (CAR). The following formula (7) allows one to compute CAR, based on the AR from formula (6):
𝐶𝐴𝑅
𝑖(𝑇
1, 𝑇
2) = ∑
𝑇𝑡=𝑇2𝐴𝑅
𝑖𝑡1
(
7)
With 𝐶𝐴𝑅𝑖(𝑇1, 𝑇2) being the cumulative abnormal return between T1 and T2 (the event window), and ARit being the abnormal return of security I at time t.
When one is interested in a collection of firms, the AR must be structured in a cross- sectional aggregation form. The following formula (8) allows one to compute the Average Abnormal Return (AAR), based on the AR from formula (6):
𝐴𝐴𝑅
𝑡=
1𝑁
∗ ∑
𝑁𝑖=1𝐴𝑅
𝑖𝑡(
8)
With AARt being the average abnormal return of company I, N being the number of securities in the sample, and ARit being the abnormal return of security I at time t.
A final form of the abnormal returns is necessary when one wishes to analyse the return across firms and time, one must aggregate the returns in a time series and a cross-sectional fashion. This sample construction is commonly described as panel data. The resulting specification is the cumulative average abnormal return variable (CAAR). The following formula (9) provides the specification, based on the AAR from formula (7):
𝐶𝐴𝐴𝑅 (𝑇
1, 𝑇
2) =
1𝑁
∑
𝑁𝑖=1𝐶𝐴𝑅
𝑖(𝑇
1, 𝑇
2) (
9)
With 𝐶𝐴𝐴𝑅𝑖(𝑇1, 𝑇2) being the cumulative average abnormal return of all the stocks in a sample between T1 and T2 (the event window), N being the number of securities in the sample and 𝐶𝐴𝑅𝑖(𝑇1, 𝑇2)being the cumulative abnormal return of security I between T1 and T2 (the event window)
To sum up, abnormal returns can be specified to measure the return of one firm (AR, CAR) or multiple firms (AAR, CAAR) at a specified point in time (AR, AAR) or over multiple trading days (CAR, CAAR).
2.1.2.4. Significance testing
The following section covers commonly used models to perform the statistical significance testing in event studies and what differentiates them.
In order to prove that an event has had a measurable impact on a company’s value, one must find a statistically significant change in the abnormal returns within the event window.
The null hypothesis assumes that there is no significant difference between the returns of the periods of the estimation window and those within the event window (Shuttleworth, 2008).
Therefore, to reject the null hypothesis, one must prove that there is a statistically significant change in the abnormal returns present within the event window.
Two main types of significance testing have been established in event study literature, parametric (e.g., t-test) and non-parametric tests (e.g., rank/sign tests) (Campbell et al., 2010).
The main difference in the application of both tests is that the parametric tests require a normal distribution of the returns (AR, AAR, CAR, CAAR) to be precise and interpretable (Mordkoff, 2016). On the other hand, Non-parametric tests, do not need this a priori assumption to provide precise and interpretable results.
The simplest method is a parametric t-test under normality assumptions (Pacicco et al., 2018). One assumes that security returns are normally distributed, with a normal distribution centred on 0, and the variance of the returns being σ2 (AR). Other specifications such as AAR, CAR, CAAR can be tested too, with the assumption of their respective distributions being centred on 0, and variances respectively being σ2(AAR), σ2(CAR), σ2(CAAR) (MacKinlay 1997; Binder 1998). This methodology is known as an event study via t-test under the normality assumption of returns.
Financial literature generally recognises that stock prices and stock returns do not fulfil the normality assumption (Brown and Warner, 1985; Fama & French, 1993; Dubin, 1988).
However, using the statistical technique of standardisation, one can adjust the data set to fulfil the normality assumption and make stock price data reliably testable through a parametric test, such as the t-test (Patell, 1976). Multiple methodologies to achieve this on a serial and cross- sectional level have emerged in event study literature (Patell, 1976; Boehmer et al., 1991;
Kolari and Pynnönen, 2010; Corrado, 1989; Cowan 1992).
