SHORT SELLERS’ TRADING ON ANOMALIES Byoung-Hyoun Hwang and Baixiao Liu1 This Draft: November 2014 We document and discuss cues that drive arbitrage activity. We focus on arbitrageurs specializing in the shorting of seemingly overpriced securities. Contrary to popular accounts that the convexity in fee structure utilized in the hedge fund industry encourages managers to speculate and take on too much risk, our evidence suggests that short arbitrageurs are non-speculative and prefer strategies with low risk, high returns and low correlations with other strategies. Correspondingly, we present evidence that short arbitrageurs act in an informedand in a market-stabilizing manner JEL Classification: G11, G12, G14, M41. Keywords: Arbitrageurs, Short Sellers, Incentive Effects of Contracts, Market Efficiency. 1 Hwang is with the Dyson School of Applied Economics and Management, Cornell University, 310A Warren Hall, Ithaca, NY 14853, and the Korea University Business School, Korea University, Anam-dong, Seongbuk-gu, Seoul, Korea 136-701. Liu is with the College of Business, Florida State University, 821 Academic Drive, Tallahassee, FL 32306. Email: [email protected] and [email protected] We thank various hedge-fund managers, Nick Barberis, Zhuo Chen, Kevin Crotty, Zhi Da, Kent Daniel, Mara Faccio, Kenneth French, Huseyin Gulen, Yeonjeong Ha, David Hirshleifer, Russell Jame, Kuan-Hui Lee, Andrea Li, Dong Lou, John McConnell, Jeffrey Pontiff, Noah Stoffman, Yue Tang, Siew Hong Teoh, Dimitri Vayanos, Jianfeng Yu, and seminar participants at Dartmouth College, Emory University, Korean Securities Association, University of Connecticut, the 2013 FMA Annual Meeting, and the 2013 KAFA Conference for helpful comments. 1. Introduction In recent years, the financial marketplace has seen a proliferation of investment companies that freely use strategies involving combinations of leverage and long/short positions in securities (e.g., Bausano and Nemes (2012)). The immense price impact that these investors can exert has led to scrutiny by regulators and the popular press, frequently pointing to the potential harm such investors can cause (Garbaravicius and Dierick (2005)). Their net effect on financial markets, however, is far from obvious. In particular, these investment companies, most of them hedge funds 1 , are perhaps the closest to what one might perceive to be “ideal arbitrageurs” (Greenspan (1998), Brunnermeier and Nagel (2004), Cao, Liang, Lo, and Petrasek (2014)). Arbitrageurs thrive on price inefficiencies and, by simultaneously taking long- and short positions, they have the potential to eliminate anomalous price differences and contribute to the price discovery process, ultimately making markets more efficient. A growing body of work examines this possibility, utilizing data on hedge fund holdings to test how stocks held by hedge funds perform going forward (e.g., Brunnermeier and Nagel (2004), Brunnermeier and Pedersen (2009), Griffin, Harris, Shu and Topaloglu (2011), Khandani and Lo (2011), Cao, Chen, Liang, and Lo (2013), Cao, Liang, Lo, and Petrasek (2014)). The goal of this study is to adopt a different, augmentative approach. We take a step back and ask how hedge funds are compensated and incentivized in the first place. This, in turn, may help us gauge hedge funds’ effect on financial markets and whether, overall, they act in a more market-stabilizing- vs. more de-stabilizing manner. Specifically, fees paid to hedge funds are of the following two types: (1) management fees, calculated as a percentage of the fund’s net asset value (NAV), and (2) performance fees, calculated as a percentage of the fund’s net profits, if the fund generates any net profits, and zero otherwise. Management fees average around 1.5%; performance fees average around 19%.2 Because hedge funds gain a lot when assets appreciate in value (due to the 19% performance fees), yet lose relatively little when the value of the portfolio goes down (the loss is (only) 1.5% of the drop in NAV), this fee structure and its asymmetric 1 Going forward, we simply refer to these investment companies as hedge funds. These numbers are based on the 2010 Vanguard report: Alternative investments versus indexing: An evaluation of hedge fund performance. 2 1 treatment of net gains versus net losses favors strategies with high volatility. It has long been suspected by academics and regulators alike that the fee structure encourages managers to take on too much risk with potentially market destabilizing effects (Garbaravicius and Dierick (2005), Hodder and Jackwerth (2007) and Goetzmann, Ingersoll, and Ross (2003)). At the same time, as we detail in the hypothesis development section, there are also powerful arguments against this kind of behavior. Ultimately, whether the speculative-investor view accurately describes hedge funds’ behavior is an empirical question. For research-design considerations, we focus on short arbitrage, i.e., arbitrage activity tied to shorting of securities that appear overpriced. Our empirical approach is as follows. We analyze a set of ten well-known anomaly strategies. If investors conducting short arbitrage (“short sellers”) trade on an anomaly, a security falling into the “short leg” of the corresponding anomaly should be accompanied by a disproportionate rise in short interest; short interest is the number of shares shorted relative to the number of shares outstanding. Prior literature, for example, finds that when forming portfolios based on accruals, the portfolio of stocks with more positive accruals (“short leg”) subsequently underperforms. To assess to what degree short sellers trade on the accruals anomaly, we examine how much securities entering the short leg of the accruals anomaly experience a disproportionate rise in short interest.3 Our results suggest that short sellers do trade on anomalies. In particular, we observe that when a security falls into the short leg of an anomaly strategy, its short interest rises disproportionately; the reverse applies when a security leaves the short leg. This pattern is present throughout our sample period (1988-2012), but strengthens nearly twofold in the second half, an episode marked by a proliferation of hedge funds (e.g., Lo (2010), Bausano and Nemes (2012)). More importantly, it is significantly stronger for some anomalies than for others. We observe the strongest disproportionate rise in short interest for firm-growth-oriented strategies (asset growth and firm 3 Specifically, we borrow from prior literature (e.g., Hong, Lim, and Stein (2000), Baker and Wurgler (2006), Lemmon and Portniaguina (2006)) and estimate monthly cross-sectional regressions of short interest on a set of firm characteristics that have been argued to increase the supply of lendable shares and/or affect shorting demand for reasons other than anomaly-based trading. We then examine whether securities entering the short leg of an anomaly experience a spike in abnormal (residual) short interest. 2 investments), failure-probability-based strategies, and strategies based on earnings quality and postearnings-announcement drift. What causes some strategies to be more popular than others? Conceptually, rational/nonspeculative short sellers should aim to maximize the Sharpe Ratio of their overall investment portfolio. To do so, short sellers should increase their weight in a new strategy if the strategy itself has low risk and high average returns, and/or if the strategy has a low correlation with other strategies and allows short sellers to diversify risk (e.g., Perold (2004), Defusco, McLeavey, Pinto, and Runkle (2011)). On the other hand, if the convexity of the fee structure encourages excess risk-taking, speculative short sellers should increase their weight in a new strategy if the strategy has high volatility and high upside, irrespective of the associated downside risk. Consistent with the rational/non-speculative view, we find that a strategy’s popularity increases with the Sharpe Ratio of its own past portfolio returns. Specifically, a strategy’s popularity is negatively linked to its riskiness; it is positively related to its average returns. Relatedly, when regressing our measure of short sellers’ involvement on the corresponding strategy’s correlation with other anomaly strategies, we observe that a strategy’s popularity decreases with its correlation with other anomalies. We find no evidence that short sellers engage in strategies with high downside risk even if the strategy itself has high upside potential. Together, our evidence suggests that short arbitrageurs do not act in a speculative and, perhaps, market-destabilizing manner. Corroborating this view, we find that a rise in short sellers’ involvement in an anomaly strategy, due to an exogenous shock to that strategy’s awareness, is subsequently associated with lower anomalous returns and lower stock return volatility. Also, consistent with short sellers’ involvement representing informed trading, we find that trading on anomalies contributes substantially to short interest’s predictability of future returns, which, going forward, we refer to simply, if not quite accurately, as “short sellers’ profitability.” Our study speaks to two lines of research. First, we discuss and provide evidence on how contracts incentivize hedge funds to trade on various strategies. This, in turn, has the potential to improve 3 our understanding of how hedge fund activity affects financial markets (e.g., Brunnermeier and Nagel (2004), Brunnermeier and Pedersen (2009), Griffin, Harris, Shu and Topaloglu (2011), Khandani and Lo (2011), Cao, Chen, Liang, and Lo (2013), McLean and Pontiff (2013), Cao, Liang, Lo, and Petrasek (2014)). Second, to the best of our knowledge, our study is the first to jointly consider a wide set of anomalies and explore which anomalies attract more involvement by short arbitrageurs and why. We show that anomalies are far from perfectly correlated with each other and that there are significant differences in short arbitrageurs’ involvement across strategies. As such, our study contributes to the short-sale literature, documenting short sellers’ decision making process and analyzing what determines their profitability (e.g., Dechow, Hutton, Meulbroek, and Sloan (2001), Diether, Lee, and Werner (2009) and Engelberg, Reed and Ringgenberg (2012)). Our paper proceeds as follows: Sections 2 and 3 place our paper in the literature and develop our main empirical predictions. Section 4 describes our data and methodology. Section 5 presents our main findings. Section 6 conducts additional tests, and Section 7 concludes. 