Destabilisation By Too Much Arbitrage.pdf

Does Too Much Arbitrage Destabilize Stock Price? Evidence from Short Selling and Post Earnings Announcement Drift

April 2018

Abstract Stein (2009) suggests that too much arbitrage capital exploiting underreaction can lead to overreaction, pushing price further away from fundamental value. I test this hypothesis by investigating the relation between changes in short interest ratio around earning announcement and the subsequent drift return. There are two main findings in this paper. First, my results suggest that too much arbitrage capital does contribute to overreaction (with a t-statistics around 4 on average). These findings are robust to alternative sample periods or length of the window for drift calculation. Second, contrary to the findings in prior literature that show that short sellers mitigate the magnitude of drift, my results show that almost all of this effect are actually contributed by the observations that are more likely to represent overreaction.

JEL classification: G12, G14 Keywords: Arbitrage, Short selling, Post earnings announcement drift, Market efficiency.

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1. Introduction: Conventional wisdom believes that as more arbitrage capital starts to trade a given anomaly, any abnormal returns will be eventually eliminated (up to risk and limits to arbitrage) and stock prices will be pushed closer to fundamental values (Friedman (1953)). In other words, the more arbitrage capital, the more efficient the market is likely to become. However, Stein (2009) questions this simple intuition and shows that when the anomaly does not have a fundamental anchor and when arbitrageurs are not aware about how many other arbitrageurs are trading the same anomaly, arbitrage activity may lead to price overshoot, pushing price further away from fundamental value. Prior literature has very little empirical evidence regarding this implication. Therefore, in this study I try to test whether too much arbitrage capital destabilizes stock price. The anomaly utilized in this paper is post earnings announcement drift (henceforth, PEAD). Three major advantages associated with PEAD makes it an ideal setting for testing the above implication. First, it does not have a fundamental anchor so that arbitrageurs do not have a benchmark to gauge the level of under or over valuation (Stein (2009)). Second, it is one of the most persistent anomalies that are often followed by actively managed hedge funds (Coskun and Gurun (2012)). Third, it allows me to pin down the time at which arbitrageurs are most likely to take actions – that is, if an arbitrageur was to maximize his profit, he would be more likely to take action in a tight window around the earnings announcement date (Zheng (2009)). Most of other non-fundamentally anchored anomalies (e.g. momentum, Lou and Polk (2013 WP)) however, do not grant this advantage since we do not know when arbitrageurs buy or sell stocks. The proxy for arbitrage capital is the change of short interest ratio around earnings announcement date1. It is

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Short interest ratio is the ratio between short interest and share outstanding. Short selling activity tend to concentrate in a tight window around earning announcement date (Zheng (2009) and Boehmer and Wu (2012)). Therefore, taking

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widely documented that short sellers tend to be informed traders who incorporate information and move prices closer to fundamental values (Diamond and Verrecchia 1987; Asquith and Meulbroek 1995; Dechow et al. 2001). Also note that, in this study, I only focus on announcements with negative earnings

surprise since these are the stocks that short sellers are more likely to target. The relation between PEAD and change of short interest ratio is illustrated in figure 1. Figure 1 Day -1 0

Day 0

Day 1

Drift Ends

-0.05 -0.1 -0.15 -0.2

Insufficient Arbitrage Sufficient Arbitrage Too Much Arbitrage

Day 0 is the date when the earning announcement is released. Day -1 is one day before and Day 1 is one day after the announcement date. Together, the 3-day window forms the initial response period in which arbitrageurs will trade most intensively (Zheng (2009)). The solid line illustrates the return pattern for negative earnings surprise announcement with insufficient arbitrage capital. In this case, a minor negative return is realized in the initial response period which is followed by a further negative drift. The dashed line illustrates the case when there is sufficient arbitrage capital. In this case, more arbitrage capital adjusts the price to fundamental value faster and therefore a moderate negative return (more negative than the solid line) is realized

the difference of short interest ratio before and after the earnings announcement date is likely to deliver a good estimate of the arbitrage capital.

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and no obvious further drift follows. The crossed line illustrates the case when there is too much arbitrage capital. In this case, due to too much arbitraging, a large negative initial response (potential overshoot) is followed by a positive drift (correction). This paper makes two major contributions. First, it complements the exploration of the effect of short selling on market efficiency. Evidence documented in prior literature (e.g., Dechow et al (2001), Desai et al (2002), Hirshleifer et al (2011), Cao et al (2007), Lasser et al (2010), Saffi and Sigurdsson (2009), and Boehmer and Wu (2012)) in general, suggests that short sellers improve market efficiency. This paper, to some extent, completes the role of short selling on market efficiency and studies whether too much arbitrage leads to overreaction, which undermines market efficiency. Overall, my evidence suggests that too much arbitrage does seem to contribute to overreaction. Second, this paper also seeks to find out whether overreaction also contributes to the identification of the previously documented relation – short selling improves market efficiency and if it does, to what extent. This seemingly controversial argument can in fact happen because both the data points that tend to represent overreaction and those that tend to represent underreaction produce qualitatively the same coefficient estimate for the proxy of arbitrage capital (i.e., if the data points that are likely to represent underreaction lead to a positive coefficient estimate, so does the data points that represent overreaction.). This paper isolates the overreaction effect and tests whether the previously documented relation still exists. Overall, my evidence suggests that overreaction contributes significantly to the relation between short selling and anomaly returns and, in the absence of the contribution from overreaction, short selling is barely related or even reversely (with respect to expected direction) related to anomaly returns.

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My findings suggest that too much arbitrage does seem to destabilize stock price. First, holding all else equal, announcements with larger increase in short interest ratio experience significantly more negative initial response (more correction). Next, I show that negative earnings announcements with positive abnormal drift have significantly higher change in short interest ratio than those with negative abnormal drift. Moreover, I find that, holding all else equal, stocks with the largest increase in short interest ratio ( SIR decile 10) is almost 10% more likely to result in overreaction than stocks with the largest decrease in short interest ratio ( SIR decile 1). In the end, I show that, holding all else equal, change in short interest ratio significantly contributes to overreaction. In particular, within stocks that have positive abnormal drift, the ones that experience the largest increase in short interest ratio average 1.55% higher drift than the ones that experience the largest decrease in short interest ratio. Robustness tests show that my results are not likely to be driven by extreme values in abnormal drift, particular year observations, or length of window for return calculations. This paper contributes to two streams of literature. First, this paper connects to the literature of arbitrage and market efficiency. In general, previous papers have numerous evidence that arbitrage activity improves price efficiency on average (e.g. Mendenhall (2004), Cao et al (2007), DellaVigna et al (2009), Hirshleifer et al (2009), Hanson and Sunderam (2014)). However, there is relatively scarce evidence of whether too much arbitrage pushes price further away from fundamental value (Lou and Polk (2013)). My paper adds exactly to this point with evidence that suggests that too much arbitrage capital does seem to contribute to overreaction. Second, my paper also connects to literature that studies the role of short selling in price discovery (e.g. Dechow et al (2001), Lasser, Wang, and Zhang (2010), and Boehmer and Wu (2012)). In particular, Boehmer and Wu (2012) find that stocks that have an increase in short interest ratio around negative earnings 4

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surprises tend to have higher drift period returns (negative drift return becomes less negative or even positive), and therefore this positive relation—increased short selling leading to less negative drift—seemingly suggests that short selling does improve market efficiency. However, the fact that stocks with larger increases in short interest exhibit “less negative” drift could mean two distinct mechanisms. First, it could indicate that an increase in short interest ratio reduces PEAD. Second, it could also mean that too much arbitrage capital generates a subsequent return reversal (i.e., as illustrated in figure 1, an unusually large spike in short interest in the initial response period causes too much correction which, in turn, leads to a positive drift following the negative earnings surprise). Clearly, the first mechanism pushes prices towards fundamental value whereas the second pushes the prices away. It is crucial to find out whether the second mechanism is at work, otherwise we cannot make the inference that the previously identified relation truly represents the stabilizing mechanism. It might as well represent the destabilizing mechanism or a mixture of both. Surprisingly, my findings suggest that the positive relation is dominantly contributed from the observations that are more likely to represent overreaction (i.e., observations that experience positive drift). Specifically, I find a strong positive relation between change in short interest ratio and drift return for the sample that only include positive drift observations (t-statistics around 6) whereas this relation is insignificant or even negative in the sample of negative drift observations. The remainder of this paper is organized as follows. In section 2, I conduct literature review and discuss why PEAD is a particular good anomaly for testing the hypothesis. Section 3 describes the data, sample selection, computation of variables, and summary statistics. Section 4 introduces test design and presents empirical results. Section 5 conducts robustness tests. Section 6 deals with identification issues and section 7 concludes the paper.