Patell (1976) developed a parametric test that standardises each abnormal return by the forecast-error-corrected standard deviation before performing a t-test. The Patell model accounts for diverse standard deviations between the estimation window residuals and the event window residuals.
Boehmer et al. (1991) present the BMP model, which improves on Patell’s (1976) model, by accounting for eventual cross-sectional increase in variance of returns within the event
window. They also prevent that those securities in the sample, which have proportionally high variances, over-influence the outcome of the abnormal return specification. The researchers found that their simple adjustment produces appropriate rejection rates of the t-test when the null is true, and the model is equally powerful tests when it is false compared to the Patell-test.
According to Kolari and Pynnönen (2010,2011) and Dutta et al. (2018), the previously presented models fail at capturing bias induced by cross sectional data. The normality assumption method, as well as the Patell and Boehmer model, all suffer from cross-sectional correlation among abnormal return. The researchers find that even relatively low levels of cross-correlation cause the aforementioned tests to over-reject the null hypothesis of zero average abnormal returns. In response, Kolari and Pynnönen (2010) developed the adjusted- Patell and the KP test. The former one improved the BMP model, while the latter one improved on the Patell model. The researchers achieved this by adjusting both models for cross- correlation between stocks. They found that their models test differences in multiple-day cumulative abnormal returns with improved power compared to previous parametric models.
Lyon et al. (1999) propose using a buy-hold abnormal return model (BHAR) instead of the traditionally used AR. Multiple critics voice their concern with this method and discourage from using it (Eckbo et al., 2000; Bessembinder & Zhang, 2013; Kolari and Pynnönen, 2010, 2013). Kolari and Pynnönen (2013) and Dutta et al. (2018) point out that for long-term event windows the size, power, and robustness of the parametric tests is weakened with the use of BHAR instead of AR. Dutta et al. (2021) recommends using the logarithmic function of the AR instead of BHAR, as it avoids scaling issues between ARs in the sample.
Non-parametric tests, such as sign and rank tests, do not rely on the normality assumption of the AR distribution, and as such, they do not risk of underperforming due to the data being non-normally distributed (Campell, 2010). Multiple papers find that non-parametric tests are superior in accurately rejecting the null hypothesis, compared to parametric tests (Kolari &
Pynnönen, 2011; Campell, 2010). Dutta et al. (2018) note that standardised cross-sectional tests still have their use in financial econometrics. According to them, the KP-test is a useful robustness check tool.
One of the earliest non-parametric tests in event study literature is the Wilcoxon (1945) sign test. it uses the statistical significance of the signs of the AAR’s instead of their actual values. Kolari and Pynnönen (2011) developed the generalized rank test (GRANK) and improve on the previous variant by incorporating the magnitude of returns. As a result, the
GRANK provides more consistent results than all of the previously parametric and non- parametric tests (Kolari and Pynnönen, 2011). Campbell (2010) performed simulation analysis, based on Brown and Warner’s work (1980, 1985), on a non-US-multi-country sample of 50,000 non-US stocks from 1988 to 2006. They found evidence that the rank and generalized rank tests are superior models, confirming Kolari and Pynnönen’s (2011, 2011) findings. Kolari and Pynnönen (2011) state that the GRANK procedure outperforms previously used rank and sign tests of CARs and is robust to AR serial correlation as well as event-induced volatility.
They state that the GRANK produces superior empirical power relative to popular parametric tests, especially in multi-day event windows.
This sub-chapter concludes that a combination of the non-parametric GRANK-test and the parametric KP-test test provide a powerful methodology to conduct an event study on long term stock returns. The GRANK is a powerful model for testing the main hypothesis of CAR
= 0 (or CAAR), and the KP-test provides a solid robustness check for the analysis.
2.2. The event: short squeezes
This paper is interested in the financial event known as a short squeeze. In order to fully understand what a short squeeze is, one must understand the market mechanisms that enable this rare financial event to occur. This section aims to explore the workings of the short-selling mechanism, how to measure the risk exposure of short investors, and what potential market or firm specific factors can lead to a short squeeze. The goal is to explore how a short squeeze can impact the long-term value of a firm. The following section will cover academia on short selling (2.2.1.), borrowing of stocks (2.2.2.), short interest (2.2.3.), what factors contribute to a short squeeze (2.2.4.), and finally, what is known long term effects of short squeezes (2.2.5.).