2. Prior Literature 2.1 Hedge Funds Arbitrage activity, frequently, is equated with hedge fund activity (Greenspan (1998), Brunnermeier and Nagel (2004), Cao, Liang, Lo, and Petrasek (2014)). Hedge funds are among the most sophisticated investors and they are estimated to control more than $2 trillion in assets (Bausano and Nemes (2012)) and a substantial portion of daily trading activity (McKinsey (2007)). Perhaps the key question surrounding the advent of hedge funds as one of the most important market participants is how their involvement affects price stability and market efficiency. A growing body of work uses data on hedge fund holdings to provide evidence on this question (Brunnermeier and Nagel (2004), Brunnermeier and Pedersen (2009), Griffin, Harris, Shu and Topaloglu (2011), Khandani and Lo (2011), Cao, Chen, Liang, and Lo (2013), Cao, Liang, Lo, and Petrasek (2014)). 4 Our study augments the hedge fund literature by taking a step back and asking how hedge funds are compensated and incentivized in the first place. Addressing this question, in turn, has the potential to provide cues as to whether hedge funds act in a more market-stabilizing manner or, perhaps, in a more market-de-stabilizing manner. We borrow from the CEO compensation literature that relates incentives created by stock options with risk taking at the firm level. The use of call options in CEOs’ compensation packages has created a convexity in CEOs’ compensation structure (Murphy (1999)), and empirical work suggests that this convexity encourages managers to choose riskier projects over safer projects (e.g., Coles, Daniel, and Naveen (2006), Low (2009), and Armstrong and Vashishtha (2012)). As we detail below, the fee structure of hedge funds (also) creates a convexity in payoffs. This, in turn, may encourage speculation. While this possibility has been discussed by theoretical work and broached by regulators and the popular press (e.g., Garbaravicius and Dierick (2005)), to the best of our knowledge, it has yet to be assessed empirically. Our study helps fill this gap. We test whether hedge funds’ involvement across trading strategies lends credence to the view that hedge funds speculate. One challenge associated with this kind of exercise is that hedge funds are not at liberty to disclose much information about their strategies. Our study circumvents this problem by focusing on arbitrage activity related to the shorting of seemingly overpriced securities.4 Short arbitrage activity can be inferred, albeit imperfectly, from short interest data. An important limitation is that our conclusions based on short arbitrage may not generalize to other areas of hedge fund/arbitrage activity. 2.2 Short Sellers By focusing on short arbitrage, our paper also relates to the literature on short selling activity. A large body of work provides evidence that short sellers are informed traders in the sense that a high fraction of 4 Hedge funds engage in the following strategy-types: “dedicated short bias”, “equity market neutral”, “long-short equity”, “event-driven”, “convertible arbitrage”, “managed futures”, “fixed-income”, “emerging markets” and “global macro” (Ibbotson, Chen, and Zhu (2010)). Of these, short arbitrage is most closely related to “dedicated short bias”, “equity market neutral”, and “long-short equity”. 5 shares shorted generally is followed by low future returns (e.g., Desai, Ramesh, Thiagarajan, and Balachandran (2002), Asquith, Pathak, and Ritter (2005)). As alluded to in the introduction, in this paper, we refer to this predictability, if not quite accurately, as “short sellers’ profitability.” Short sellers may profit because they trade on private information and are able to correctly anticipate future news announcements. Alternatively, short sellers may profit from their ability in processing publicly available information. Consistent with the first view of short sellers’ profitability, Khan and Lu (2013) provide evidence that short sellers correctly anticipate large insider sales and, essentially, front-run insider trades. Desai, Krishnamurthy, and Venkataraman (2006) find that short sellers build up short positions prior to an earnings restatement and, subsequently, benefit from the negative price reaction associated with the restatement news. Our study focuses on anomaly strategies and, as such, is more closely related to the literature surrounding the second view of short sellers’ profitability. Chi, Pincus, and Teoh (2014) provide evidence that investors misprice book-tax differences based on publicly available accounting data and that short sellers take advantage of this mispricing. Hirshleifer, Teoh, and Yu (2011) present evidence that investors engage in short arbitrage of the accruals anomaly. Dechow, Hutton, Meulbroek, and Sloan (2001) and Hanson and Sunderam (2014) suggest that short sellers increase short positions for firms with low bookvalue-to-market-value ratios (“growth firms”). Growth firms, in turn, are known to underperform (Basu (1977)). Hanson and Sunderam also find that short sellers increase their positions in stocks with poor stock-market performance as these stocks can be expected to underperform based on the momentum effect (Jegadeesh and Titman (1993)). Together, the above work on individual anomalies shows that short sellers trade on anomalies rooted in publicly available accounting- and stock-market data. Our paper contributes to the literature by jointly considering a wide set of anomalies rather than focusing on an individual anomaly. This simple augmentation allows us to provide novel evidence on aspects of short sellers’ decision making process and the considerations that they face. 6 3. Empirical Predictions 3.1 The Non-Speculative Investor View We begin with the “non-speculative investor view”. In this study, we refer to “non-speculative investors” as those that are risk-averse, mean-variance optimizers who aim to construct portfolios delivering the highest returns at the lowest risk/volatility possible. Consider a short arbitrageur constructing a portfolio p and considering various strategies. The short arbitrageur wants to maximize the Sharpe Ratio, i.e., the reward-to-risk ratio, of his/her overall portfolio p and will add strategy i to his/her portfolio only if the strategy has a positive αi , i.e., αi = E(r ) − (r + βi (E(r ) − r )) > 0, where βi is the beta from strategy i’s excess returns against portfolio p’s excess returns (e.g., Perold (2004), Defusco, McLeavey, Pinto, and Runkle (2011)). In other words, adding strategy i to portfolio p will increase portfolio p’s Sharpe Ratio only if the strategy’s risk premium satisfies: E(r ) − r > βi ((r ) − r ) (1) The beta can be expressed as a function of the correlation coefficient and the standard deviations: βi = (r ,r ) σ2 = ρ σ σ σ2 = ρ σ σ (2) Plugging equation (2) into equation (1), we have: E(r ) − r > E(r )−r σ ρ σ σ > ρ ∗ ∗ (E(r ) − r ) (E(r )−r ) (3) (4) σ Sharpe Ratio > ρ ∗ Sharpe Ratio (5) Equation (5) reveals that the strategy most popular among short arbitrageur should be those that have low risk and high returns (high Sharpe Ratio) and those that have a low correlation with other strategies. Hypothesis 1: Under the “Non-Speculative Investor View”, a strategy’s popularity should decrease with risk, increase with average returns and decrease with its correlation with other strategies. 7 3.2 The Speculative Investor View Equation (5) contrasts sharply with the “speculative investor view”. Fees paid to hedge funds are of the following two types: (1) management fees, which are calculated as a percentage of the fund’s net asset value (on average around 1.5%), and (2) performance fees, which are calculated as a percentage of the fund’s net profits, if the fund generates any net profits, and zero otherwise (on average around 19%). The performance fees are intended to encourage managers to generate profits, but they have also been criticized for their asymmetric treatment of net gains versus net losses. Figure 1: Performance and Compensation. Figure 1 illustrates the intuition. Figure 1 depicts two trading strategies, L and H. Each strategy has a fifty percent chance of generating a gain (and increasing assets), and a fifty percent chance of generating a loss (and decreasing assets). The low volatility strategy’s (L) performance fluctuates between -4% and +5%. The high volatility strategy’s (L) performance fluctuates between -10% and +10%. As can be inferred from Figure 1, a manager with a performance of -10% receives a similar compensation as his counterpart with a performance of -4%; at the same time, due to the performance fees, which, on average, is around 19% of the profits, he experiences a much higher compensation if his performance is +10% as opposed to +5%. In terms of expected compensation level; a strategy whose performance fluctuates between -10% and +10% (strategy H), thus, is more appealing to the manager than a strategy whose performance fluctuates between -4% and +5% (strategy L), despite the latter having the higher mean performance and the higher Sharpe Ratio. 