2. Literature review 5

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Lou and Polk (2012 WP) tries to test whether too much arbitrage activity exploiting underreacction leads to overreaction. In particular, they use comomentum (average correlation among past winner or past loser stocks) to gauge the extent of exploitation of momentum strategy and show that high exploitation of momentum strategy negatively predicts momentum returns. My study also connects to the literature that tests the relation between short interest and anomalies related to firm fundamentals. Hirshleifer et al (2011) show that short seller trade on stocks with high accrual and mitigate anomaly magnitude. However, their effectiveness is limited by short sale constraints. Dechow et al (2001) show that short sellers exploit anomalies that are related to fundamental ratios (e.g. earnings to price) and they tend to mitigate the magnitude of anomaly. Cao et al (2007 WP) find relatively weak evidence that short interest reduces drift. They also show that the majority of this effect concentrates in stocks that have relatively high availability of share for borrowing. Lasser, Wang and Zhang (2010) find evidence that high level of short interest contributes to initial reaction for positive earnings surprise stocks as short sellers cover their short positions and relatively weak evidence that such action mitigates positive drift. All the studies above rely on short interest level data reported in COMPUSTAT. However, since short interest data is updated monthly, it tend to deliver a coarse measure of short sellers’ activities. Two papers overcome this limitation by using daily short selling data. Zheng (2009 WP) study the relation between short selling and PEAD and find no evidence that short selling affect PEAD. Boehmer and Wu (2012), on the contrary, claim that they find strong evidence that short selling significantly reduces the magnitude of drift.

3. Data and Variables Computation 3.1 Data

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My quarterly earnings announcement data are from COMPUSTAT fundamental quarterly file. I exclude all observations prior 1995 due to inaccuracy of announcement date. I also exclude all firm-quarter observations that have missing values in any of the following: announcement date, earning per share, and total share outstanding. I further exclude observation with report date that is associated with multiple quarter-ends or is more than 180 days away from last quarter-end.2 My short interest data are from COMPUSTAT supplemental short interest file. Short interest is reported once a month prior January 2007 at mid-month. After January 2007, short interest data are reported twice a month at mid-month and month-end respectively. For most of the observations, the report dates are 15th and 30th. If 15th or 30th happens to be weekend or holiday, short interest is reported on the prior trading day. I only use post 2007 data due to better measurement frequency. My daily stock data are from CRSP daily file. I combine it with delisting file to account for cases where stocks are delisted. I only consider common shares (CRSP share code of 10 or 11) and exclude stocks with price less than $5 or a market capitalization less than 5 million dollars. To arrive at the final sample, I first sort all announcements into deciles in each quarter according to the earning surprise distribution in the previous quarter. Next I only keep announcements in the bottom five deciles because prior literature has shown that these announcements on average tend to have negative drift returns (Bernard and Thomas (1989)). Finally, I delete any announcements that have a positive earnings surprise in the bottom 5 deciles3. For more details on merging among different data files, please refer to the appendix. After deleting

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Here is an example for one report date that is associated with multiple quarter-ends. Worlds Inc. issued its quarterly report on March 24th 2008. However, this report is associated with 12 different quarter-ends starting from April 30th 2005 to January 31st 2008. Since I cannot pin down the exact quarter-end, I delete all such observations. 3 Note that an alternative way to rank earning surprise is to first only look at announcements with negative earnings surprise and then form quarterly quintiles (instead bottom 5 deciles). However, this design tends to distort the true earning surprise distribution (since all positive earnings surprise observations are not included in the sample), I did not employ it.

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observations that do not have sufficient data to calculate variables that come in the next section, my final sample covers 28,337 firm-quarter observations with negative earnings surprise from January 2007 to December 2015. 3.2 Key variables and summary statistics I follow Ng et al (2008) and define earnings surprise (𝑈𝐸) as

UE =

Et − Et − 4 MVt −4

In the equation above, E t is the current quarter earnings and Et −4 is the earnings four quarters ago. It is calculated as earnings per share multiplied by common shares outstanding used to calculate earnings per share4. MVt − 4 is the market value of equity four quarters ago. It is calculated as share outstanding multiplied by quarter-end close price. I follow common practice in the PEAD literature and transform the current quarter earnings surprise of each announcement into deciles according to the distribution of earnings surprise in the previous quarter. My main independent variable is change in short interest ratio (henceforth, SIR ). Following Hanson and Sunderam (2014), short interest ratio is the ratio between the total number of shares sold short and the total number of share outstanding. Change in short interest ratio is calculated as the difference between the short interest ratios on the report dates immediately after and before a particular announcement date. For example, Energy West issued its quarterly report on Apr. 4th, 2011. Its short interest ratio on Mar. 31st 2011 was 0.0249%, and that on Apr. 15th, 2011 was 0.0671%. Therefore its change in short interest ratio is calculated as 0.0671% - 0.0249%

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‘Common share outstanding used to calculate earnings per share’ is different from ‘common share outstanding’.

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= 0.0422%. This is the proxy for the arbitrage capital intended to trade PEAD associated with Energy West. My main dependent variable is the 10 day abnormal drift return after the earnings announcement date. It is calculated as the cumulative return in the (+2, +11) window after the announcement date adjusted by Fama-French 3 (FF3) factors. This is done following the next three steps. First, for each announcement, I regress the previous 250 trading day returns up to two days prior to the earnings announcement on the corresponding FF3 factors to estimate the coefficients associated with each factor. Second, I use these estimated coefficients from step one to calculate daily FF3 return for each day in the (+2, +11) window as     FF 3i ,t =  i +  i ,1 Mkti ,t +  i , 2 SMBi ,t +  i ,3 HMLi ,t , for announcement i and day t = 2…11

In the end, for announcement i, the 10 day abnormal drift return is given by 11

11

t =2

t =2

AbDrift i =  (1 + Ri ,t ) −  (1 + FF 3i ,t ) , for announcement i.

where Ri ,t is the announcement i’s return in day t and FF 3i ,t is the Fama-French 3 factor return as calculated in step two. Another important variable is the initial response. It is calculated as the cumulative return in (-1, +1) window around the earning announcement date. To account for risk factors, this variable is also adjusted by FF3 factor return in the same way as before. In particular, abnormal initial response is given by 1

1

t = −1

t = −1

Abresponse i =  (1 + Ri ,t ) −  (1 + FF 3i ,t ) , for announcement i

I also introduce several control variables that have been identified to affect PEAD in prior literature. Mendenhall (2004) has shown that higher idiosyncratic risk serves as limits to arbitrage and 9

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therefore positively predicts magnitude of drift. Following Mendenhall (2004) I define idiosyncratic risk of a particular stock as the variance of the residual from a regression of its monthly returns on those of the S&P 500 estimated over the 48 months ending 1 month prior to the earnings announcement. To account for trading cost, I include the average dollar volume over the -270 to -20 day period prior to the earnings announcement. Hirshleifer, Lim, and Teoh (2009) and Dellavigna and Pollet (2009) both show that stocks with lower investor attention tend to have smaller initial response and larger drift. In particular, announcements on days where there are more announcements coming out and announcements on Friday tend to have larger drifts. Therefore, I include Number , the number of announcements that come out on a particular day, and a dummy variable Friday, an indicator that equals one if the day of the announcement is Friday, as proxies for investor attention. To account for investor sophistication, I follow Hand (1990) and control for the percentage of outstanding shares held by 13f institutions at the end of the previous quarter. Prior literature also shows that PEAD is affect by information asymmetry (Francis et al (2007)). Since information asymmetry is closely related with firm size, I include quarterly percentile of market equity. Finally, Lasser, Wang, and Zhang (2010) and Cao et al (2007 WP) both have shown that the level of short interest ratio is closely related to PEAD, therefore short interest level right before the earning announcement is also included as a control variable. [Insert Table 1 here] Table 1 presents the summary statistics across the bottom 5 earnings surprise deciles. Note that there are unequal numbers of observations in each decile. This happens because I sort earning surprise (using all announcements in each quarter) first and then merge it with short interest data. Many announcement observations are lost during the merging process and this causes unequal deciles. An alternative way that generates equal deciles is to merge the two datasets first and then 10