2.2.1. Short selling
Investors usually invest in companies to either make a return on the dividends paid out to them while they hold the stock or the premium they earn when they sell the stock at a later stage. This is known as going long on a stock or holding a long position. An investor expects the company to do well in the future. However, some investors might wish to benefit from negative price movements instead of the positive ones. These investors can benefit from such price fluctuations by using a trading technique called short selling.
Shorting selling is selling a stock, without owning it, usually by selling a borrowed share from a third party (Miller, 1977). A sale with no borrowed share to cover the trade is called
naked short selling, while the alternative is known as short borrowing (Mitchell, 2021). Both are forms of a short position. A short seller increases his return with a decrease and not an increase of the security’s price. Both types of short selling benefit in a similar fashion from the negative price movement. The investor sells a security for price X at time T and buys it for an lower price at T+1 for price Y to cover his first trade. The profit, excluding any transaction fees or borrowing costs, consists of X-Y. As a result, the profit of a short position is capped at the value of X as the price Y can (generally) not be negative. This is distinct from a long position as the price, and profit, of selling a held stock can theoretically be indefinitely high.
The popularity of short selling has been on the rise in recent decades. According to researchers, short-selling popularity has increased from making up 9% of the New York Stock Exchange (NYSE) trading volume in 1984 to 24% in 2005 and 31% of the NASDAQ in 2005 (Brent et al., 1990; Diether et al., 2009). Angel et al. (2003) find that 1 out 42 trades involved a short sale in 2000. They note that short selling is most common in stocks with high returns and high trading volume.
Part of the literature argues that short selling is harmful to the market and its participants.
Deshmukh et al. (2017) find that short sellers contribute to market instability. Lecce et al.
(2012) find slightly higher stock return volatility and a small reduction in the liquidity of stocks in markets where naked short sales are allowed. Henry & Koski (2010) note that short selling most often enhances price efficiency but do document that short selling reduces price efficiency during seasoned equity offering (SEO) events, which is similar to Deshmukh et al.’s (2017) findings. Miller (1977) finds that short-sale constraints lead to overvaluation and thus harm price discovery. Angel et al. (2003) find that short selling is especially present on stocks when the previous days on a stock had unusually low returns. Thus, short selling risks impact the market when returns and liquidity are already low, further causing both to decline.
Other researchers find that short selling can improve market conditions. Woolridge &
Dickinson (1994) find that short seller provide liquidity in bull markets, while reducing short positions in bear markets. Other researchers find that price discovery decreases from short-sale restrictions (Brenner & Subrahmanyam, 2008; Diamond & Verrecchia, 1987; Dechow, 2001).
This can be attributed to the restrictions not only keeping manipulative short sellers from trading but also informed short sellers. Manipulative short selling consisting of shorting with the aim to manipulating prices downwards, while informative short selling consisting of investors anticipating an exogenous change in a securities price (Deshmukh et al., 2017).
Deshmukh et al. (2017) findings are similar to Brenner and Subrahmanyam (2008). They note that restrictions slow down the price discovery mechanism by keeping informed short sellers from entering their short positions. To sum up, short-sale restrictions reduce trading volume and liquidity, and hinder market participants from entering profitable positions.
Restrictions on short selling do not solely protect other market participants but also short sellers themselves from excessive risk taking. Short sellers are exposed to additional risk compared to investors holding long positions. A long investor has the luxury of waiting out a market dip to sell his stock further down the road when its selling price is profitable, and possibly collecting dividends while waiting. Contrarily, short sellers commonly borrow their shares which they sell, and as a result, must pay interest on the borrowed asset while waiting for the right moment to buy back a stock to clear their debt. This interest entails that short sellers are much more time-restricted than long investors.