8 In the absence of financing costs, managers can simply scale up strategy L by a factor of two. In other words, rather than making a gross investment of $100 million in strategy H, which generates performances of either -$10 million or +$10 million, managers can borrow and invest $200 million in strategy L, generating performances of either -$8 million or +$10 million. However, the process of scaling-up, i.e., increasing the gross investment from $100 million to $200 million, is not without costs. Moreover, portfolio managers working for a hedge fund, sometimes, are given a limit on the total gross dollar amount that they are allowed to invest. As such, it is plausible that, in certain situations, preference will be given to strategy H over strategy L. Hypothesis 2: Under the “Speculative Investor View”, a strategy’s popularity should increase with risk; holding risk constant, a strategy’s popularity should also increase with average returns. The notion that the convexity of fee structures encourages risk-taking has long been suspected by academics and regulators alike (Goetzmann, Ingersoll, and Ross (2003), Hodder and Jackwerth (2007), Stulz (2007)). For instance, Stulz (2007) notes that “it is not always easy to resist the temptation to take large risks. As an example, the trader apparently responsible for the large losses at Amaranth in 2006 is reported to have earned between $80 million and $100 million there in 2005. 5 As long as no illegal actions took place, the trader will not have to return his past compensation to the fund – in fact, he is planning to start a hedge fund of his own.” At the same time, there are also powerful arguments against this kind of behavior. In particular, loading up on high-volatility strategies increases the risk of margin calls, investors withdrawing money from the fund, and the fund eventually failing should mispricing temporarily worsen. Moreover, while the fee structure is convex at the fund level, how the individual portfolio managers themselves are evaluated is unclear. Individual portfolio managers also face career considerations and may not want to take on too 5 Amaranth is a large hedge fund that in September 2006 is reported to have lost more than $6 billion in only one month (Stulz (2007)). 9 much risk as much of their financial and human capital is tied to the fund in question. Ultimately, whether short arbitrageurs’ behavior can be better described by the non-speculative-investor view or the speculative-investor view is an empirical question. 4. Data and Descriptive Statistics 4.1 Data Our sample consists of NYSE, AMEX, and NASDAQ ordinary shares during the 1988-2012 period with data necessary to compute monthly abnormal short interest (to be discussed below).6 We exclude stocks with a stock price < $5 as of the portfolio formation date (e.g., Jegadeesh and Titman (2001), and Daniel and Titman (2006)). Our results are robust to more restrictive liquidity cutoff points based on dollar trading volume and market capitalization, including, but not limited to a minimum of $500 million in market capitalization and a minimum of $1 million in daily trading volume. NYSE, AMEX, and NASDAQ member firms are required to report to the exchange their short positions as of settlement on the 15th of each month, or on the preceding business day if the 15th is not a business day. We obtain monthly short-interest data from the COMPUSTAT monthly securities database, which pools data from the NYSE, AMEX, and NASDAQ exchanges. For the 1988-2002 analysis period, we augment this dataset with monthly short-interest data obtained directly from the stock exchanges. We do so because we notice that many short positions reported by the stock exchanges during the early part of our analysis period are missing in the COMPUSTAT database7; there are also a few short positions reported in COMPUSTAT that are not in the stock-exchange-provided data, but this subset is very small and economically inconsequential. We obtain financial-market data from the Center for Research in Security Prices (CRSP) and financial-statement data from the COMPUSTAT industrial files. We use these data sources to construct 6 Our sample covers more than 60% of the number of observations and more than 75% of the total market capitalization in the CRSP file over the 1988-2012 period. 7 This holds particularly true in the beginning of our sample period. The magnitude of this problem lessens over time and starting in 2000 becomes economically inconsequential. 10 portfolio returns as well as variables to capture the following 10 anomalies, all of which are described in Appendix A.1. 8 Stocks Expected to Outperform (“Long leg”) A1 (Failure Probability) Low failure probability A2 (O-Score) Low O-Score [≈ low distress risk] A3 (Total Accruals) Low total accruals A4 (Net Operating Assets) Low net operating assets A5 (Gross Profitability) High gross profitability A6 (Return on Assets) High return on assets A7 (Asset Growth) Low asset growth A8 (Investment over Assets) Low past investment ratio A9 (PEAD) High/positive unexpected earnings A10 (E/P Ratio) High earnings-to-price ratio Stocks Expected to Underperform (“Short leg”) High failure probability High O-Score [≈ high distress risk] High total accruals High net operating assets Low gross profitability Low return on assets High asset growth High past investment ratio Low/negative unexpected earnings Low earnings-to-price ratio Our focus in this study is on accounting-based anomalies. Accounting-based anomalies stand out by their being anchored on estimates of fundamental values. As such, they are perhaps the most likely place where mispricing can be detected and where informed arbitrage activity occurs (Stein (2009)). Having said that, in additional tests, we include momentum as the most prominent non-accounting-based anomaly and we observe that its inclusion has limited impact on our overall inferences (Section 5.1). In the end, it is impossible to construct an exhaustive list of anomalies and, at a very detailed level, many anomalies are strongly related to each other. Our list appears to include the most important anomaly strategies. We have experimented with permutations of which anomalies to include in our study. In short, none of our overall inferences were materially altered (results available upon request). 4.2 Descriptive Statistics - Anomaly Performance Prior to presenting our main results, we provide some descriptive evidence on the performance of the anomaly strategies examined in this study. For every portfolio formation month, we sort stocks into decile portfolios based on the anomaly variables discussed above and construct value-weighted decile portfolio 8 See, among others, Campbell, Hilscher, and Szilagyi (2008) for anomaly 1; Ohlson (1980) for anomaly 2; Sloan (1996) for anomaly 3; Hirshleifer, Hou, Teoh and Zhang (2004) for anomaly 4; Novy-Marx (2012) for anomaly 5; Fama and French (2006) for anomaly 6; Cooper, Gulen, and Schill (2008) for anomaly 7; Titman, Wei, and Xie (2004) and Xing (2008) for anomaly 8; Ball and Brown (1968) and Bernard and Thomas (1989, 1990) for anomaly 9; and Basu (1977) and Ball (1992) for anomaly 10. 11 returns. In accordance with prior literature, for anomalies (3)-(5), (7)-(8), and (10), we form portfolios as of the end of each June in year t (using accounting data from the fiscal year ending in calendar year t-1) and compute returns from July in year t to June in year t+1. For anomalies (1)-(2), (6), and (9), we form portfolios as of the end of each calendar quarter t (using accounting data from the fiscal quarter ending in calendar quarter t-1) and compute returns over the ensuing calendar quarter t+1. For instance, when forming portfolios at the end of Mar2000 (using quarterly accounting data from the fiscal quarter ending in Oct1999, Nov1999, or Dec1999), we compute returns on those portfolios from Apr2000 to Jun2000. We report excess returns, as well as benchmark-adjusted returns, for the “long leg,” hereafter defined to be decile portfolio 10, and the “short leg,” hereafter defined to be decile portfolio 1, with decile 10 being the higher-performing decile, as reported in previous studies. Following Brennan, Chordia, and Subrahmanyam (1998), benchmark-adjusted returns, Adj.Ret, are defined as returns net of what is attributable to exposures to the market, size, and value factors (Fama and French (1993)): , − = + + + + , → . , = + , . (6) Table 1 shows that most of the 10 strategies, each purchasing stocks in the long leg and shorting stocks in the short leg, continue to produce high returns and strong positive alphas relative to the FamaFrench (1993) three-factor model, consistent with their being identified as anomalies for this study. The average monthly benchmark-adjusted return across all 10 long-short strategies is 0.80%. The average monthly benchmark-adjusted return across all 10 short strategies is -0.39%. Some of our anomaly performances are weaker than the ones documented in prior studies. The reason is that data requirements to compute abnormal short interest eliminate roughly 1/3 of the “original” observations; the observations eliminated represent mostly small- and micro-cap securities. When repeating our analysis on the full original sample, our results become comparable to those in prior literature. Table 2 presents a correlation matrix of the anomaly strategies’ benchmark-adjusted long-short portfolio returns. While the anomalies are clearly related to each other, none of the correlation 12 coefficients is higher than 0.43; the average correlation coefficient across all anomaly pairs is 0.05, suggesting that each anomaly has its own distinct character. We make very similar observations when considering short-portfolio returns only. 5. Short Arbitrage 5.1 Methodology We infer short arbitrageurs’ involvement in anomaly strategies via changes in short interest. If short arbitrageurs consider anomalies, we should observe a rise in short interest once a security falls into the short leg of an anomaly. Prior literature, for example, finds that when forming portfolios based on total accruals at the end of each June in year t, the portfolio of stocks with more positive accruals (short leg) performs poorly over the ensuing one-year portfolio-holding period, i.e., from July in year t to June in year t+1. To assess whether short sellers attempt to capitalize on the poor performance accrued from July in year t to June in year t+1, we examine whether, by the end of June in year t, short-leg securities experienced a rise in short interest. One concern with our approach is that the level of short interest fluctuates for a number of reasons. In particular, short interest represents the intersection of shorting demand and the supply of lendable shares, and a security may experience a rise in the level of short interest not because it fell into the short leg of an anomaly strategy, but simply because its non-anomaly-based shorting demand or its supply of lendable shares increased. Moreover, a security may experience a rise in the level of short interest simply because of a general upward-time trend in short selling activity. We now discuss the remedies that we apply to address these concerns (please see Appendix A.2 for additional facets of our empirical design). 