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conduct sorting. However, this practice distorts the true distribution of earning surprise (since many observations fail to be included in the final sample) which biases rankings of earning surprises. Therefore, I utilize the first method. Overall, variable values are in line with prior literature. Idiosyncratic risk and change in short interest ratio are decreasing from big negative earnings surprise decile (UE decile 1) to small negative earnings surprise decile (UE decile 5). Size, dollar volume, and initial response are increasing from UE decile 1 to UE decile 5. Number of announcements and Friday dummy are somewhat larger in UE decile 1 than in UE decile 5. Institutional holding is somewhat smaller in UE decile 1 than in UE decile 5. [Insert Table 2 here] Table 2 presents the summary statistics across quintiles of change in short interest ratio. In particular, quintile 1 contains announcements that have the largest decline in short interest ratio and quintile 5 contains those that have the largest increase in short interest ratio. Evidence shows that stocks with the largest increase in short interest ratio average more negative initial return. This is potentially consistent with the idea that more arbitrage capital can improves market efficiency and adjust prices faster towards equilibrium. At the same time, this could also be consistent with too much arbitrage capital contributing to overreaction. Another interesting phenomenon is that there is no obvious patterns across change in short interest ratio quintiles in terms of idiosyncratic risk, dollar volume, and number of announcements. Moreover, there is a striking U shape in institutional holding and firm size. That is, the announcements with the largest decrease in short interest ratio and those with the largest increase in short interest ratio both tend to be the firms that have higher institutional holding and larger market equity. This is potentially consistent with the

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fact that institutional holding (and size) is positively correlated with shares available for short selling.5 [Insert Table 3 here] To see how short selling capital interacts with earning surprise, I conduct an independent double sort using the bottom 5 earnings surprise deciles and SIR quintiles. There are some interesting patterns that warrant attention. Panel A shows that, within each earning surprise decile, earning surprise is fairly constant across SIR quintiles. An important implication from this pattern is that if short selling is to affect post earnings announcement drift, the effect is not likely to be driven from its correlation with earnings surprise. Panel B and Panel C show that consistent with prior literature, big negative earnings surprise announcements tend to be small firms with less institutional holding.

4. Test design and empirical results The ultimate goal of this study is to test whether too much arbitrage leads to overreaction. I test this hypothesis in three steps. First, I test whether change in short interest ratio is negatively correlated with initial response holding all else equal. A negative relation means larger increase in short interest ratio leads to more negative initial response, and hence a higher extent of correction. This relationship is crucial to establish at the very beginning since after all, we need to show that short selling capital indeed contribute to the correction of underreaction associated with PEAD. Next I test whether change in short interest ratio is positively correlated with the probability of It might seem a little odd that the announcements in SIR quintile 1 also tend to be firms that are more likely to be held by institutions and larger in size. However, note that in these announcements, SIRs are actually negative which means short sellers are covering their short selling positions. But in order to do so, they must have been able to short in the first place which requires the stocks to be big in size and high in institutional ownership. 5

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overcorrection holding all else equal. That is, I test whether announcements that have larger increase in short interest ratio are more likely to result in positive abnormal drift. I couple this test with a comparison of change in short interest ratio between positive and negative abnormal drift samples and test if change in short interest ratio is significantly higher in the former than in the latter. In the end, I move on to the sample that contain only those stocks with positive abnormal drift and test whether change in short interest ratio is positively correlated with the positive abnormal drift holding all else equal.6 4.1 Initial response and change in short interest ratio [Insert Table 4 here] To test whether change in short interest ratio is negatively correlated with initial return (i.e., announcements with larger increase in short interest ratio are associated with more negative initial response), I first conduct a double sort based on bottom 5 earnings surprise deciles and change in short interest ratio quintiles and test whether announcements with the largest increase in short interest ratio have significantly lower initial return than those with the largest decrease in short interest ratio. Panel A presents the results for abnormal initial response and Panel B for raw initial response. Holding earning surprise constant, stocks with largest increase in short interest ratio, in general, also experience significantly more negative initial return than stocks with the largest decrease in short interest ratio. Next I conduct regression analysis to quantify the influence of change in short interest ratio in initial response with the presence of control variables. For both raw and abnormal initial

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I will explain why focusing on this special sample suits my purpose particularly well and why there is little concern of selection bias in later section.

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response, I find a significantly negative correlation between change in short interest ratio and initial response, though the evidence is stronger for raw response. Table 5 presents the results. [Insert Table 5 here] The sample contains 28,337 announcements with negative earnings surprise in the bottom 5 quarterly earnings surprise deciles from January 2007 to Dec 2015. In panel A, the dependent variable is abnormal initial return and in Panel B, raw initial return. All independent variables are transformed into quarterly deciles (i.e. taking values from 0, 1, up to 9). All standard errors are clustered on firm and calendar quarter. Column (1) is a univariate regression with SIR being the only independent variable. Column (2) adds in quarterly ranking of earning surprise. Column (3) add in control variables including: average dollar volume in the prior 20 days before earning announcement, percentile of market equity in the prior quarter end, number of announcements, Friday dummy, percentage of institutional holding in the prior quarter end, idiosyncratic risk and short interest level. To alleviate concerns that outliers drive the results, I exclude observations with initial response that are three standard deviation below zero. Column (4) shows that my results still holds with slightly stronger significance. To alleviate concerns that the 2008 financial crisis drives the results, I exclude announcements that are released in 2008. Column (5) shows that my results are actually much stronger in years other than 2008. To make sure that my results are not entirely driven by a particular subsample of stocks or a particular period, I further test the results in subsample that includes only announcements with positive drift, subsample that only includes announcements that have an increase in short interest ratio and subsamples that excludes any one of the years between 2007 and 2015. The results are not tabulated here, but in all subsamples, the negative relation between initial response (both raw and abnormal) and change in short interest ratio maintains its significance 14

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4.2 Probability of overreaction and change in short interest ratio [Insert Table 6 here] In this section I test whether announcements with larger change in short interest ratio are more likely to result in overreaction. I first conduct a double sort based on the level of initial response and whether the abnormal drift is positive and compare the average change in short interest ratio between announcements with positive abnormal drift and announcements with negative abnormal drift. The idea is that if a large increase in short interest ratio indeed contributes to overreaction, we should expect to see that announcements with positive abnormal drift have larger increase in short interest ratio than announcements that have negative abnormal drift. Evidence in Table 6 confirms this relation. In each abnormal initial response tercile, announcements with positive abnormal drift have significantly larger increase in short interest ratio than announcements with negative abnormal drift. This is consistent with the hypothesis that too much arbitrage capital causes overreaction and destabilizes stock prices. [Insert Table 7 here] Next I conduct logit regression to test whether change in short interest ratio positively contributes to the probability of having a positive abnormal drift. The dependent variable is Positive. It is a dummy variable that equals 1 if abnormal drift is positive and 0 otherwise. I include the same set of control variables as in Table 5. In addition, abnormal initial return is also included as a control variable. All independent variables except initial return are transformed into quarterly decile rankings. Consistent with the hypothesis that higher level of short selling tends to cause overreaction, marginal effect of change in short interest ratio is both statistically and economically significant. In particular, stocks with the largest increase in short interest ratio ( SIR decile 10) is

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almost 10% more likely to result in overreaction than stocks with the largest decrease in short interest ratio ( SIR decile 1). 4.3 Abnormal drift and change in short interest ratio So far, we have supporting evidence that short selling capital speeds up the price adjustment process and more short selling capital increases the probability of overreaction. Next I turn to quantify the effect of short selling on the magnitude of overreaction. My baseline regression equation takes the form of

AbDrift =  + 1 Abresponse +  2 SIR +  ' Controls + 

(1)

All variables in the equation above are defined the same as before. Control variables include quarterly ranking of earning surprises, average dollar volume in the prior 20 days before earning announcement, percentile of market equity in the prior quarter end, number of announcements, Friday dummy, percentage of institutional holding in the prior quarter end, idiosyncratic risk and level of short interest. I only use announcements that have a positive abnormal drift. 7 This design deviates from common practice in the PEAD literature, in that conventional practice in the PEAD literature does not distinguish announcements with positive drift from those with negative drift and includes all observations in regression. But this is problematic for my purpose. Suppose I have a significant positive estimate of  2 and both negative and positive observations are included in the regression, then we don’t know whether the positive coefficient is identified through a shrinking negative abnormal drift associated with an increasing short interest ratio or through an increasing positive abnormal drift associated with an

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The number of announcements with positive abnormal drift account for 41.6%, 44.2%, 46.2%, 47.8%, and 50.4% from the earnings surprise decile 1 (big negative earnings surprise) to earnings surprise decile 5 (small negative earnings surprise).