2.2.2. Borrowing shares and naked short selling
Traders, who engage in short selling without covering their trade with a borrowed security, practice naked short selling. This kind of short trade is generally strongly restricted in financial markets due to the high-risk exposure for the trader selling the stock and for the trader who is the buying party. In addition, the buyer is at risk of not acquiring the asset he paid for as his opposing party does not have it in its possession at the moment the trade takes place.
Long-term-oriented investors usually lend out stocks. Duffie et al. (2002) find that institutional investors entering a short position do so through their broker, who source the necessary number of shares on loan to enter the position. The researchers note that the shares are most often lent out by companies that are unlikely to change their portfolio composition due to a short-term price fluctuation in a single security. Examples are insurance companies, pension funds and index funds.
Short selling comes with increased risk. In most markets, including the US market, traders have to put up collateral and pay a loan fee until a short position is closed. This entails that a short trader is exposed to common leverage risk and short position-specific risk. The common risk attributed to leveraged positions consists of leverage fees, margin calls and the possibility of regulatory changes of their broker or the regulatory agency. The additional risk short investors take on consists of possible loan recalls from the lender and changes in the interest
rate paid on the shorted stock. A short trader must thus be careful when entering a short position.
The cost of leverage contributes to why short sales are less common than long positions.
Lamont and Thaler (2003) found that short sellers trade at a less high frequency compared to other market participants and tend to underperform. They attribute this to that shorting can simply be impossible, due to short constraints and secondly, that short positions can have large costs.
A considerable cost factor is due to leverage regulation. In the US a trader must tie up high amounts of funds in order to short trade. According to Regulation T, a borrower must present collateral worth the full value of the short position, plus an additional maintenance margin requirement of 50% of the short sale value (Langager, 2021). The latter adjusts to the stock price as it fluctuates. If the trader cannot guarantee the increase of the maintenance margin after a price spike, a margin call will be executed, clearing his short position with the funds from the total margin account. A high volume of short positions getting margin called contributes to the short squeeze phenomenon.
Borrowing stocks, compared to a traditional margin account, comes with additional risks and costs. Lending agreements between the short investors and lending parties are usually renewed on a daily basis. Thus, a lender can back out of his lending position each day and the short trader must return the borrowed stock. This can be done through a so-called recall notice.
In the US, failing to comply with a recall notice entails sanctions by the U.S. Securities and Exchange Commission (SEC) as well as significant reputation damage. Suppose the short seller cannot return the borrowed stock within the agreed-upon settlement time. In that case, the lending party can use the collateral to buy back replacement security on the market. If the collateral does not cover the cost of doing so, the borrower is still liable for compensating the lender. A high volume of short positions getting recall notices contributes to the short squeeze phenomenon.
2.2.3. Short interest
Short interest is a commonly used metric to measure the frequency of short selling on a security. Short interest is defined as the shares sold short divided by the total outstanding shares (Mitchell, 2021). Past literature does not agree on what, if at all, role short interest plays regarding stock prices.
Early studies found no correlation between short interest and stock prices. Mayor (1968) and Hurtado-Sanchez (1978) conducted a multiple regression analysis on short interest and stock prices. Both determined that short sellers do not impact stock prices. Major (1968) argued in favour of the random walk theory, also known as the weak form of the EMH, that stock prices can not be predicted through past or future information. Wolldrige and Dickinson (1994) confirmed these findings with a simple regression model. They concluded that short traders are not able to produce abnormal returns by profiting from less informed traders. Aksu and Gunay (1995) test the co-integration of price, short interest, and trading volume and find neither a positive nor a negative relationship.
Another view in academia is that short interest has a positive relationship with stock returns.
This viewpoint is referred to as the contrarian school (Aksu & Gunay, 1995) or Wall Street wisdom (Epstein, 1995). This view theorizes that high levels of short interest predict the high demand of stocks in the future to cover the open short positions that need to be closed. This future demand creates buying pressure and can result in an upward price trend. When a high price spike characterises this price trend, then a short squeeze occurs. Short investors outbid one another to cover their positions. This view assumes that the weak form of EMH is not valid, as it necessitates that the future price (predictions) of a security impacts the current price.