5.1.1 Remedy 1 To better tie variation in short interest to anomaly-based shorting, we follow prior literature (e.g., Hong, Lim, and Stein (2000), Baker and Wurgler (2006), and Lemmon and Portniaguina (2006)) and residualize 13 our variable of interest. Specifically, we estimate monthly cross-sectional regressions of short interest on a set of firm characteristics, X, that have been found to relate to the level of short interest for nonanomaly-based reasons (Brent, Morse, and Stice (1990), and Kot (2007)). As we would rather err on the side of understating the magnitude of anomaly-related shorting activity than on the side of overstating it, we choose our control set, X, to be as large as possible. Further below, we describe results for the “other extreme,” where the control set is empty and we don’t apply Remedy 1. To preview, our results strengthen if we don’t apply Remedy 1 (please see Appendix A.3). The first component of our control set is intended to remove variation in short interest attributable to the supply of lendable shares. Using a proprietary dataset from a consortium of more than one hundred stock lenders, Beneish, Lee, and Nichols (2014) find that the supply of lendable shares varies substantially across stocks. We approximate the supply of lendable shares via Institutional Holdings. Institutional investors are the main suppliers of stock loans (D’Avolio (2002)). Consequently, institutional holdings likely explain much of the variation in the supply of lendable shares. Institutional Holdings, along with the second component of our control set, ln(Market Capitalization), also provides information about a stock’s liquidity and, hence, its attractiveness to investors as a short-sale candidate for hedging purposes (Hwang, Liu, and Xu (2014)). Other parts of short interest that we intend to remove, because they cannot be tied to anomaly-based shorting activity, are as follows: Investors may short to arbitrage price differentials between securities tied to the same underlying asset (Brent, Morse, and Stice (1990)), which provides an explanation for why, in the data, the level of short interest increases with the presence of convertible securities (ConvertibleSecurity). Shortselling activity also has been argued to increase with investor disagreement (IdiosyncraticVolatility), as pessimistic investors short against the more optimistic investors’ beliefs. In addition, short interest increases with a stock’s market beta (Beta), perhaps as some investors desire to construct portfolios with zero exposure to market fluctuations and as one requires a smaller short position to do so when the stock itself has a high beta. Finally, short sellers target firms that appear overvalued based on very firmspecific, fundamentals-based reasons (ln(Market/Book), PastReturn); e.g., Dechow, Hutton, Meulbroek, 14 and Sloan (2001)). Consistent with prior studies, we observe that the level of short interest increases with past returns, market-to-book ratio, market beta, idiosyncratic volatility, convertible debt, and institutional holdings. It is unrelated to market capitalization once controlling for institutional holdings. To capture anomaly-related shorting activity, we compute to what degree securities that fall into the short leg of anomaly i experience an increase in abnormal (residual) short interest, ∆AbnShort(ShortLeg)i,t; in other words, short interest that is less likely to be determined by the supply of lendable shares and/or non-anomaly-based shorting demand. In line with the horizon over which our 10 anomaly portfolios are formed, ∆AbnShort(Short-Leg)i,t represents the change in abnormal short interest over the 12-month portfolio formation period for the annually-formed anomalies and over the 3-month portfolio formation period for the quarterly-formed anomalies. To facilitate comparison, we annualize ∆AbnShort(Short-Leg)i,t for the quarterly-formed anomalies. Our results are robust to alternative portfolio-formation periods. 5.1.2 Remedy 2 ∆AbnShort(Short-Leg)i,t still suffers from one shortcoming. In particular, ∆AbnShort(Short-Leg)i,t may reflect a general, market-wide, upward time-trend in short-selling activity that is not fully captured by the firm characteristics against which short interest is residualized. In our final step, we therefore repeat our exercise for securities that fall into the long leg of anomaly i, ∆AbnShort(Long-Leg)i,t, and we compute the difference between ∆AbnShort(Short-Leg)i,t and ∆AbnShort(Long-Leg)i,t. In other words, we assess whether securities that fall into the short leg of an anomaly experience a disproportionate rise in short interest relative to their long-leg counterparts. This “difference-in-difference measure,” ∆∆AbnShorti,t, represents our main variable of interest. Later, we also present results for ∆AbnShort(Short-Leg)i,t, i.e., results if we don’t apply Remedy 2. To preview, again, our results strengthen. 15 5.2 The Evidence: Trading on Anomalies Every month, we sort stocks into decile portfolios based on the anomaly variable in question. We then compute for each decile portfolio the average change in abnormal short interest, ∆AbnShort(Decile)i,t. Figure 2 plots the time-series mean of ∆AbnShort(Decile)i,t for each decile portfolio, and Table 3 reports the time-series mean for the two extreme deciles, ∆AbnShort(Short-Leg)i,t and ∆AbnShort(Long-Leg)i,t, as well as the difference between the short leg and the long leg, ∆∆AbnShorti,t. A positive difference implies that securities that fall into the short leg, on average, experience a disproportionate rise in short interest; a negative number implies that securities that fall into the short leg, on average, experience a disproportionate drop in short interest. Panel A of Table 3 shows that the average ∆AbnShort(Short-Leg)i,t is +0.24%. This contrasts with an average ∆AbnShort(Long-Leg)i,t of +0.04%. That is, securities falling into the short leg of an anomaly experience a disproportionate rise in short interest. Table 3 reports that this pattern reverses when a security subsequently leaves the short leg. To put the differential change of +0.20% in perspective, the average level of short interest across all stocks in our sample is 2.51%. The increase in the abnormal short interest of 0.20% is thus economically meaningful. Relatedly, when gauging the net dollar amount invested in each strategy by multiplying the disproportionate rise in short interest with the market capitalization of the corresponding short-leg securities, we infer that each year, on average, $1.12 billion is invested in each anomaly strategy, with the most capital being tied up in the asset-growth anomaly ($4.8 billion). Panel B of Table 3 shows results by subperiods. In the first half of our sample period (19882000), the average ∆∆AbnShorti,t is +0.13%; in the second half of our sample period (2001-2011), that number increases to +0.27%. The substantially stronger result in the more recent sample period coincides with the proliferation of hedge funds, which are heavily involved in shorting activity (e.g., Lo (2010) and Bausano and Nemes (2012)). For some of the anomalies considered in this study, this period also coincides with the publication of academic work discussing the anomaly in question and, perhaps, raising awareness of seemingly anomalous returns. Section 5.2 further delineates these time-series patterns. 16 5.3 The Evidence: Differences in Popularity While securities falling into the short leg of an anomaly in general experience a disproportionate rise in short interest, as perhaps best illustrated by Figure 2, this pattern is much stronger for some anomalies than for others. The “popularity ranking” is as follows: asset growth (most popular), post-earningsannouncement drift, investment-over-assets, failure probability, total accruals, Ohlson’s O, net-operatingassets, gross profitability, return-on-assets, and earnings-to-price ratio (least popular).9 Appendix A.4 shows that these differences in popularity persist (a) when repeating our exercise for short-leg securities that are in the short leg of only one anomaly, 10 and (b) when basing our comparisons on medians rather than averages, i.e., means. We now turn to our key question, which is what causes these differences in anomaly-based shorting activity. From the non-speculative-investor perspective, the anomalies most popular among short sellers should be those that have high average returns, low risk and low correlations with other anomalies. From the speculative-investor perspective, the anomalies most popular should be those that have high average returns and, for a given level of average returns, have high volatility. To test these opposing predictions, we follow a regression approach. Our dependent variable is our measure of anomaly-based shorting activity in anomaly i as of month t, ∆∆AbnShorti,t. Dependent Variable: Differential ∆∆AbnShort as of month t Month t-12 Month t [Month t-72, Month t-13] Independent Variables Figure 3: Timing of regression variables. Our independent variables are as follows: (1) Correlation with Other Anomalies, which is the 9 With respect to the failure probability/Ohlson’s O anomaly, only $425 million is estimated to be invested in each anomaly. In comparison, for the other anomalies identified as being popular (accruals, net operating assets, asset growth, investment over assets, and post-earnings-announcement drift), we estimate that, on average, $1.7 billion is invested in each anomaly. 10 While focusing on securities that are in the short leg of one anomaly has the potential to more accurately capture trading only on the specific anomaly in question, doing so also reduces our sample by roughly two thirds. 