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increasing short interest ratio. The reason why we need to distinguish these two cases is that they are likely to represent different mechanisms. In the first case, increasing short interest ratio is likely to represent an efficiency improving mechanism since it mitigates magnitude of negative drift and pushes price to equilibrium more quickly. Whereas in the second case, increasing short interest ratio is more likely to represent overreaction and pushes price further from equilibrium. Because in this study, I am trying to identify whether the second mechanism is at work, I only include observations with positive abnormal drift. I also want to point out that, focusing only on stocks with positive abnormal drift is unlikely to introduce selection bias. First of all, I use a 10 day window to calculate drift. This is essentially a much shorter window compared with 60 day window that is commonly used in the PEAD literature. Therefore, my drift return tend to reflect more of the consequences of arbitrage process and less effect from exogenous events that follow the earning announcements. Second, it does not seem likely that change in short interest ratio should be related to exogenous good news in any systematic way. And even if it does, we should expect an exogenous good news be accompanied by a decrease in short interest ratio, which only biases me against finding the results that I present next. For the argument above, this design can potentially deliver a clearer identification of whether change in short interest ratio contributes to overreaction without raising much selection bias concern. If too much short selling capital indeed contributes to overreaction, one should expect  2 to be positive and significant. Also, since most of the correcting effort is conveyed in initial response (more negative initial response implies more correcting effort and hence more positive abnormal drift), I expect  1 to be negative and significant. [Insert Table 8 here]

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My sample for this test includes 13,192 observations with negative earnings surprise but positive abnormal drift returns from January 2007 to December 2015. As before, all independent variables except abnormal initial return are transformed into quarterly deciles. Evidence in Table 8 strongly confirms my expectation. Column (1) is a univariate regression with change in short interest ratio being the only independent variable. Consistent with the too much arbitrage contributing to overreaction,  2 is highly positive with a t-statistic of 5.60. Column (2) add in abnormal initial response as a second independent variable. Consistent with the idea that higher extent of correction tend to cause overreaction,  1 is highly negative with a t-statistic of -5.87. Note that adding in initial response does not reduce the significance of change in short interest ratio at a material extent. To further make sure that change in short interest ratio derives its explaining power not from its correlation with variables that are previously identified as affecting PEAD, I add in the same set of control variables as before. Evidence in Column (3) shows that change in short interest ratio maintains its significance in the presence of all the control variables. To alleviate the concern that the result is entirely driven by extreme values, I exclude those observations whose abnormal drift is three standard deviations above zero. Column (4) shows that change in short interest ratio still maintains its significance at 1% level after deleting extreme values. To deal with the concern that the results are driven by crisis period, I exclude announcements that are released in 2008. As before, evidence in Column (5) become stronger for years other than 2008. This, coupled with the fact that the relation between initial response and change in short interest ratio is also stronger after excluding 2008 announcements, gives additional support that arbitraging activity indeed affects PEAD. Not reported here, I also conduct same tests in subsamples that exclude one of the nine years between 2007 and 2015. In all subsamples, change in short interest ratio maintains its significance at 1% level. Therefore, my results are not likely to be driven by a particular year.

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It is also interesting to find out whether the efficiency improving mechanism is at work at all. Boehmer and Wu (2012 RFS) conclude that short selling improves efficiency based on estimation from regression that includes observations with both positive and negative abnormal drift. 8 This encounters the problem that I have just described above. Therefore, I next try to distinguish between the two stories by testing to what extent the efficiency improving mechanism contributes to the positive relation. I use the whole sample that includes both positive and negative abnormal drift observations. I introduce a dummy variable, Indicator that equals 1 if an observation has a positive abnormal drift and equals 0 otherwise. I interact it with SIR to capture the effect that come from the efficiency destroying mechanism and keep SIR in my regression to capture the effect that comes from efficiency improving mechanism.9 [Insert Table 9 here] As before, all independent variables except abnormal initial response are transformed into quarterly deciles. Evidence in Table 9 shows that the efficiency improving mechanism hardly contributes to the significance at all. Column (1) takes change in short interest ratio as the only independent variable. It has a positive coefficient with a t-statistic of 4.74, consistent with prior literature. However, as shown in Column (2), once the interaction term of Indicator and SIR is included in the regression, SIR is not significant anymore whereas the interaction term is highly significant with a t-statistics of 6.86. Column (3) shows that same picture holds even after including control variables. A particular severe concern arises from the fact that Indicator is

8

Note that their change of short interest variable is defined as the negation of my change of short interest ratio. In other words, largest value of my change of short interest ratio is the smallest value in theirs. Therefore, the significant negative relation in their paper is equivalent to the positive relation in this paper. 9 An alternative way to do the test is to use the sample that only contains observations that have negative abnormal drift and run the same regression. But then the results could be driven by a systematic difference in those control variables between the positive and negative samples. Therefore, I use the whole sample and introduce the interaction of change in short interest ratio and positive dummy.

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observed ex post and therefore the significant positive coefficient associated with the interaction term can be entirely driven by the fact that all positive return observation have Indicator equals 1 and all negative return observations have Indicator equals 0. To address this issue, I include Indicator as a separate independent variable. Column (4) shows that change in short interest ratio has explaining power beyond those that come from Indicator. To further strengthen my results, I conduct a falsification test. In particular, for each observation in my sample, I replace the value of

SIR by a random draw from the universe of SIR values in the whole sample with replacement. Next I run regression in column (2) (only two independent variables: SIR and SIR *Indicator) and record the t-statistics from the regression. Finally, I repeat the above steps 1,000 times and plot the distribution of the t-statistics as shown in figure 1. [Insert Figure 1 here] It turns out that my t-statistics in the original sample, 6.86, is even larger than the largest value generated from the process above. This provides highly strong evidence that the destabilizing mechanism dominates the stabilizing mechanism in terms of contribution to the positive relation. [Insert Table 10 here] In the end, to get a closer inspection of relation between change in short interest ratio and abnormal drift, I conduct independent double sorts based on bottom 5 earnings surprise deciles and the top and bottom change in short interest ratio quintiles for positive abnormal drift and negative abnormal drift samples separately. In each cell, the first to last row contains the mean value for abnormal drift, change in short interest ratio, and earnings surprise respectively. Within sample difference is the difference for each of the three variables between announcements with largest decrease in short interest ratio and announcements with largest increase in short interest

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ratio within positive or negative abnormal drift sample. All mean values are limits to arbitrage stratified (proxied by idiosyncratic risk; similar results persist using other proxies, not reported). Evidence in table 10 is highly consistent with the regression results. In particular, for the positive abnormal drift sample, the magnitude of positive drift is significantly higher for announcements with largest increase in short interest ratio than for announcements with largest decrease in short interest ratio. This is true for all earning surprise deciles. Further note that this result is not driven by difference in earnings surprise since there is no significant difference between bottom and top change in short interest quintile announcements. However, for the negative abnormal drift sample, no significant difference (decile 4 has a significant difference but with the wrong sign) shows up in abnormal drift for top and bottom change in short interest ratio quintiles. Also note that there is no obvious difference in terms of earnings surprise between the positive and negative samples. Overall, there are two key takeaways from my evidence. First, shorting selling capital does seem to contribute to overreaction. Second, contrary to claims of prior literature, the previously identified relation between PEAD and short selling capital hardly represent efficiency improving mechanism.

5. Robustness I test the robustness of my results by varying the length of the window for calculating returns. Zheng (2009 WP) shows that there is a significant increase in short selling at the earnings announcement day and that significance last until day +3. Therefore, I redefine my response window as (-1, +2), (-1, +3) and my drift window as (+3, +12) and (+4, +13) to alleviate the concern that the results are driven by a particular length of window for return calculation. [Insert Table 11 here] 21

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Panel A is for the combination of (-1, +2) and (+3, +12) windows and Panel B is for (-1, +3) and (+4, +13) windows. Column (1) tests the relation between abnormal initial response and change in short interest ratio. Column (2) tests the relation between the probability of overreaction with change in short interest ratio. Column (3) directly tests the relation between overreaction and change in short interest ratio. Column (4) tests whether the significant positive coefficient of change in short interest ratio in Column (3) is driven by observations with positive abnormal drift. All regressions use the same control variables as those in the main tests. In all regressions and in both combinations of window length, the results hold with similar significance as those in my main tests. Therefore, my results are robust to alternative definitions of window length.