Some empirical evidence has been found in favour of the contrarian school. Miller (1977) finds that different investors expect different price levels for future stock prices, and this uncertainty creates risk and volatility. Hannah (1976) finds a significant positive relationship between the stock interest ratio and a stock’s short interest. The short interest ratio measures the short interest in respect to the average daily volume of shares traded. The author argues that high levels of short interest ratio are a bullish signal in the long term. Brent et al. (1990) find that short interest is positively related to a stock’s option volume, which is also a bullish signal.
Aksu and Gunay (1995) present evidence in favour of a contemporaneously interrelated positive relationship between short interest, stock prices, and average daily trading volume.
The most common viewpoint is that short interest holds a negative relationship with stock prices, this view will be referred to as the bearish viewpoint from here on. This view, similar to the contrarian school, assumes that past and future information influences present stock prices. Under this view, high levels of short interest are a bearish signal. Short interest indicates pessimism within investors, specifically informed investors (Aksu & Gunay, 1995; Miller, 1977). As was covered before (in section 2.2.2.), short selling entails substantial additional risk
compared to holding long stock positions and has capped gains. Due to both of these characteristics most short sellers are professional investors (Woolridge & Dickinson, 1994;
Brent et al., 1990). The literature assumes that professional investors to be well informed, thus a high level of short interest indicates that more negative information should be incorporated into the stock price (Ackert & Athanassakos, 2005). This indicates that the price of a stock that is heavily shorted should fall to adjust to this decrease in negative information in the long term.
Many papers have found empirical evidence in favour of the bearish viewpoint. Seneca (1967) and Kerrigan (1974) perform a regression analysis on the S&P 500 index and short interest. Both their results show a negative relationship between the two variables. Figlewski (1981) and Asquith and Meulbroek (1996) did a similar study but looked at the abnormal return of individual firms and their short interest. Similar to the studies on index returns, they find a negative relationship between both variables. Aitken et al. (1998) and Desai et al. (2002) performed a calendar-time portfolio study and found evidence in favour of a negative relationship between stock prices and short interest. Aitken et al. (1998) studied the Australian stock market, while Desai et al. (2002) analysed stocks on the US NASDAQ. Desai et al.
(2002) reported negative abnormal returns for highly shorted stocks, noting that the relationship between short interest and negative stock returns remains significant for up to 12 months after the release of short interest data. Angel et al. (2003) found similar results to Desai et al. (2002) over a 3-month period. Boehmer et al. (2008) examined daily short activities and find that lightly shorted shares perform better than heavily shorted shares suggesting a negative relationship.
To sum up, academia surrounding the relationship of short interest and stock prices can be separated into three viewpoints. Early papers suggest no relationship between the variables, while newer academia provides strong theoretical arguments in favour of a short-term positive relationship, but only scarce empirical proof supports these theories. Most academics agree that short interest remains a bearish signal and back these claims up with strong empirical analysis with a large variety of empirical models.
2.2.4. Short squeeze
This paper wishes to look further explore the phenomenon of a short squeeze and what contributes to it occurring. According to the SEC (“Division of Market Regulation: Key Points About Regulation SHO”, 2015) a short squeeze refers to:
“… the pressure on short sellers to cover their positions as a result of sharp price increases or difficulty in borrowing the security the sellers short. The rush by short sellers to cover produces additional upward pressure on the price of the stock, which then can cause an even greater squeeze.” (P.1)
A short squeeze can occur when a high level of short interest is present on a stock.
According to the contrarian view, investors holding short positions predict future high demand for the stock caused by other short traders covering their open short positions. This anticipated future demand creates buying pressure and can result in an upward price trend.
The bearish viewpoint explains the short squeeze phenomenon through a less direct manner (Vryghem, 2017). Investors with the bearish viewpoint on short interest believe that a company is underperforming, and overvalued. If news emerges indicating that the company is indeed doing well, or will do so in the future, the short sellers will readjust their opinion on the company and try to exit their short position. Such news could in the form of an unexpected positive earnings announcement or the unexpected economic recovery after a financial crisis boosting consumer spending in the sector the company participates in. Short investors face unlimited negative returns in case of a stock price increase and the risk of panic trying to close their position. In the bearish viewpoint, a short squeeze is thus only possible if the informed short investors were actually not better informed than the average long position holder on the stock. At this point, the reasoning coincides with the contrarian one.