17 rolling five-year Pearson correlation coefficient between the strategy’s monthly benchmark-adjusted short-portfolio return and the monthly anomaly index; the monthly anomaly index represents the benchmark-adjusted return of a portfolio that invests an equal portion in each of the 10 anomaly-based short portfolios considered in this study.11 (2) Sharpe Ratio, which is the average monthly benchmarkadjusted short-portfolio return over the previous five years (multiplied by negative one) divided by its standard deviation. (3) Past Performance, which is the average monthly benchmark-adjusted shortportfolio return over the previous five years (multiplied by negative one). (4) Past Return Std. Dev., which is the standard deviation of monthly benchmark-adjusted short-portfolio returns over the previous five years. (5) Downside Risk, which is the rolling five-year 99th percentile of monthly benchmarkadjusted short-portfolio returns (multiplied by negative one). (6) Upside Potential, which is the rolling five-year 1st percentile of monthly benchmark-adjusted short-portfolio returns (multiplied by negative one). Our observations likely are correlated in the time-series across year-months. Observations likely are also correlated in the cross-section across different anomalies. To account for both time-series- and cross-sectional dependence, we follow Cameron, Gelbach, and Miller (2011), who propose the following variance-covariance matrix (Vanomaly,time): Vanomaly,time = Vanomaly + Vtime – VWhite (7) The standard errors clustered by anomaly capture time-series dependence. The standard errors clustered by year-month capture cross-sectional dependence. Since both the anomaly- and the time-clustered variance-covariance matrix include the diagonal of the variance-covariance matrix, we subtract the White variance-covariance matrix. We adopt one minor modification: Our panel consists of 10 anomaly strategies and 213 yearmonths. We thus have only ten clusters in the time-series. “Since the clustered standard error places no restriction on the correlation structure of the residuals within a cluster, its consistency depends on having 11 We choose equal-weighting for simplicity. We obtain similar results when weighing each anomaly by the total market capitalization of its short-leg securities. 18 a sufficient number of clusters” (Petersen (2009), p. 455). According to the simulation results presented in Petersen, “ten clusters is too small” (p. 456). Clustering by anomaly is, thus, not an option. For Vanomaly, we, therefore, choose to compute Newey-West standard errors with a lag length of 36 year-months. This choice is conservative, and the statistical significance increases notably relative to the one presented in this study when decreasing the lag length. Before presenting our main findings, we note that our independent variables are persistent and that there is wide cross-sectional dispersion. That is, past performance is highly indicative of future performance, and so are the statistics describing aspects of the performance distribution.12 Table 4 reports results from our regression analysis and addresses which features of the performance distribution appeal the most to short sellers. Our first regression equation is organized around the non-speculative-investor prediction that Sharpe Ratioi > ρip ∗ Sharpe Ratiop (equation (6)) and contains the following independent variables: Correlation with Other Anomalies and Sharpe Ratio. Our second regression equation splits up the Sharpe Ratio into its numerator (Past Performance) and its denominator (Past Return Std.Dev.). Our third regression equation experiments with an alternate measure of risk, Downside Risk. The results support the non-speculative-investor view. In particular, the slope on Sharpe Ratio is highly significant, both statistically and economically (0.521, t-statistic = 2.50). The estimate on Sharpe Ratio suggests that a one-standard-deviation rise in Sharpe Ratio leads to a 0.09% rise in anomaly-based shorting activity. Relatedly, our regressions produce a strong positive slope on Past Performance (17.264, tstatistic = 2.78), yet negative slopes on Past Return Std.Dev. (-7.603, t-statistic = -1.91) and Downside Risk (-3.605, t-statistic = -2.20). The estimate on Past Return Std.Dev. implies that a one-standarddeviation increase in Past Return Std.Dev. is associated with a 0.08% drop in anomaly-based shorting 12 For instance, when ranking anomaly strategies based on Correlation with Other Anomalies, which is computed from t-72 to t13, we observe that over the ensuing non-overlapping twelve-month period, the three strategies with the highest Correlation with Other Anomalies, on average, experience a post-ranking Correlation of 0.59. The corresponding number for the three strategies with the lowest Correlation with Other Anomalies is 0.27. The difference in post-ranking Correlation with Other Anomalies thus equals 0.32 (t-statistic = 11.71). We find the same degree of persistence and cross-sectional dispersion for all of our independent variables. 19 activity; the estimate on Downside Risk implies that a one-standard-deviation increase in Downside Risk is associated with a 0.09% drop in anomaly-based shorting activity. The coefficient estimate on Correlation with Other Anomalies ranges from -0.605 (t-statistic = 2.42) to -0.679 (t-statistic = -2.83), depending on the regression specification, suggesting that anomaly popularity increases as the anomaly in question is less correlated with other anomalies. The estimate on Correlation with Other Anomalies suggests that a one-standard-deviation drop in Correlation with Other Anomalies leads to a 0.12% rise in anomaly-based shorting activity. Our fourth and fifth regression equations are organized around the speculative-investor view and contain the following independent variables: Past Performance and Past Return Std.Dev. for regression (4), and Past Performance, Downside Risk, and Upside Potential for regression (5). The coefficient estimates on Past Return Std.Dev. and Downside Risk continue to be negative and statistically significant, suggesting that short arbitrageurs do pay close attention to risk. Unlike the coefficient estimate on Past Performance, the estimate on Upside Potential is not statistically significant (-1.524 (t-statistic = -0.74)), suggesting that anomaly popularity is not related with upside potential irrespective of the associated downside risk, further echoing the non-speculative-investor view. 6. Additional Analyses 6.1 Value and Momentum Because we control for book-to-market ratio and past returns to construct abnormal short interest, in our main analysis, we do not analyze whether short sellers target low book-to-market firms and past losers. Momentum also has the disadvantage of not being anchored in estimates of fundamentals. In this subsection, we nevertheless modify our measure of anomaly-related short selling and extend our analysis to the value- and the momentum anomaly. For the value-anomaly, we do not orthogonalize short interest with respect to a stock’s market-to-book ratio. Similarly, for the momentum-anomaly, we do not orthogonalize short interest with respect to a stock’s recent market performance. 20 Appendix A.5 shows that, for the value anomaly, the average ∆AbnShort(Short-Leg)i,t is +0.39%. This contrasts with an average ∆AbnShort(Long-Leg)i,t of -0.13%. The difference is +0.52% (t-statistic = 4.25). In other words, securities falling into the short leg of the value anomaly ( growth stocks) experience a disproportionate rise in short interest. Put bluntly, short sellers trade on the value-anomaly. Our results imply that short sellers also trade on momentum. The average change in abnormal short interest among past losers is +0.42%. This compares to an average change in abnormal short interest among past winners of +0.18%; the difference is +0.24% (t-statistic = 5.51). More importantly, when including value and momentum into our analysis, our results continue to imply that a strategy’s popularity decreases with its riskiness and increases with its average performance (results available upon request). 6.2 Short Arbitrage and Price Efficiency Overall, our findings suggest that short arbitrageurs act in a (rational) non-speculative manner. From this, one may (indirectly) infer that short arbitrageurs are informed and market-stabilizing, ultimately making markets more efficient. The last two subsections provide evidence to this regard. The question of how arbitrage involvement influences stock prices is difficult to establish empirically, because both can be determined simultaneously by a third omitted factor. To circumvent this problem, we conduct a difference-in-difference analysis around the times when a long-short anomaly strategy is publicized in an academic outlet. The dissemination of knowledge via academic outlets alleviates the aforementioned endogeneity concern, as a journal publication can be thought of as a “positive shock” that increases awareness of the strategy among systematic traders and as it is unclear why a journal publication would affect future anomaly profits outside of the “awareness” channel. McLean and Pontiff (2013) provide related evidence on how journal publications relate to anomaly profits of various long-short strategies. For each anomaly i and each month t, we compute ∆∆AbnShorti,t. We then compare the average ∆∆AbnShorti,t in the three years prior to journal publication to the average ∆∆AbnShorti,t in the three years 21 following journal publication. To ensure that our before/after-publication comparison is distinct from the general upward trend in arbitrage activity that we document in Section 3.2, we subtract from ∆∆AbnShorti,t the ∆∆AbnShortj,t averaged across all anomalies excluding anomaly i itself and excluding anomalies x whose before/after comparison overlaps with that of anomaly i (because anomalies x were published around the same time as anomaly i). For example, in the three years prior to the publication of Titman, Wei and Xie (2004) and their discussion of the investment anomaly, securities falling into the investment-short leg, on average, experienced a disproportionate rise in short interest of 0.37%. In the three years following the publication, that spread increased to 0.83% (∆=+0.46%). In