6. Identification 6.1 Interaction of abnormal response and change in short interest ratio Short sellers are not the only agent in the market that sell stocks when negative earnings announcements come out. Other agents (e.g. people that long the stock) also contribute to initial response by selling their original position. Therefore, to better identify that short selling indeed contributes to correction and can potentially lead to overreaction, I introduce an interaction term of abnormal initial response and change in short interest ratio into regression equation. Specifically, my regression equation is now

AbDrift =  + 1 Abresponse +  2 Abresponse * SIR +  'Controls + 

(2)

If short selling is indeed at work, we should expect  2 to be negative and significant. [Insert Table 12 here] All variables except abnormal initial response are transformed into quarterly diciles. As expected, evidence in Table 12 confirms this negative relation. Column (1) presents the results 22

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without controls and Column (2) add in control variables. In both cases, the interaction term maintains its significance at 1% level. In other words, short selling contributes to overreaction in addition to the selling from other agents. 6.2 Effect of top quintile of change in short interest ratio Evidence in previous sections have shown that increase in short interest ratio contributes to overreaction. If this is really the case then it is reasonable to expect larger increase in short interest ratio to have a more significant effect. Or we should even expect the majority of the previously identified effect should come from announcements whose change in short interest ratio is among the highest level. Therefore I introduce a dummy variables, Top_short that equals 1 if the announcement has a change in short interest ratio that is in the top quintile in a certain quarter and 0 otherwise. Next, I interact Top_short with SIR and my regression equation is now AbDrift =  + 1 SIR +  2 SIR * Top _ short +  3 Abresponse +  ' Controls + 

(3)

If majority of the effect come from announcements whose SIR are among the highest level (top quarterly quintile), we should expect  2 to be significantly positive and  1 to be insignificantly positive or even negative. For the same reason as discussed in 6.1, I also interact Top_short with the interaction of Abresponse* SIR and run the following regression AbDrift =  + 1 Abresponse +  2 Abresponse * SIR +  3 Abresponse * SIR * Top _ short +  ' Controls + 

If the contribution from short selling to Abresponse truly comes from the top quintile

SIR observations, we should expect  3 to be significantly negative and  2 to be insignificantly

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negative or even positive. As before, all independent variables except abnormal initial response are transformed into quarterly deciles. [Insert Table 13 here] Results in Table 13 shows that observations whose change in short interest ratio in the top quintile indeed dominate. Column (1) shows that  2 is significantly positive with a t statistic of 2.88 and at the meantime,  1 is not significant any more. Therefore the previously identified positive relation between abnormal drift and change in short interest ratio comes entirely from announcements with SIR in top quintile. Similar results show up in the second regression.  3 is negative and significant with a t-statistics of -2.09 whereas  2 is not significant any more. Therefore the contribution to overreaction from short selling beyond other selling agents come entirely from announcements whose change in short interest ratio is at the highest level.

7. Conclusion In this paper I try to test whether too much arbitrage capital can cause overreaction in the process of correcting underreaction. I use negative earnings surprises that subsequently experience positive drift to test whether the extent of positive drift is related to changes in short interest ratio when earnings are announced I contribute to the literature by finding robust evidence that too much arbitrage capital indeed contributes to overreaction. Specifically, announcements with positive abnormal drift have significantly more arbitrage capital than those that have negative abnormal drift. Moreover, within the subsample that includes only announcements with positive abnormal drift, change in short interest ratio contributes to overreaction significantly. This significant contribution is not due to

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its correlation with other market agents’ selling action or other variables that have been previously identified as affecting PEAD magnitude and this effect comes almost entirely from the announcements whose change in short interest is among the highest level. This paper also connects to prior studies on short selling’s effect on market efficiency. Contrary to the interpretation of prior studies, my evidence shows that the very relation between short selling and abnormal drift based on which prior studies interpret as efficiency improving, is actually dominated by efficiency destroying mechanism. The efficiency improving effect, which is concluded by prior studies, hardly contributes to the identified relation. An important point raised by this study for future research is that when we conduct regression analysis, we should carefully distinguish observations that are likely to represent opposing mechanisms when they both contribute to the significance of coefficient in the same direction. We cannot identify which mechanism is mainly contributing to the regression coefficient if the regression involves both types of observations.

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Reference 1.

Baker, Malcolm, and Jeffrey Wurgler. "Investor Sentiment and the Cross‐Section of Stock Returns." The Journal of Finance 61.4 (2006): 1645-1680.

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Cao, Bing, et al. "Bears and Numbers: Investigating How Short Sellers Exploit and Affect EarningsBased Pricing Anomalies." 2007 WP.

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Christophe, Stephen E., Michael G. Ferri, and James J. Angel. "Short‐Selling Prior to Earnings Announcements." The Journal of Finance 59.4 (2004): 1845-1876.

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Coval, Joshua, and Erik Stafford. "Asset Fire Sales (and Purchases) in Equity Markets." Journal of Financial Economics 86.2 (2007): 479-512.

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Dechow, Patricia M., et al. "Short-Sellers, Fundamental Analysis, and Stock Returns." Journal of Financial Economics 61.1 (2001): 77-106.

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10. DellaVigna, Stefano, and Joshua M. Pollet. "Investor Inattention and Friday Earnings Announcements." The Journal of Finance 64.2 (2009): 709-749. 11. De Long, J. Bradford, et al. "Noise Trader Risk in Financial Markets." Journal of political Economy (1990): 703-738. 12. Fama, Eugene F., and Kenneth R. French. "The Cross‐Section of Expected Stock Returns." the Journal of Finance 47.2 (1992): 427-465. 13. Foster, George, Chris Olsen, and Terry Shevlin. "Earnings Releases, Anomalies, and the Behavior of Security Returns." Accounting Review (1984): 574-603. 14. Hanson, Samuel G., and Adi Sunderam. "The Growth and Limits of Arbitrage: Evidence from Short Interest." Review of Financial Studies 27.4 (2014): 1238-1286. 15. Hirshleifer, David, Sonya Seongyeon Lim, and Siew Hong Teoh. "Driven to Distraction: Extraneous Events and Underreaction to Earnings News." The Journal of Finance 64.5 (2009): 2289-2325. 16. Hirshleifer, David, Siew Hong Teoh, and Jeff Jiewei Yu. "Short Arbitrage, Return Asymmetry, and the Accrual Anomaly." Review of Financial Studies24.7 (2011): 2429-2461. 17. Jegadeesh, N., and J. Livnat. 2006. Post-Earnings-Announcement Drift: the Role of Revenue

Surprises. Financial Analysts Journal 62 (2): 22–34. 18. Livnat, J., and R. R. Mendenhall. 2006. Comparing the Post-Earnings Announcement Drift for

Surprises Calculated from Analyst and Time Series Forecasts. Journal of Accounting Research 44 (1): 177–205. 19. Lou, Dong, and Christopher Polk. 2013. Comomentum: Inferring arbitrage activity from return

correlations. Paul Woolley Centre for the Study of Capital Market Dysfunctionality. 20. Mendenhall, Richard R. "Arbitrage Risk and Post‐Earnings‐Announcement Drift." The Journal of Business 77.4 (2004): 875-894. 21. Milian, Jonathan A. "Unsophisticated Arbitrageurs and Market Efficiency: Overreacting to a History of Underreaction?" Journal of Accounting Research 53.1 (2015): 175-220.

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22. Ng, Jeffrey, Tjomme O. Rusticus, and Rodrigo S. Verdi. "Implications of Transaction Costs for the Post–Earnings Announcement Drift." Journal of Accounting Research 46.3 (2008): 661-696. 23. Shleifer, Andrei, and Robert W. Vishny. "The Limits of Arbitrage." The Journal of Finance 52.1 (1997): 35-55. 24. Sias, Richard, H. J. Turtle, and Blerina Zykaj. "Hedge Fund Crowds and Mispricing." Management Science 62.3 (2015): 764-784. 25. Stein, Jeremy C. "Presidential Address: Sophisticated Investors and Market Efficiency." The Journal of Finance 64.4 (2009): 1517-1548 26. Wurgler, Jeffrey, and Ekaterina Zhuravskaya. "Does Arbitrage Flatten Demand Curves for Stocks?" The Journal of Business 75.4 (2002): 583-608. 27. Lin, Zheng. “Short Sale and Post Earnings Announcement Drift” 2009, Working Paper.