Both views explain the need to cover short positions abruptly. However, from there on, the concept of demand and supply explain how prices can rise to extraordinary heights (Locke, 1691). If the holders of the outstanding shares of the stock do not mirror the spike in demand for shares by selling their shares, a very sharp price spike can occur.
During a short squeeze, holders of the underlying asset dry out the supply to squeeze out the short positions to make them pay very high prices to cover their position. A short squeeze causes margin calls from brokers, as well as recall notices from lenders that wish to cash out on the price spike. Additionally, even if the lender does not recall his share the short investor still has to cover other costs if he wishes to wait out the short squeeze. He has to pay interest to the lender for each day passing on, so he does not exit his position. The accumulation of having to buy a share during the spike and the interest on the borrowed share can raise significant costs for short sellers. During the 2021’s GameStop short squeeze, short sellers cumulatively lost an estimated $383 million a day (Lipschultz, 2021).
There are multiple factors contributing to a short squeeze. A high level of existing short interest facilitates a short squeeze’s occurrence. Most often there is still the need of a catalyst to start the price spike. This catalyst can be a firm specific announcement, such as a M&A announcement, or a macro level announcement such as a recovering economy during a financial crisis. Other examples are reports about a company’s trading activity, new partnerships or equity buy-backs.
A distinct catalyst for short squeezes is market manipulation by a big speculative entity (Jarrow, 1992). This is almost always an institutional investor, and the practice is called a market corner. In this scenario, a big shareholder of a stock calls in all his shares from his broker in order to hold more shares than are readily available on the market. The goal is that after the removal of the shares from the market, there are less shares outstanding than that are being shorted. If this is the case, at least some of the short investors must buy the barrowed shares of the big shareholder at some point. The latter can ask any price for them as there is no alternative seller on the market to cover the demand. This kind of market manipulation occurred with commodities markets, such as the silver market, but also in the stock market, e.g., during the 2008 Volkswagen short squeeze. In 2021, for the first time in US stock market history, a collection of retail investors collaborated on online forums to corner the market on GameStop shares (Umar et al., 2021). What traditionally used to be a trading technique reserved for powerful institutions seems to be available to coordinated groups of retail investors now.
2.2.5. Long term effects of a short squeeze
Even though the concept of short interest and short constraints has been much explored, the long-term effect of a short squeeze on an individual affected stock has been relatively little explored. No peer-reviewed paper has been published in English on the long-term return after short squeezes. However, some research on the subject can be found online; Vryghem (2017) finds no significant relationship between the two variables. However, academia has widely covered the role that uninformed and informed investors play in the stock market. Informed investors are better informed than the general market, and liquidity investors are the remaining investors. Both are key players during a short squeeze. The literature finds that a higher ratio between informed traders (short traders) and liquidity traders (all other traders) causes higher volatility in markets (Allen et al., 2021). This higher volatility is due to the market jumping between the previously perceived fundamental value and the new updated perception of fundamental value of security (Holden & Subrahmanyam, 1992). Glosten and Milgrom (1985)
find that this increase in volatility can be interpreted as informed investors incorporating their information into the price.
Another perspective on short squeezes’ impact on the stock is to look at the underlying mechanisms that cause them. The previously presented studies on short interest and returns present themselves. Multiple papers found strong evidence that high short interest is a bearish signal for long term returns (Lecce et al., 2012; Desai et al., 2002; Deshmukh et al., 2017).
After a short squeeze, short interest on a stock drastically decreases, and as such this decrease should be seen as a bullish signal.
Another underlying mechanism of the short squeeze is the stock price spike. Long et al.
(1991) find that price spikes attract noise traders. Noise traders are traders who trade on false beliefs. They are uninformed. They find that noise traders tend to outperform informed traders over the short term and tend to be overconfident and late regarding their trades, especially after previously performing well on a similar trade. It follows that the noise traders might stick with their long position long after a short squeeze or even enter a long position during/after the short squeeze based on its previous daily returns alone. This buying pressure should have a certain price effect on the stock itself if enough noise traders follow this behaviour. The resulting lingering price pressure should be measurable in the medium-term to long-term.
