Short-Term Reversals: The Effects of Institutional Exits and Past Returns. Si Cheng Allaudeen Hameed Avanidhar Subrahmanyam Sheridan Titman

Transcription

1 October 25, 2014 Short-Term Reversals: The Effects of Institutional Exits and Past Returns Si Cheng Allaudeen Hameed Avanidhar Subrahmanyam Sheridan Titman Cheng is from Queen s University Management School, Belfast. Hameed is from the National University of Singapore. Titman is from the McCombs School of Business, University of Texas at Austin. Subrahmanyam is from the Anderson School, University of California at Los Angeles. We thank Aydogan Alti, Tarun Chordia, Elroy Dimson, John Griffin, Raghu Rau, Pedro Saffi, Tao Shu, Elvira Sojli, Avi Wohl, and seminar participants at ABFER and Asian Finance Association conferences, Erasmus University, Hebrew University Conference to Honor Dan Galai and Itzhak Venezia, Hong Kong University of Science and Technology, National University of Singapore, Rutgers University, Stevens Institution of Technology, University of Cambridge, University of Queensland, and the University of Texas at Austin for helpful comments. Corresponding author: Avanidhar Subrahmanyam (subra@anderson.ucla.edu), The Anderson School at UCLA, 110 Westwood Plaza, Los Angeles, CA , telephone (310)

2 Abstract Short-Term Reversals: The Effects of Institutional Exits and Past Returns Return reversals depend on de facto market making by active informed investors as well as uninformed market makers. Accordingly, we find that reversals are higher following declines in the number of active institutional investors. Price declines over the past quarter, which serve as a proxy for declines in active investors, lead to stronger reversals across the subsequent two months; indeed reversals are concentrated primarily in past quarter losers. We provide evidence that price pressure induced by fire sales in response to past stock price drops cannot fully account for our results. Further, the evidence is consistent with market makers reacting more quickly to changes in the number of informed investors in the more recent period, particularly for large firms.

3 1 Introduction Since the discovery of the phenomenon of monthly reversals by Jegadeesh (1990), considerable effort has been spent to understand why these reversals occur. A common explanation for the reversals is that they provide compensation to liquidity providers for bearing inventory imbalances. 1 This explanation raises the issue of whether reversals are less pronounced when liquidity provision is more effective and vice versa. In this paper we shed light on this question by arguing that reversals do vary with the effectiveness of liquidity provision. In doing so, we provide new empirical evidence on the determinants of cross-sectional variation in monthly contrarian profits. Specifically, we investigate the notion that shifts in liquidity provision, which arise from the entrance and exits of active investors, affect the magnitude of return reversals. To motivate our empirical analysis, we present a basic model where liquidity is provided by two groups: traditionally informed traders, and quantitative traders or market makers, who are uninformed about fundamentals, but make trades based on their knowledge of the price process. Because these investors are risk averse, the random liquidity demands of the noise traders generate negative serial correlation in stock returns. Our model allows for endogenous entry of uninformed market makers and exogenous shocks to the number of informed investors, which might arise from (unmodeled) shocks to either the costs or the benefits of becoming informed. Regardless of the cause, numerical analysis shows that when a shock to informed participation is followed by an offsetting change in the participation by market makers, there is only minor changes in expected return reversals. 2 However, as we illustrate, a decrease in 1 Conrad, Kaul and Nimalendran (1991), Jegadeesh and Titman (1995), and Kaniel, Saar and Titman (2008) discuss how market microstructure phenomena such as inventory control effects can cause reversals. The inventory theory of price formation has been elucidated by Stoll (1978), Ho and Stoll (1983), O Hara and Oldfield (1986), Grossman and Miller (1988), and Spiegel and Subrahmanyam (1995). 2 As we discuss later, because the risk of the stock (conditional on the market price) will change 1