comparison, over the same horizon, other anomalies not affected by a journal publication experienced a drop in ∆∆AbnShortj,t from 0.42% to 0.24% (∆=-0.18%). The difference-in-difference for the investment anomaly thus equals +0.64% (∆∆=0.46% - (-0.18%)). The average difference-in-difference across all anomalies for which a before/after-publication comparison can be made is 0.47% (t-statistic = 2.31; N = 6). This result suggests that journal publication indeed increases involvement by short arbitrageurs. To study how the increase in arbitrage involvement relates to price efficiency, we compute for each of the 6 anomalies for which a before/after-comparison can be made the change in anomaly profits from three years before- to three years after journal publication. Again, to ensure that our before/afterpublication comparison is distinct from a general time trend in anomaly performance, we subtract from anomaly performance i the anomaly performance averaged across all anomalies excluding anomaly i itself and excluding anomalies x whose before/after-comparison overlaps with that of anomaly i. We then correlate this difference-in-difference in anomaly performance with the abnormal change in shorting activity. We detect a negative correlation of -79.4% (p-value = 0.06). That is, while anomaly profits decrease in general post-journal publication (McLean and Pontiff (2013)), the novel evidence that we uncover is that they do particularly so for anomaly strategies that experience the greatest rise in anomalybased shorting activity following journal publication, perhaps as those anomaly strategies had been less 22 well known to parts of the investment community prior to the anomaly being discussed in an academic outlet. This result is consistent with the idea that increased arbitrage involvement helps make markets more efficient. To expound on this point, we assess whether journal publication also translates to a disproportionate drop in volatility for the corresponding strategy’s portfolio return. If short sellers, in general, trade away anomalous returns, their involvement will either decrease or have no impact on the volatility of the short leg following the portfolio formation date (Lo (2010)).13 If, instead, short sellers tend to move market prices away from fundamentals and, in general, make markets less efficient, their involvement will increase the volatility of the short leg. In the data, we observe that after an article discussing anomaly x is published in an academic journal, not only do anomaly profits weaken; relative to other anomalies not affected by the publication, the corresponding strategy’s short-leg volatility also declines by 1.82% (p-value=0.01). Moreover, we observe a negative relation between rise in anomaly-based shorting activity and change in volatility (-0.81, p-value=0.05). While much more work needs to be done, combined with the drop in anomaly profits, our volatility result provides evidence that, at least for the anomalies examined in this study, short arbitrageurs’ involvement is stabilizing and helps make markets more efficient. 6.3. Anomaly-Based Shorting Activity and Short Sellers’ Profitability Our overall conclusion implies that short sellers’ involvement represents informed trading. In our final analysis, we assess the validity of that notion. Our empirical design is as follows: In our first stage, we estimate monthly cross-sectional regressions of short interest on Anomaly Signal Score and the same set of firm characteristics used before that we believe to be tied to the supply of lendable shares and/or non13 Loosely speaking, consider the scenario in which short-portfolio returns, following the portfolio formation date, are either 4% or 2% (with equal probability) without arbitrage involvement (StDev=1.41%). As arbitrageurs construct portfolios and short over-priced short-leg securities, their price impact will partially eliminate mispricing. The ensuing short-portfolio returns will thus be lower with arbitrage involvement than without arbitrage involvement. If total price impact is assumed to be fixed (e.g., 1%), then subsequent returns will be either 3% or 1% (StDev=1.41%). If total price impact is assumed to be proportional (e.g., 50% of mispricing), then subsequent returns will be either 2% or 1% (StDev=0.71%). 23 anomaly-based shorting demand. Anomaly Signal Score equals zero if the corresponding stock is in the short leg of none of the ten anomalies considered in this study, one if the corresponding stock is in the short leg of one of the ten anomalies, etc. Theoretically, realizations of Anomaly Signal Score can range from zero to ten. In practice, realizations of Anomaly Signal Score range from zero to nine. The fitted value associated with Anomaly Signal Score can be interpreted as reflecting short interest primarily associated with anomaly characteristics (“Short Interest-Tied to Anomalies”). The remainder can be viewed as short interest unrelated to anomaly strategies (“Short Interest-NOT Tied to Anomalies”). As reported in Column 1 of Table 5 and consistent with our previous tests, a higher Anomaly Signal Score translates to a higher level of short interest. The estimate on Anomaly Signal Score equals 0.006 (t-statistic = 9.05).14 Columns (2)-(3) of Table 5 report estimates from Fama-MacBeth regressions of stock returns on lagged measures of shorting activity. When regressing stock returns on lagged short interest by itself, we obtain a slope of -0.094 (t-statistic = -5.08). When regressing returns on the lagged values of Short Interest-Tied to Anomalies and the lagged values of Short Interest-NOT Tied to Anomalies, Table 5 reports that the estimate on Short Interest-Tied to Anomalies equals -0.626 (t-statistic = -6.23); the estimate on Short Interest-NOT Tied to Anomalies equals -0.083 (t-statistic = -4.46). Comparing these two estimates, our analysis implies that a 1% increase in anomaly-based short interest precedes 0.626% lower returns in the next month. An equivalent increase in non-anomaly-based short interest predicts (only) 0.083% lower future returns.15 In the end, it appears that anomaly-related shorting represents activity by informed short arbitrageurs 14 The estimates on the control variables are not tabulated. They are consistent with prior literature and available upon request. Rather than controlling for firm characteristics tied to the supply of lendable shares and/or non-anomaly-based shorting demand in the first-stage regression, one could include these firm characteristics as additional control variables in the FamaMacBeth regressions of stock returns on lagged measures of shorting activity. When doing so, we obtain very similar results to the ones presented in our current Table 5 (results available upon request). In addition, we note that when including both valueand momentum anomaly in the Anomaly Signal Score, our inferences regarding how anomaly-based short-selling activity contributes to short sellers’ profitability remain unchanged. The estimate on Short Interest-Tied to Anomalies turns to -0.586 (tstatistic = -2.45), while the estimate on Short Interest-NOT Tied to Anomalies turns to -0.088 (t-statistic = -4.97). These numbers imply that a 1% increase in anomaly-based short interest is followed by 0.59% lower returns, whereby a 1% increase in nonanomaly-based short interest is followed by (only) 0.09% lower returns. 15 24 7. Conclusion Investment companies that freely use strategies involving combinations of leverage and long/short positions in securities have been growing tremendously over the recent past. Given the growing relevance, natural questions arise as to their decision making process and their impact on financial markets. While basic and fundamental, these questions are difficult to assess empirically as these investment companies are not at liberty to disclose much information about their strategies. In this study, we study one aspect of arbitrage involvement, short arbitrage, which can be inferred from short interest data. We provide evidence that some strategies are more popular among short arbitrageurs than others. We identify these more popular strategies and suggest that their popularity is linked to their high average returns, low risk and diversification benefits. Short arbitrageurs do seem to resist the temptation to take large risks. We also provide evidence that short arbitrage involvement is informed and helps make markets more efficient. 25 References Armstrong, C., Vashishtha, R., 2012. Manager stock options, differential risk-taking incentives, and firm value. Journal of Financial Economics 104, 70–88. Baker, M., Wurgler, J., 2006. 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Journal of Finance 54, 207-225. Sloan, R.G., 1996. Do stock prices fully reflect information in accruals and cash flows about future earnings? Accounting Review 71, 289-315 Titman, S., Wei, K., Xie, F., 2004. Capital investments and stock returns. Journal of Financial and Quantitative Analysis 39, 677–700. White, H., 1980. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817-838. Xing, Y., 2008. Interpreting the value effect through the Q-theory: An empirical investigation. Review of Financial Studies 21, 1767-1795. 