2.3. Hypothesis
This paper concludes from the existing literature that a stock should experience medium- term to long-term positive abnormal returns after a short squeeze. Two drivers are identified:
First, the periodic decrease in short interest is a long-term bullish signal (Lecce et al., 2012;
Desai et al., 2002; Deshmukh et al., 2017). Second, the higher returns during the initial short squeeze can fundamentally change retail investors’ opinion of the stock, which should also contribute to long-term positive returns (Long et al., 1991).
This paper presents the following two hypotheses:
o Hypothesis (I)
After a short squeeze, a stock experiences medium-term positive abnormal returns.
o Hypothesis (II)
After a short squeeze, a stock experiences long-term positive abnormal returns.
This paper will test hypotheses (I) and (II) by performing the KP-test and GRANK test on the CAAR of a 11 US firm sample with three different estimation models, the HMM, market- model and FF3F model.
In order to test hypothesis (I), the following null and alternative hypotheses are presented:
𝑁𝑢𝑙𝑙 ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 (𝐼): 𝐶𝐴𝐴𝑅 = 0 𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒 ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 (𝐼): 𝐶𝐴𝐴𝑅 > 0
With CAAR consisting of 11 firms over an six trading day long post-event window of [T+1;T+6], with T= short squeeze date.
In order to test hypothesis (II), the following null and alternative hypotheses are presented:
𝑁𝑢𝑙𝑙 ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 (𝐼𝐼): 𝐶𝐴𝐴𝑅 = 0 𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒 ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 (𝐼𝐼): 𝐶𝐴𝐴𝑅 > 0
With CAAR consisting of 11 firms over a 101 trading day long post-event window of [T+6;T+106], with T = short squeeze date.
3. Methodology 3.1. Assumptions
This paper assumes:
1. The semi-strong form of the EMH.
2. The short squeeze’s effect is not already pre-priced into the stock.
3. No significant confounding effects are present in the estimation/event window.
These assumptions are essential to give interpretability to the results of the analysis. Some are solely upheld a priori, while others are strengthened through the construction of the study.
The first assumption is upheld through the existing event study literature, which is laid out throughout Section 2.2.. Moreover, the specific construction of this study allows to strengthen the latter two assumption further.
One tool to do so is through the specification of the estimation/event window length. The wider the window, the higher the chance that confounding effects affect the abnormal returns.
As a result, a small window is favourable for the third assumption. On the other hand, if the
event window is too narrowly defined, one risks of missing the market’s initial reaction to the event, and as a result weakening the second assumption (Campbell et al., 2010; MacKinlay, 1997; Ball & Torous, 1988). Additionally, if the estimation window is too small, the results of an event study risk becoming unreliable (Armitage, 1995, Park, 2004) It must be noted that strengthening the second assumption through the event window length weakens the third assumption. One must find a compromise to achieve strong internal validity.
A second tool is the event date specification. This tool can reduce the presence of confounding effects across the sample and is inherent to the research design. Each company is attributed an individual event date, as short squeezes are not a market-wide event but a firm- specific attack on short positions. If each company has a distinct event date, the chances of spillover effects from one event affecting another stock’s return within its estimation or/and event window are unlikely. The sample of this study spans over 20 years, covering multiple economic cycles and financial crises. This makes it unlikely that the sample as a whole is affected by a common trend.
A third tool is the use of multiple estimation models. This study uses three distinct estimation models with varying degrees of systematic risk inclusion. This removes a certain degree of confounding effects from the analysis. This range of CAARs provides more robustness to the analysis. It makes the interpretation more nuanced as a variety of abnormal returns are analysed for each firm. As a result, the third assumption is further strengthened.
To sum up, the first assumption is a priori assumed through event study literature, and the latter are reinforced through the specific setup of estimation and event windows. All three are necessary to give interpretability to the statistical analysis.
3.2. Defining the event date, estimation window, event window
The following section will present how this paper defines its event dates, estimation windows and event windows.