Appendix Starting out in short interest data, I first merge in ‘permno’, ‘share code’, and ‘share outstanding’ from CRSP daily file and delete observations whose ‘report date’ (datadate) is before 2007, whose ‘permno’ is missing, whose ‘share code’ is not 10 or 11 or whose ‘share outstanding’ is missing. Following Hanson and Sunderam (2014), I define short interest ratio to be ‘short interest’ (shortint) divided by ‘share outstanding’ (shrout). Note that I need to calculate change in short interest ratio before and after a particular announcement. Therefore I need to create date pairs so that for any announcement that occurs in between these date pair, I can use the data on the pair of dates to calculate the change in short interest ratio. To do this, for each report date, I merge in both the ‘short interest ratio’ and the ‘report date’ (datadate) of the next report date. For example, my original dataset have observations that look like: 28

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Permno

Report date

SIR

001010

2007/03/30

0.001

After the merge, my new dataset have observations that look like: Permno

Report date

SIR

Next report date

Next SIR

001010

2007/03/30

0.001

2007/04/15

0.002

This is what I call data pairs since each observation has a pair of data. I can calculate my main independent variable SIR as SIR = Next SIR – SIR. So far, my paired short interest ratio dataset have 843,890 observation. Now I move to the quarterly announcement data. First of all, I need to clean up unqualified observations. I delete all announcement whose announcement date (rdq) is before 2007. I also delete observations that have missing values in any of the following: announcement date (rdq), earning per share (epsfxq), common share used to calculate earnings per share (cshprq), shares outstanding (cshoq), and quarter-end close price (prccq). In the end, I delete announcements that are associated with multiple quarter-ends or are more than 180 day away from last quarter-end. Next I turn to calculation of earnings surprise. For each announcement I require it to have nonmissing value in earning per share (epsfxq), common share used to calculate earnings per share (cshprq), shares outstanding (cshoq), and quarter-end close price (prccq) in the current and four quarters ago (Observations that do not have sufficient data are deleted). I follow NG et al (2008) and define earnings surprise as:

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UE =

where E t is the current quarter earnings and

Et − Et − 4 MVt −4

Et − 4

is the earnings four quarters ago. It is calculated

as earnings per share multiplied by common shares outstanding used to calculate earnings per share10. MVt − 4 is the market value of equity four quarters ago. Finally, I come to define the ranking of earnings surprise. This is done following the next few steps. First, I define January, February, and March as quarter 1, April, May and June as quarter 2, July, August, and September as quarter 3, and October, November and December as quarter 4. Next, within each quarter, I group all observations into deciles according to their earning surprise in that quarter and mark down the cutoff between the 10 decile bins. Lastly, for each quarter, I sort all announcements into deciles according to the cutoffs in the previous quarter and assign the ranking to each announcement according to which bin it stands in. I delete all observations that do not have sufficient data to do the above steps. In the end, following Jegadeesh and Livnat (2006) and Livnat and Mandenhall (2006), I truncated the sample at the 0.5% and 99.5%. This process leaves me with 546,322 firm quarter observations. The final step involves merging the two datasets that I created above (the short interest date pairs and the earnings announcements dataset). For ease of instruction, I call the earlier date in the date pair ‘early date’ and the latter date ‘latter date’. The problematic situation is when the ‘latter date’ is a Monday and when the ‘earlier date’ is a Friday. In the first case, the two days immediately prior to the ‘latter date’ are Saturday and Sunday and in the second case the two days immediately after the ‘early date’ are Saturday and Sunday. Therefore, in order to make sure the reported short

10

‘Common share outstanding used to calculate earnings per share’ is different from ‘common share outstanding’.

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interest data actually reflect short sellers’ action I need to give at least one trading day before and after the report date. As a result, for each short interest date pair, I only merge in the announcement that is no earlier than 3 days after the ‘early date’ and no later than 3 days before the ‘latter date’. This process leaves me with 89,390 observations. To make sure that my sample on average has a negative drift return, I delete observations that are in the top 5 deciles and this leaves me with 40,792 observations. Next to make sure my sample includes only announcements with negative earnings surprises, I further delete any observations that have a positive earnings surprise and this further shrink my sample size to 38,121 observations. In the end, I delete firms whose price is less than $5 or whose market capitalization is less than 5 million dollars and my final sample contains 28,733 observations.

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Table 1: Summary statistics across bottom 5 earnings surprise deciles UE decile 1 UE decile 5 (Big (Small negative UE decile 2 UE decile 3 UE decile 4 negative earnings N=5212 N=7392 N=8975 earnings surprise) surprise) N=2469 N=4314

Idio_risk Volume Rank_Size Number Friday Institution ∆𝑆𝐼𝑅

Response AbResponse

0.0328 35 million 0.5246 232 0.10 0.6327 0.1272% -2.9765% -2.8383%

0.02745 31 million 0.5371 239 0.09 0.6325 0.0812% -2.1818% -2.2051%

0.0242 35 million 0.5704 233 0.09 0.6440 0.0209% -1.5053% -1.4165%

0.0213 44 million 0.6176 227 0.08 0.6457 0.0027% -0.8949% -0.9031%

0.0229 53 million 0.6591 224 0.08 0.6671 -0.0150% -0.3431% -0.3325%

The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. The sample only includes common shares (CRSP share code of 10 or 11). Stocks with price less than $5 or a market cap less than 5 mil are also deleted. Observations are truncated at 0.5 and 99.5 earnings surprise percentile. Note that I have unequal numbers of observations in each decile. This happens because I sort earning surprise (using all announcements in each quarter) first and then merge it with short interest data. Many announcement observations are lost during the merging process and this causes unequal deciles. I follow Ng et al (2008) and define unexpected earnings (UE) as UE =

Et − Et − 4 . In this equation, Et is the current MVt − 4

quarter earnings and Et − 4 is the earnings four quarters ago. It is calculated as epsfxq*cshprq, where epsfxq is Earnings Per Share (Diluted) - Excluding Extraordinary items, and cshprq is Common Shares Used to Calculate Earnings Per Share. MVt − 4 is the market value of equity four quarters ago. It is calculated as cshoq*prccq, where cshoq is share outstanding and prccq is the quarter end close price. Idio_risk is the residual variance from a regression of its returns on those of the S&P 500 estimated over the 48 months ending 1 month prior to the earnings announcement. Size is the market equity at the quarter end. It is calculated as quarter end stock price multiplied by quarter end share outstanding. Rank_Size is the quarterly percentile. Number is the number of announcement on a particular day. Friday is a dummy variable that indicates whether the day of the announcement is a Friday. Institution is the percentage of share that is held by 13f institutions at the prior quarter-end. SIR is the difference between short interest ratios on the report dates immediate before and after the announcement date. Response is the cumulative return from day -1 to day 1 around the earnings announcement date.

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Table 2: Summary statistics across ∆ short interest ratio quintiles Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 N=5644 N=6487 N=5077 N=5399 N=5730

Idio_risk Volume Rank_Size Number Friday Institution ∆𝑆𝐼𝑅

Response AbResponse

0.0248 42 million 0.6595 231 0.06 0.7564 -0.9375% -1.0467% -1.1239%

0.0226 43 million 0.5605 227 0.09 0.5924 -0.1238% -1.3322% -1.2505%

0.0248 37 million 0.4625 227 0.12 0.4752 -0.0088% -0.9426 % -1.0341%

0.0238 36 million 0.5538 231 0.10 0.5863 0.1404% -1.1269% -1.0156%

0.0261 39 million 0.6542 235 0.07 0.7412 1.0003% -2.2271% -2.0580%

The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. The sample only includes common shares (CRSP share code of 10 or 11). Stocks with price less than $5 or a market cap less than 5 mil are also deleted. Observations are truncated at 0.5 and 99.5 UE percentile. Reason why there are unequal numbers of observations in each quintile is that I form quintile first and then delete observations that have negative earning surprises. I argue that sorting first and then delete observations is preferred because any exclusion of observations will distort the true distribution of either earnings surprise or SIR . I follow Ng et al (2008) and define unexpected earnings (UE) as UE =

Et − Et − 4 In this MVt − 4

equation, 𝐸𝑡 is the current quarter earnings and 𝐸𝑡−4 is the earnings four quarters ago. It is calculated as epsfxq*cshprq, where epsfxq is Earnings Per Share (Diluted) - Excluding Extraordinary items, and cshprq is Common Shares Used to Calculate Earnings Per Share. MVt − 4 is the market value of equity four quarters ago. It is calculated as cshoq*prccq, where cshoq is share outstanding and prccq is the quarter end close price. Idio_risk is the residual variance from a regression of its returns on those of the S&P 500 estimated over the 48 months ending 1 month prior to the earnings announcement. Size is the market equity at the quarter end. It is calculated as quarter end stock price multiplied by quarter end share outstanding. Rank_Size is the quarterly percentile. Number is the number of announcement on a particular day. Friday is a dummy variable that indicates whether the day of the announcement is a Friday. Institution is the percentage of share that is held by 13f institutions at the prior quarterend SIR is the difference between short interest ratios on the report dates immediate before and after the announcement date. Response is the cumulative return from day -1 to day 1 around the earnings announcement date.