29 Appendix A.1 (Anomaly Description) The data are from the Center for Research in Security Prices (CRSP) and Compustat. We exclude stocks with a stock price < $5 as of portfolio formation. We further exclude stocks with one-digit SIC code = 6 (financial industry). Most of the variables used to forecast returns are measured once a year. Thus, we use information in June of calendar year t (incl. accounting data from the fiscal year ending in the previous calendar year t-1) to forecast the returns in July of t to June of t+1. The exception are the variables for anomaly 1, 2, 6, and 9, which are formed quarterly. In particular, Anomaly 1 (Failure Probability): Anomaly 2 (O-Score): Anomaly 3 (Total Accruals): Anomaly 4 (Net Operating Assets): Anomaly 5 (Gross Profitability): Anomaly 6 (Return on Assets): Anomaly 7 (Asset Growth): Anomaly 8 (Investment over Assets): Anomaly 9 (Post-earnings announcement drift (PEAD)): Anomaly 10 (Earnings-to-Price Ratio): Please see Chen, Novy-Marx, and Zhang (2010) for a detailed description. Please see Chen, Novy-Marx, and Zhang (2010) for a detailed description. ((∆ACTi,t-2,t-1 - ∆CHEi,t-2,t-1) - (∆LCTi,t-2,t-1 - ∆DLC i,t-2,t-1))/CEQi,t-1. NOAi,t-1/ATi,t-2, where NOA = (AT-CHE) – (AT-DLC-DLTT-MIB-PSTK-CEQ). (SALEi,t-1 – COGSi,t-1)/ATi,t-1. IBQi,t-1/ATQi,t-1. (ATi,t-1 –ATi,t-2)/ATi,t-2. (CEi,t-1/(CEi,t-2 + CEi,t-3 + CEi,t-4)/3) – 1, where CE = CAPX/SALE. ((EPSi,t-1 - EPSi,t-5)-Ci,t-1)/Sigma i,t-1, where EPS is IBQ/CSHOQ and Ci,t-1 and Sigma i,t-1 are the standard deviation and average, respectively, of (EPSi,t-1 - EPSi,t-5)over the preceding eight quarters. IBi,t-1/(CSHOi,t-1 * PRCC_Ci,t-1 30 Appendix A.1. Continued. New COMPUSTAT Data Item Legacy COMPUSTAT Data Item Description ACT AT CAPX CEQ CHE COGS CSHO CSHOQ DLC DLTT LCT MIB PRCC_C PSTK SALE ATQ IBQ 4 6 128 60 1 41 25 61 34 9 5 38 199 130 12 44 8 Current Assets - Total Assets - Total Capital Expenditures Common/Ordinary Equity - Total Cash and Short-Term Investments Cost of Goods Sold Common Shares Outstanding QUARTERLY: Common Shares Outstanding Debt in Current Liabilities - Total Long-Term Debt - Total Current Liabilities - Total Minority Interest (Balance Sheet) Price Close - Annual Preferred/Preference Stock (Capital) - Total Sales/Turnover (Net) QUARTERLY: Assets - Total QUARTERLY: Income Before Extraordinary Items 31 Appendix A.2 (Additional Points on the Methodology) Three additional facets of our empirical design may be noteworthy: First, in our analysis, we are agnostic about whether investors, shorting securities in the short leg, simultaneously purchase securities in the long leg. This is comparable to our uncertainty as to whether investors shorting individual firms for non-anomaly-based reasons (e.g., by skillfully processing publicly available news about the firm in question (Engelberg, Reed and Ringgenberg (2012)) also simultaneously go long on “positive-news firms.” As long-short strategies allow investors to hedge against industry- and market risk, our suspicion is that an observed disproportionate rise in short interest more often than not would be accompanied with offsetting positions in the long leg. Given the lack of direct evidence, however, we note that a rise in short selling is consistent with both short-only arbitrage and long-short arbitrage. A second note pertains to features of our analysis, either chosen by us to be conservative or born of necessity, which likely cause us to understate the true extent of anomaly-based shorting activity: (a) For one, because we orthogonalize short interest with respect to a very wide set of firm characteristics, we sometimes will miscategorize short interest that is grounded in anomaly-based shorting activity as non-anomaly-related. In this regard, we note that we observe stronger results when we base our analysis on raw short interest as opposed to abnormal short interest. (b) Short sellers trade in different stock universes and use different cutoff points, which results in different definitions of what constitutes a “short-leg security.” Influenced by this point, we form decile portfolios and report the average disproportionate change in short interest for each decile portfolio, i.e., we report the full distribution. (c) Moreover, short sellers use variations of the anomaly variable proposed in the academic literature (e.g., industry-adjustment), which again clouds the definition of what constitutes a “short-leg security.” We acknowledge this possibility, but we also suspect that whatever adjustment short sellers choose, the adjusted variable and the original variable are positively correlated with each other, thus still rendering our analysis useful. Finally, some firm characteristics against which short interest is residualized may be more correlated with the underlying anomaly variables than others. We have experimented with various permutations. We observe that the individual ranking as to which anomaly is the most popular changes slightly as we alter the set of firm characteristics against which short interest is residualized. However, the main conclusion that short sellers trade on anomalies and that they prefer strategies with high Sharpe Ratios and low correlations with other anomaly strategies remains. 32 Appendix A.3 (Raw Short Interest) This table mirrors Table 2, but we now base our analysis on raw short interest as opposed to abnormal short interest. Tstatistics are based on Newey-West (1987) standard errors with 36 lags and are reported in parentheses. (1) ∆RawShort in Long Leg (2) ∆RawShort in Short Leg (2) – (1) ∆∆RawShort Subsequent relative ∆RawShort for former ShortLeg Securities (1) Failure Probability 0.20% 0.54% (2) Ohlson’s O 0.22% 0.62% (3) Total Accruals 0.21% 0.54% (4) Net Operating Assets 0.30% 0.53% (5) Gross Profitability 0.29% 0.32% (6) Return on Assets 0.69% 0.55% (7) Asset Growth 0.02% 0.83% (8) Investment over Assets 0.23% 0.48% (9) PEAD 0.22% 0.71% (10) Earnings-to-Price Ratio 0.40% 0.28% 0.34% (3.21) 0.40% (2.65) 0.33% (3.72) 0.24% (2.37) 0.03% (0.22) -0.14% (-1.05) 0.81% (6.51) 0.25% (2.62) 0.49% (5.21) -0.12% (-0.93) -0.44% (-2.19) -0.39% (-0.64) -0.18% (-1.11) -1.63% (-2.85) 0.76% (0.63) -0.14% (-0.52) -0.50% (-3.91) -0.13% (-0.90) 0.14% (1.08) 0.63% (1.73) Anomalies 33 Appendix A.4 (Medians and Short Leg of One Anomaly Only) This table mirrors Table 2, but, in Panel A, we now report the time-series mean of the annual cross-sectional medians, and, in Panel B, we now report the time-series mean of the cross-sectional means based solely on securities that are in the short leg (long leg) of one anomaly only. T-values in Panel A are based on the Markov chain marginal bootstrap method proposed by He and Hu (2002) and are reported in square brackets. T-statistics in Panel B are based on Newey-West (1987) standard errors with 36 lags and are reported in parentheses. (1) ∆AbnShort in Long Leg (2) ∆AbnShort in Short Leg (2) – (1) ∆∆AbnShort Subsequent relative ∆AbnShort for former ShortLeg Securities (1) Failure Probability 0.01% 0.31% (2) Ohlson’s O -0.03% 0.25% (3) Total Accruals -0.11% 0.22% (4) Net Operating Assets 0.13% 0.09% (5) Gross Profitability -0.03% 0.15% (6) Return on Assets -0.33% 0.12% (7) Asset Growth -0.10% 0.35% (8) Investment over Assets -0.11% 0.21% (9) PEAD 0.00% 0.35% (10) Earnings-to-Price Ratio 0.06% 0.17% 0.30% [3.10] 0.26% [1.41] 0.29% [2.58] 0.05% [0.43] 0.07% [0.44] -0.24% [-1.45] 0.55% [6.53] 0.32% [2.02] 0.38% [3.39] -0.07% [-0.48] -0.42% [-2.36] -0.44% [-1.03] -0.08% [-0.63] -0.52% [-0.70] -0.86% [-0.65] -0.10% [-0.42] -0.15% [-0.46] -0.14% [-0.33] -0.19% [-1.02] 0.38% [1.42] 0.27% (1.74) 0.20% (0.94) 0.24% (1.91) 0.06% (0.65) -0.07% (-1.16) -0.55% (-3.14) 0.45% (3.15) 0.26% (2.31) 0.17% (1.26) 0.02% (0.10) -0.15% (-0.33) 0.67% (1.49) -0.57% (-1.62) -1.98% (-0.65) 0.38% (1.10) 0.45% (0.83) -0.25% (-0.77) -0.44% (-1.57) -0.25% (-1.38) 0.11% (0.38) Anomalies Panel A: Median Panel B: Mean (Short leg (Long leg) of one anomaly only) (1) Failure Probability -0.06% 0.21% (2) Ohlson’s O 0.02% 0.22% (3) Total Accruals -0.02% 0.21% (4) Net Operating Assets 0.05% 0.11% (5) Gross Profitability 0.15% 0.07% (6) Return on Assets 0.51% -0.04% (7) Asset Growth -0.15% 0.30% (8) Investment over Assets -0.01% 0.24% (9) PEAD -0.00% 0.18% (10) Earnings-to-Price Ratio 0.25% 0.27% 34 Appendix A.5 (Value and Momentum) This table mirrors Table 3 for the value- and the momentum anomaly. For the value-anomaly, when computing abnormal short interest, we do not orthogonalize short interest with respect to a stock’s market-to-book ratio. For the momentumanomaly, when computing abnormal short interest, we do not orthogonalize short interest with respect to a stock’s past market performance. T-statistics are based on Newey-West (1987) standard errors with 36 lags and are reported in parentheses. Anomalies (1) ∆AbnShort in Long Leg (2) ∆AbnShort in Short Leg (2) – (1) ∆∆AbnShort Subsequent relative ∆AbnShort for former ShortLeg Securities (1) Value -0.13% 0.39% (2) Momentum 0.18% 0.42% 0.52% (4.25) 0.24% (5.51) -1.12% (-2.97) -0.04% (-1.34) 35 Figure 2 Anomalies and Short Interest This figure plots changes in anomaly-based short selling for portfolios based on 10 anomalies. The sample period is 19882011. Every month t and for each anomaly i, we sort stocks into decile portfolios based on the anomaly variable in question, and we compute, for each decile portfolio, the average change in abnormal short interest (as described in Section 2.3). We plot the time-series mean of the cross-sectional means for each decile portfolio. A positive number implies that securities falling into that specific leg, on average, experienced a rise in anomaly-based short selling; a negative number implies that securities falling into that specific leg, on average, experienced a drop in anomaly-based short selling. The long- and short leg represent the two extreme deciles, with the long leg being the higher-performing decile as reported by previous studies. 36 Figure 2. Continued. 