3.2.1. Event date: the short squeeze
The definition by the financial service and information provider IHS Markit was used to identify short squeezes on the stock of 11 companies between 2011 and 2021. First, a pre- selection was made by searching online newspaper mentions of short squeezes on the google search engine (“Google”, 2021). The pre-selection was accompanied by investigating data sets
of previous literature on short squeezes and researching them financial services provider platforms. Next, statistical analysis was used to determine if the pre-selected stock’s price movement event qualifies as a short squeeze according to the IHS Markit (2015) definition.
Focus was given on the following two conditions: First off, referred to as Condition (1) from here on, that the stock witnessed a short-term price increase of at least three standard deviations compared to the previous 60 trading days over one to three days. Secondly, Condition (2) refers to the increase in price, followed by a decrease in shares on loan (over at least five consecutive days).
Both conditions are verified through the statistical analysis presented in Chapter 4. The first condition is verified, with the help of Excel, by computing the standard deviation of the previous 60 trading days and comparing them to the price spike on the event date. The second condition is harder to verify as daily data on shares on loan is not publicly available. Pay-to- access financial information providers, such as IHS Markit and www.shortsqueeze.com, offer datasets on a selection of companies. However, their products are out of budget for the scope of this master’s thesis.
As a consequence, the condition had to be loosened to a less precise interval. It was possible to acquire bimonthly data on the short interest ratio through NYSE and NASDAQ datasets, which has been found to be a reliable proxy for shares on loan (Beneish, Lee, & Nichols, 2014).
This data was then used to identify if the short interest decreased from the closes data point before the short squeeze to the first one past the short squeeze. Due to the inferior precision in checking for the second condition, the selection process focussed on the pricing condition.
However, to improve the accuracy of determination of a short squeeze this study investigated each short squeeze in financial media publications. Finally, online research provided additional cited third-party information regarding short interest changes and shares on loan.
3.2.2. Estimation window
The estimation window provides a reference point to how a stock would have performed if the event did not occur. It spans from T0 to T1, with T0 being 130 trading days before the event date and T1 being 30 days before the event date.The estimation window is defined as 101 trading days long and follows the literature’s recommendation of exceeding 100 trading days and is within the common estimation window length of previous papers on the subject (Holler, 2014; Armitage, 1995, Park, 2004). Following Pacicco et al.’s (2018) recommendations, the
upper bound of our estimation window is 30 trading days before the event date. This specification is of high importance for studying short squeezes.
Short interest on a stock builds up progressively before investors start squeezing the high number of short positions. Thus, the estimation window being too close to the event date, could cause the estimated returns to be unrepresentative of the stock’s normal returns. This adjustment is different to Vryghem’s (2017) analysis, which also looked at long term short squeeze effects. He estimated all the way up to the event date, risking harming the internal validity of the results.
This paper’s specification of the estimation window being further away from the event improves robustness. Specifically, the estimation window is less likely to be unrepresentative of the actual security’s normal return in case of misdating the event date, as well as in the case of failure of the second assumption (i.e., the event is unforeseen by the market).
3.2.3. Event windows
This event study covers one event window and two post-event windows. The first event window going from T2 to T3 and tests if the return of stocki over the event window is significantly different to pre-event window levels. Regarding the hypothesis this means that the CAAR over the event window is significantly different to 0. The alternative hypothesis is that CAAR > 0, as we expect a positive significant relationship. To add more nuance to our results, we also individually test if the CARi of each individual stock i is significantly higher than 0.
Next, we will measure the medium-term and long-term effects of our event on the abnormal returns. The first one lasting from the 1st until the 6th trading day after the event date, from T3
to T4 and making up the first post-event window. The second one lasting from 6th until the 126th trading day, from T4 to T5, making up the second post-event window. These post-event windows are within the recommended and typical durations observed in past literature. In order for the alternative hypothesis (1) and (2) to be confirmed, the CAAR of the post-event window must be significantly higher than 0.
To sum up, the event study consists of one 100-day estimation window, one 3-day event window around the event date, and two post-event windows, respectively 6 and 120 days long.