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Table 3: Summary statistics based on double sort of UE and ∆𝑺𝑰𝑹 Quintile 1 Quintile 5 (Small (Big change in change in Quintile 2 Quintile 3 Quintile 4 short short ∆𝑺𝑰𝑹 ∆𝑺𝑰𝑹 ∆𝑺𝑰𝑹 interest interest ratio) ratio) ∆𝑺𝑰𝑹 ∆𝑺𝑰𝑹 Panel A Earnings Surprise UE decile 1(Big negative) UE decile 2 UE decile 3 UE decile 4 UE decile 5(Smallnegative)

UE decile 1(Big negative) UE decile 2 UE decile 3 UE decile 4 UE decile 5(Smallnegative)

-0.1345 -0.0276 -0.0101 -0.0037 -0.0016

-0.1357 -0.1327 -0.0270 -0.0280 -0.0097 -0.0103 -0.0033 -0.0038 -0.0016 -0.0019 Panel B 𝑹𝒂𝒏𝒌_𝑺𝒊𝒛𝒆

57% 49% 43% 61% 50% 43% 65% 54% 47% 69% 59% 52% 72% 64% 60% Panel C Institutional holding

-0.1283 -0.0278 -0.0101 -0.0037 -0.0018

-0.1402 -0.0281 -0.0102 -0.0038 -0.0017

50% 51% 54% 61% 62%

59% 61% 65% 68% 73%

UE decile 1(Big negative) 72% 58% 48% 53% 73% UE decile 2 73% 59% 47% 57% 72% UE decile 3 76% 59% 47% 59% 74% UE decile 4 76% 58% 48% 61% 75% UE decile 5(Smallnegative) 79% 62% 50% 59% 77% All three tables are based on independent sorts on bottom 5 deciles of earnings surprise and quintiles of SIR . The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. Earnings surprise, Rank_Size, and institutional holding are calculated the same way as before. Quintile 1 of SIR represents the smallest in SIR and quintile 5 represents the largest change in SIR . Earnings surprise decile 1 represents largest negative earnings surprise decile in a quarter. Earnings surprise decile 5 represents smallest negative earnings surprise decile in a quarter.

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Table 4: Double sort of UE and ∆SIR Quintile 1 (Small change in short interest ratio) ∆𝑺𝑰𝑹

Quintile 2 ∆𝑺𝑰𝑹

Quintile 3 ∆𝑺𝑰𝑹

Quintile 4 ∆𝑺𝑰𝑹

Quintile 5 (Big change in short interest ratio) ∆𝑺𝑰𝑹

Difference

Panel A Abnormal initial response UE decile 1 (Big negative)

-0.02391

-0.02490

-0.02708

-0.02277

-0.03778

UE decile 2

-0.02391

-0.02161

-0.01994

-0.01619

-0.02575

UE decile 3

-0.01084

-0.01457

-0.00963

-0.00110

-0.02205

UE decile 4

-0.00694

-0.00791

-0.00542

-0.00820

-0.01579

UE decile 5 (Small negative)

-0.00410

-0.00297

-0.00246

-0.00013

-0.00632

-0.01387** (t = -1.96) -0.00184 (t = -0.47) -0.01122*** (t = -3.23) -0.00885*** (t = -2.90) -0.00212 (t = -0.50)

Panel B Initial response UE decile 1 (Big negative)

-0.02385

-0.02588

-0.02565

-0.02371

-0.04204

UE decile 2

-0.02117

-0.02079

-0.01928

-0.01707

-0.02745

UE decile 3

-0.01097

-0.01606

-0.00884

-0.01330

-0.02302

UE decile 4

-0.00547

-0.00845

-0.00419

-0.00914

-0.01623

-0.01819** (t = -2.39) -0.00628 (t = -1.52) -0.01205*** (t = -3.27) -0.01076*** (t = -3.40) -0.01038** (t = -2.34)

UE decile 5 0.00042 -0.00491 -0.00197 0.00003 -0.00996 (Small negative) This table presents the information of initial response around the earnings announcement dates. The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. Response is the cumulative return in (-1, +1) window around the earnings announcement date. AbResponse is Response adjusted by Fama-French 3 factor returns. . *, **. *** means a significance at 10%, 5% and 1% level.

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VARIABLES

Table 5: Regression of initial response on ∆SIR Column Column Column Column (1) (2) (3) (4) Panel A Abnormal initial response

UE ∆𝑆𝐼𝑅

-1.609*** (-4.20)

Controls N Adj R-Square

No 28,337 0.3%

6.189*** (13.31) -1.421*** (-3.73)

No Yes 28,337 28,337 0.8% 1.0% Panel B Initial response

∆𝑆𝐼𝑅

-2.304*** (-5.71)

6.356*** (12.92) -2.112*** (-5.25)

Controls N Adj R-Square

No 28,337 0.1%

No 28,337 0.8%

UE

5.351*** (10.87) -1.404*** (-3.68)

Column (5)

4.655*** (10.39) -1.538*** (-4.40)

5.367*** (10.66) -1.759*** (-4.49)

Yes 28,004 1.5%

Yes 24,378 1.1%

5.572*** (10.74) -2.124*** (-5.28)

4.883*** (10.33) -2.297*** (-6.23)

5.697*** (10.87) -2.590*** (-6.34)

Yes 28,337 0.9%

Yes 28,004 0.9%

Yes 24,378 1.3%

This table presents results of regression of initial response on SIR . The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. Panel A takes abnormal initial response as the dependent variable and Panel B uses raw initial response. All independent variables are transformed into quarterly deciles. In both panels, Column (1) is a univariate regression with SIR being the only independent variable; Column (2) adds in rank of earning surprise measured using the distribution of earning surprise in the previous quarter; Column (3) add in control variables including: average dollar volume in the prior 20 days before earning announcement, market equity in the prior quarter end, number of announcements, dummy variable indicating Friday, percentage of institutional holding in the prior quarter, idiosyncratic risk that is the residual variance from a regression of its returns on those of the S&P 500 estimated over the 48 months ending 1 month prior to the earnings announcement and short interest level; Column (4) excludes observations that have immediate initial response that are three standard deviation lower than 0; Column (5) exclude observations that are in the crisis period, i.e. excluding announcements that are released in year 2008. Overall, the evidence supports a strong negative relation between immediate initial response and SIR . *, **. *** means a significance at 10%, 5% and 1% level. All estimates are multiplied by 1000.

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Table 6 average ∆𝑺𝑰𝑹 in double sorts of abnormal initial response and abnormal drift Positive Abnormal Negative Abnormal Difference Drift Drift Small AbResponse (Top Tercile)

0.354

-0.09

0.445** (1.99)

Medium AbResponse (Middle Tercile)

0.132

-0.160

0.293* (1.83)

Big AbResponse (Bottom Tercile)

1.118

0.542

0.576** (2.34)

This table presents the mean value of SIR for announcements with positive and negative abnormal drift condition on abnormal initial response. The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. Abnormal drift is defined as the cumulative return in (+2, +11) window adjusted by Fama-French 3 factor. Abnormal initial response is defined as the cumulative return in (-1, +1) window around announcement date adjusted by Fama-French 3 factor. All reported figures are multiplied by 1000. *, **. *** means a significance at 10%, 5% and 1% level.

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∆𝑆𝐼𝑅 Controls N

Table 7 Logit Regression Coefficient estimation 0.0044*** (p-value < 0.0001)

Marginal Effect 0.0107***

Yes 28,337

This table presents the results from logit regression of Positive on SIR and other control variables. The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. Positive is a dummy variable that equals 1 if abnormal drift return is positive and 0 otherwise. Control variables include quarterly earnings surprise rankings, abnormal initial response, average dollar volume in the prior 20 days before earning announcement, market equity in the prior quarter end, number of announcements, dummy variable indicating Friday, percentage of institutional holding in the prior quarter, idiosyncratic risk, and level of short interest. All variables except abnormal initial response are transformed into quarterly deciles. Coefficient estimation is the estimated coefficient associated with each independent variable. Marginal effect is the average marginal effect calculated by taking the average of the estimated marginal effect of each observation. *, **, and *** signify a significance at 10%, 5% and 1% level.