37 Table 1 Descriptive Statistics: Anomaly Returns This table reports summary statistics of returns based on 10 anomalies. The sample period is 1988-2012. Every portfolio formation month, we sort stocks into decile portfolios based on the anomaly variables described in Appendix A.1., and we construct value-weighted portfolio returns over the portfolio-holding period. In accordance with prior literature, for anomalies (3)-(5), (7)-(8) and (10), we form portfolios as of the end of each June in year t and compute returns from July in year t to June in year t+1. For anomalies (1)-(2), (6) and (9), we form portfolios as of the end of each calendar quarter and compute returns over the ensuing calendar quarter (e.g., portfolios are formed at the end of Mar2000 and returns on those portfolios are computed over the Apr2000:Jun2000 period). The longand short leg represent the two extreme deciles, with the long leg being the higher-performing decile as reported by previous studies. Panel A reports results for excess raw returns. Panel B reports results for benchmark-adjusted returns. The average benchmark-adjusted returns represent estimates of αi from the following time-series regression: (reti,t - rft) = αi + bi(MKTt-rft) + ci(SMBt) + di(HMLt) + εi,t. Monthly benchmark-adjusted returns equal αi + εi,t. All t-statistics are based on the heteroskedasticity-consistent standard errors of White (1980) and are reported in parentheses. Average Long Leg Average Short Leg 1.15% -0.04% (2) Ohlson’s O 1.09% 0.53% (3) Total Accruals 1.06% 0.44% (4) Net Operating Assets 1.27% 0.52% (5) Gross Profitability 1.24% 0.79% (6) Return on Assets 1.25% 0.61% (7) Asset Growth 1.03% 0.73% (8) Investment over Assets 0.98% 0.77% (9) PEAD 1.49% 0.42% (10) Earnings-to-Price Ratio 1.34% 0.82% Anomalies Panel A: Excess Raw Returns (1) Failure Probability Average Long- Minus Short Leg (LS) 1.19% (3.61) 0.56% (1.98) 0.61% (2.54) 0.76% (3.53) 0.46% (1.32) 0.64% (2.05) 0.29% (1.30) 0.20% (0.70) 1.07% (5.92) 0.52% (1.59) 38 StDev(LS) % Months where LS ≥ 0% % Months where LS < 0% Average(LS) across lowest 6 obs. 5.56% 60.99% 39.01% -14.65% 4.75% 54.96% 45.04% -12.85% 4.01% 57.25% 42.75% -10.07% 3.55% 59.78% 40.22% -8.44% 5.72% 55.80% 44.20% -18.31% 5.25% 58.16% 41.84% -13.27% 3.78% 52.90% 47.10% -9.61% 4.83% 51.09% 48.91% -13.66% 3.03% 65.96% 34.04% -6.91% 5.41% 54.35% 45.65% -14.09% Table 1. Continued. Anomalies Average Long Leg Panel B: Benchmark-Adjusted Returns (1) Failure Probability 0.29% Average Short Leg -1.30% (2) Ohlson’s O 0.31% -0.61% (3) Total Accruals 0.21% -0.52% (4) Net Operating Assets 0.33% -0.37% (5) Gross Profitability 0.51% -0.49% (6) Return on Assets 0.53% -0.47% (7) Asset Growth 0.10% -0.11% (8) Investment over Assets 0.05% -0.19% (9) PEAD 0.56% -0.44% (10) Earnings-to-Price Ratio 0.34% -0.27% Average Long- Minus Short Leg (LS) 1.59% (5.37) 0.92% (4.21) 0.72% (3.05) 0.70% (3.28) 0.99% (3.76) 0.99% (4.12) 0.21% (1.09) 0.23% (0.83) 1.00% (5.78) 0.60% (2.45) 39 StDev(LS) % Months where LS ≥ 0% % Months where LS < 0% Average(LS) across lowest 6 obs. 4.97% 67.38% 32.62% -12.03% 3.68% 57.09% 42.91% -9.50% 3.94% 60.87% 39.13% -9.69% 3.52% 57.25% 42.75% -8.63% 4.39% 63.77% 36.23% -13.65% 4.05% 58.87% 41.13% -8.16% 3.20% 49.64% 50.36% -7.73% 4.67% 49.64% 50.36% -13.09% 2.90% 64.54% 35.46% -6.46% 4.10% 58.70% 41.30% -10.23% Table 2 Descriptive Statistics: Correlation of Anomaly Returns This table reports the correlation matrix for returns based on 10 anomalies. We compute monthly benchmark-adjusted long-short portfolio returns as described in Table 1 and we report the Pearson Correlation Coefficient. P-values are reported in squared brackets. Anomalies (1) Failure Probability (2) Ohlson’s O (3) Total Accruals (2) (3) (4) (5) (6) (7) (8) (9) (10) 0.314 [0.00] -0.089 [0.14] -0.056 [0.36] 0.012 [0.84] 0.120 [0.05] 0.236 [0.00] 0.343 [0.00] 0.241 [0.00] -0.103 [0.09] -0.187 [0.00] 0.132 [0.03] -0.043 [0.47] 0.061 [0.31] 0.191 [0.00] 0.009 [0.88] 0.356 [0.00] 0.436 [0.00] 0.043 [0.48] 0.080 [0.19] 0.336 [0.00] -0.045 [0.45] 0.080 [0.19] 0.122 [0.04] -0.062 [0.30] 0.127 [0.03] 0.033 [0.58] 0.117 [0.05] -0.015 [0.80] -0.099 [0.10] -0.070 [0.24] -0.163 [0.07] -0.050 [0.42] 0.010 [0.87] -0.119 [0.05] -0.043 [0.48] -0.089 [0.14] 0.091 [0.13] -0.051 [0.40] -0.042 [0.49] 0.075 [0.21] -0.039 [0.51] 0.058 [0.34] -0.043 [0.48] -0.044 [0.47] -0.1046 [0.08] (4) Net Operating Assets (5) Gross Profitability (6) Return on Assets (7) Asset Growth (8) Investment over Assets (9) PEAD (10) Earnings-to-Price Ratio 40 Table 3 Short Sellers’ Involvement in Anomaly Strategies This table reports changes in anomaly-based short selling for portfolios based on 10 anomalies. The sample period is 1988-2011. Every month t and for each anomaly i, we sort stocks into decile portfolios based on the anomaly variable in question. We compute ∆AbnShort(Short-Leg) and ∆AbnShort(Long Leg), where the long- and short leg represent the two extreme deciles, with the long leg being the higher-performing decile as reported by previous studies, and where ∆AbnShort represents the average change in abnormal short interest (as described in Section 2.3). A positive number implies that securities falling into that specific leg, on average, experienced a rise in anomaly-based short selling; a negative number implies that securities falling into that specific leg, on average, experienced a drop in anomaly-based short selling. We report the time-series mean of the cross-sectional means. The final column measures the average ∆AbnShort of securities that, subsequent to portfolio formation, fall out of the short leg relative to that of former long-leg securities. All t-statistics are based on Newey-West (1987) standard errors with 36 lags and are reported in parentheses. (1) ∆AbnShort in Long Leg (2) ∆AbnShort in Short Leg (2) – (1) ∆∆AbnShort (1) Failure Probability 0.00% 0.31% (2) Ohlson’s O 0.05% 0.26% (3) Total Accruals -0.10% 0.20% (4) Net Operating Assets 0.08% 0.22% (5) Gross Profitability 0.03% 0.11% (6) Return on Assets 0.36% 0.22% (7) Asset Growth -0.17% 0.39% (8) Investment over Assets -0.10% 0.23% (9) PEAD 0.03% 0.41% (10) Earnings-to-Price Ratio 0.02% 0.22% 0.31% (2.77) 0.21% (1.60) 0.31% (4.43) 0.14% (1.74) 0.08% (0.94) -0.14% (-1.17) 0.55% (5.46) 0.33% (3.42) 0.38% (3.77) -0.21% (-1.80) Anomalies Subsequent relative ∆AbnShort for former Short-Leg Securities Panel A: Full Sample Period 41 -0.40% (-2.09) -0.42% (-0.70) -0.08% (-0.61) -0.81% (-1.53) -0.56% (-0.52) -0.44% (-1.66) -0.15% (-1.10) -0.14% (-0.99) -0.51% (-0.98) 0.38% (1.10) Table 3. Continued. Anomalies ∆∆AbnShort: 1988 - 2000 ∆∆AbnShort: 2001- 2011 0.21% (1.71) 0.17% (1.14) 0.29% (3.89) 0.09% (1.00) 0.04% (0.45) -0.09% (-0.57) 0.38% (3.38) 0.20% (1.72) 0.14% (1.35) -0.15% (-1.14) 0.39% (2.07) 0.31% (1.35) 0.33% (2.65) 0.19% (1.39) 0.12% (0.82) -0.21% (-1.06) 0.74% (4.65) 0.48% (3.13) 0.64% (3.76) -0.27% (-1.36) Panel B: Subperiods (1) Failure Probability (2) Ohlson’s O (3) Total Accruals (4) Net Operating Assets (5) Gross Profitability (6) Return on Assets (7) Asset Growth (8) Investment over Assets (9) PEAD (10) Earnings-to-Price Ratio 42 Table 4 Short Sellers’ Involvement in Anomaly Strategies: Determinants of Anomaly Popularity This table reports estimates from regressions of our measure of short sellers’ involvement in anomaly strategies on lagged anomaly characteristics. The observations are on an anomaly/year-month level. Every month t and for each anomaly i, we sort stocks into decile portfolios based on the anomaly variable in question, and we compute, for each decile portfolio, the average change in abnormal short interest (as described in Section 2.3). Our dependent variable is the spread between ∆AbnShort(Short-Leg)i,t and ∆AbnShort(Long-Leg)i,t. The independent variables are all lagged and are: (1) Correlation with Other Anomalies, which is the rolling five-year Pearson correlation coefficient between the strategy’s monthly benchmark-adjusted short-portfolio return and the monthly anomaly index, which represents the benchmark-adjusted return of a portfolio that invests an equal portion in each of the 10 anomaly-based short portfolios considered in this study. (2) Sharpe Ratio, which is the average monthly benchmark-adjusted shortportfolio return over the previous five years (multiplied by negative one) divided by its standard deviation. (3) Past Performance, which is the average monthly benchmark-adjusted short-portfolio return over the previous five years (multiplied by negative one). (4) Past Return Std. Dev., which is the standard deviation of monthly benchmarkadjusted short-portfolio returns over the previous five years. (5) Downside Risk, which is the rolling five-year 99th percentile of monthly benchmark-adjusted short-portfolio returns (multiplied by negative one). (6) Upside Potential, which is the rolling five-year 1st percentile of monthly benchmark-adjusted short-portfolio returns (multiplied by negative one). The t-statistics account for time-series dependence and cross-sectional dependence and are reported in parentheses (please see Section 3.3 for more details). *,**,*** denote statistical significance at the 10%, 5% and 1% level, respectively. Variables Correlation with Other Anomalies Sharpe Ratio (1) -0.679*** (-2.83) 0.521*** (2.50) Past Performance Past Return Std. Dev. (2) (3) -0.611*** (-2.46) -0.605** (-2.42) 17.264*** (2.78) -7.603* (-1.91) 21.803*** (3.23) Downside Risk (4) 12.415** (2.29) -9.115*** (-3.12) -3.605** (-2.20) 2,120 2.45 2,120 2.72 43 2,120 3.10 18.761** (2.34) -4.667** (-2.52) -1.524 (-0.74) Upside Potential Number of Observations Adj. R-square [%] (5) 2,120 1.20 2,120 1.66 Table 5 Short Sellers’ Involvement in Anomaly Strategies and Short Sellers’ Profitability This table reports estimates from Fama-MacBeth regressions of future returns on short interest and a measure of short sellers’ involvement across anomaly strategies. The observations are on an anomaly/year-month level. In Column (1), the dependent variable is short interest and the independent variables are Anomaly Signal Score, which is the number of anomalies in which the stock is in the short leg of, as well as Institutional Holdings, ln(Market Capitalization), ConvertibleSecurity, IdiosyncraticVolatility, Beta, ln(Market/Book), and PastReturn (all described in Section 2.3). We only tabulate the estimate on Anomaly Signal Score. In Columns (2)-(3), the dependent variable is the monthly stock return at time t+1. The independent variables are all as of time t. In Column (3), we first estimate a regression of short interest on Anomaly Signal Score, Institutional Holdings, ln(MarketCapitalization), ConvertibleSecurity, IdiosyncraticVolatility, Beta, ln(Market/Book), and PastReturn. Short Interest-Tied to Anomalies is the fitted value tied to Anomaly Signal Score; Short Interest-NOT Tied to Anomalies is the fitted value tied to the other independent variables plus the residual. T-statistics are reported in parentheses. *,**,*** denote statistical significance at the 10%, 5% and 1% level, respectively. Short Interest Stock Returns Variables (1) Anomaly Signal Score (2) 0.006*** (9.05) Short Interest -0.094*** (-5.08) Short Interest – Tied to Anomalies -0.626*** (-6.23) -0.083*** (-4.46) Short Interest – NOT Tied to Anomalies Number of Observations Average Adj. R-square [%] (3) 292 19.37 44 292 0.39 292 0.45

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