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VARIABLES

Table 8: Regression of abnormal drift on ∆SIR Column Column Column Column (1) (2) (3) (4)

∆𝑆𝐼𝑅

2.179*** (5.60)

-59.01*** (-5.87) 2.055*** (5.31)

Controls N Adj R-Square

No 13,192 0.2%

No 13,192 0.8%

AbResponse

Column (5)

-49.33*** (-5.15) 1.722*** (4.63)

-20.18*** (-3.64) 1.150*** (4.40)

-41.33*** (-3.92) 1.888*** (4.91)

Yes 13,192 6.7%

Yes 12,859 7.2%

Yes 11,421 7.4%

This table presents results of regression of abnormal drift on SIR . The sample covers 13,192 announcements with negative earnings surprise but positive abnormal drift from Jan. 2007 to Dec. 2015. Column (1) is a univariate regression with SIR being the only independent variable; Column (2) adds in abnormal initial response as defined before; Column (3) add in control variables including: quarterly ranking of earning surprise, average dollar volume in the prior 20 days before earning announcement, percentile of market equity in the prior quarter end, number of announcements, dummy variable indicating Friday, percentage of institutional holding in the prior quarter, idiosyncratic risk and level of short interest; Column (4) exclude observations that have abnormal drift three standard deviation above 0; Column (5) exclude observations that are in the crisis period, i.e. excluding announcements that are released in year 2008. Overall, the evidence supports a strong positive relation between abnormal drift and SIR . *, **. *** means a significance at 10%, 5% and 1% level. All estimates are multiplied by 1000.

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Table 9 Regression of abnormal drift on ∆𝑺𝑰𝑹 and Indicator Column Column Column (1) (2) (3) 23.4*** (4.74)

∆𝑆𝐼𝑅 ∆𝑆𝐼𝑅*Indicator

-0.834 (-1.23) 38.61*** (6.86)

-0.420 (-0.62) 38.35*** (6.73)

Column (4) -1.038*** (-2.93) 3.421*** (6.45) 108.98*** (87.37)

Indicator N Controls Adj-R square

28,337 No 0.1%

28,337 No 0.2%

28,337 Yes 1.2%

28,337 Yes 4.6%

This table presents the result of the regression of abnormal drift on SIR and the interaction term of SIR and Indicator. The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. Indicator is a dummy variable that equals 1 if the announcements have positive abnormal drift and 0 otherwise. Column (1) takes ∆𝑆𝐼𝑅 as the only independent variable. Column (2) includes the interaction term of SIR and Indicator. Column (3) include same set of control variables as in previous regression plus the abnormal initial response. All independent variables are transformed into quarterly decciles. Overall, evidence shows that the significant positive relation between abnormal drift and SIR is almost entirely driven by abnormal positive drift observations. All estimates are multiplied by 1000.

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Table 10 Comparison of drift,  SIR, and UE Positive abnormal drift Negative abnormal drift Largest Largest Largest Largest Within Within decrease increase decrease increase Sample Sample Difference Difference 𝑺𝑰𝑹 𝑺𝑰𝑹 𝑺𝑰𝑹 𝑺𝑰𝑹 UE decile 1 Drift

0.070 -0.012 -0.135

0.093 0.016 -0.140

0.023 (2.76) 0.028 (15.8) -0.005 (-0.53)

-0.094 -0.011 -0.134

-0.092 0.013 -0.140

0.001 (0.21) 0.024 (25.5) -0.006 (-0.63)

UE decile 2

0.067 -0.010 -0.028

0.077 0.012 -0.028

0.009 (1.93) 0.022 (27.6) 0.001 (0.75)

-0.072 -0.010 -0.027

-0.078 0.012 -0.029

-0.006 (-1.51) 0.023 (30.9) 0.002 (-2.13)

UE decile 3

0.060 -0.010 -0.010

0.066 0.011 -0.010

0.007 (1.80) 0.020 (35.8) 0.000 (-0.47)

-0.063 -0.010 -0.010

-0.064 0.010 -0.010

-0.000 (-0.04) 0.020 (35.2) 0.000 (-0.16)

UE decile 4

0.049 -0.009 -0.004

0.060 0.010 -0.004

0.011 (3.86) 0.019 (37.6) 0.000 (-0.41)

-0.050 -0.010 -0.004

-0.061 0.011 -0.004

0.011 (-3.94) 0.020 (31.2) -0.000 (-0.67)

UE decile 5

0.050 -0.009 -0.002

0.062 0.010 -0.002

0.012 (3.10) 0.019 (27.9) 0.000 (-1.08)

-0.057 -0.010 -0.002

-0.056 0.011 -0.002

0.001 (0.15) 0.021 (27.0) 0.000 (-1.28)

 SIR

UE

This table presents the mean values for abnormal drift, SIR, and earning surprise based on double sort of bottom 5 earnings surprise deciles and the bottom and top SIR quintiles. It is presented for positive abnormal drift and negative abnormal drift separately. The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. Abnormal drift, SIR, and earning surprise are all defined the same as before.

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VARIABLES ∆𝑆𝐼𝑅

Table 11 Robustness tests Panel A for (-1, +2) and (+3, +12) window Column Column Column (1) (2) (3) -1.55*** 7.06*** 2.36*** (-2.77) (p-value<.0001) (5.52)

Indicator*∆𝑆𝐼𝑅 Controls N Adj R-Square ∆𝑆𝐼𝑅

Yes Yes Yes 28,337 28,337 28,337 1.0% 1.3% Panel B for (-1, +3) and (+4, +13) window -1.14** 3.10*** 1.85*** (-1.95) (p-value=.0084) (4.18)

Indicator*∆𝑆𝐼𝑅 Controls N Adj R-Square

Yes 28,337 1.0%

Yes 28,337

Yes 28,337 1.2%

Column (4) -0.056 (-0.89) 61.2*** (6.83) Yes 28,337 1.5% -0.109* (-1.82) 64.2*** (7.26) Yes 28,337 1.3%

This table presents regression results for robustness test. Panel A is for the combination of (-1, +2) and (+3, +12) windows. Panel B is for the combination of (-1, +3) and (+4, +13) windows. The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. In column (1) is the result of OLS that regresses abnormal initial response on change of interest ratio. Column (2) presents the results for logit regression where the dependent variable is a dummy variable that equals 1 of the observation has a positive abnormal drift and 0 otherwise and the independent variables are change in short interest ratio and the same set of controls as before. Column (3) presents the results for OLS that regresses abnormal drift on change in short interest ratio and column (4) includes the interaction term of indicator and change in short interest ratio. In all regressions, control variables include, quarterly ranking of earning surprise, abnormal initial response (only for column 2, 3 and 4), average dollar volume in the prior 20 days before earning announcement, percentile of market equity in the prior quarter end, number of announcements, dummy variable indicating Friday, percentage of institutional holding in the prior quarter, and idiosyncratic risk.

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Table 12: Regression of abnormal drift on ∆SIR and Response * ∆SIR Column Column VARIABLES (1) (2) AbResponse

-0.020*** (-1.49)

-0.018 (-1.44)

AbResponse*∆𝑆𝐼𝑅

-0.019*** (-3.09)

-0.016*** (-2.62)

Controls N Adj R-Square

No 13,192 0.7%

Yes 13,192 6.7%

This table presents the results of the regression of abnormal drift on initial response and the interaction term of response and change in short interest ratio. The sample covers 28,733 announcements with negative earnings surprise in the bottom 5 quarterly deciles of earnings surprise from Jan. 2007 to Dec. 2015. Column (1) conduct the test without control variables and Column (2) includes the same set of control variables as before. Overall, evidence shows that SIR contributes to initial response beyond the contribution from other agents in the market.

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VARIABLES

Table 13: Testing top quintile ∆SIR effect Column (1)

AbResponse ∆𝑆𝐼𝑅 Top_short*∆𝑆𝐼𝑅

-49.24*** (-5.16) 0.582 (1.25) 1.425*** (2.88)

-30.83*** (-2.38) 1.465*** (3.95)

0.036 (0.01) -1.605** (-2.09)

AbResponse*∆𝑆𝐼𝑅 Top_short *AbResponse*∆𝑆𝐼𝑅 Controls N Adj R-Square

Column (2)

Yes 13,192 7.4%

Yes 13,192 6.3%

This table presents the results of regressions that test the effect come from observations in the top quintile of SIR . Top_short is a dummy variable that equals 1 if the observation have a SIR that is in the top quarterly quintile and 0 otherwise. Independent variables in column (1) includes abnormal initial response, SIR , the interaction term of SIR and Top_short and same set of control variables as before. Independent variables in column (2) includes abnormal initial response, SIR , the interaction term of SIR and initial response, the triple interaction of SIR , initial response, and Top_short and the same set of control variables as before. Overall, the evidence shows that the previously identified relation entirely comes from top quintile SIR observations. All estimates are multiplied by 1000.

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Figure 2.

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