4 informed participation, which cannot be immediately offset by market maker participation, does lead to an increase in the magnitude of return reversals. This main implication, that a shock to informed participation reduces liquidity provision, and thus increases return reversals, is the focus of our empirical analysis. Specifically, we look directly at the relation between the magnitude of return reversals and changes in the percentage of informed institutional investors who hold each stock in our sample. We use measures of active institutional investors proposed in Aberbanell, Bushee and Raedy (2003) and Gasper, Massa and Matos (2005) as proxies for the number of informed investors that actively follow and trade the stock. The return reversals are based on stock returns measured relative to the market (Jegadeesh (1990)) or returns relative to the industry benchmark (Da, Liu and Schaumburg (2014) and Hameed and Mian (2014)). In all specifications, we find that the magnitude of return reversals is higher for those stocks that experience a decline in the percentage of active institutional holdings during the previous quarter. While the average risk-adjusted reversal profit is insignificant for all stocks during the sample period, it becomes highly significant when conditioned on stocks with declines in active institutional holdings. For example, the reversal strategy based on returns in formation month 0 and holding period being month 1, yields significant risk-adjusted profits of between 0.5 to 0.63 percent per month across all size groups when conditioned on decreases in percentage of active institutional investors (Gasper, Massa and Matos (2005)) over the months 3 to 1. On the other hand, the reversal profits are small and not significantly different from zero for the stocks that had an increase in active investors in the previous quarter. Although these findings are consistent with our model, the estimated relation between return reversals and changes in institutional ownership is weaker for large stocks in the recent decade. There are at least two potential explanations for the when the number of informed investors change, return reversals can change. This is likely to be a second order effect. 2

5 relatively weak evidence in the post-2000 period. The first explanation is that the provision of liquidity was more efficient in the recent decade for the large firms. In particular, a reduction in the liquidity provided by institutional investors may be quickly offset by an increase in liquidity provision from market makers for these stocks. The second explanation has to do with distortions that can arise from endogeneity and measurement issues. Specifically, anticipated changes in liquidity may influence the portfolio choices of the active institutional investors, so we may have a reverse causality problem. In addition, the stock level holdings of active institutions is only available at quarterly intervals, implying a time lag in the measurement of changes in institutional holdings and the monthly reversal strategy returns. To address these issues we use past returns as a proxy for changes in informed investor participation. We propose that past returns may influence institutional exits because of the following arguments. First, institutional funds holding stocks that have performed poorly may face more outflows and be forced to sell some of the stocks they own. Alternatively, window-dressing concerns, viz. Ritter and Chopra (1989), and Asness, Liew and Stevens (1997), might deter the inclusion of loser stocks in institutional portfolios. 3 As we show, the percentage of active institutional investors holding a stock does indeed decline following large negative stock return realizations. Our linking of past returns and contrarian profits, however, is based on the premise that past stock price performance is a better proxy for informed investor participation than institutional exits. We argue that this can be the case because past returns are updated each month, unlike the institutional holdings data, which are available only at quarterly 3 Negative stock returns can also ensue from institutional selling that is prompted by unfavorable information. With short-selling constraints, institutions have less incentive to actively collect information on stocks that they do not own, so any event that prompts institutional selling is likely to lead to decreased market making capacity and increased contrarian profits. Finally, it should be noted that institutions may be selling losers to capture the momentum effect documented in Jegadeesh and Titman (1993). However, our results hold when the reversal profits are momentum-adjusted as well. 3

6 intervals. Further, while we do not consider this in our model, behavioral biases can generate links between past returns and the participation of active investors. Indeed, since these biases (e.g., the Barberis, Shleifer and Vishny (1998) extrapolation bias and the Daniel, Hishleifer and Subrahmanyam (1998) self-attribution bias), can affect active individuals as well as smaller institutions that are not included in our institutional database, past returns may capture this phenomenon better than institutional exits we do observe. We find that the profitability of the monthly return reversal strategies is substantially larger if stock return in the prior quarter is strongly negative. Specifically, the negative relation between returns in month 0 and month 1 is much stronger for stocks that experienced the lowest returns in months 3 through 1. We find that the riskadjusted profits from the reversal strategy is large and significant only for stocks that belong to the lowest quintile based on returns in the prior quarter (i.e., months 3 to 1). The average monthly risk-adjusted reversal profit for these loser quintile stocks ranges from 0.81 percent to 1.68 percent, across all size groups. On the other hand, there is no reliable evidence of return reversals among stocks that are not extreme losers in the previous quarter. Moreover, in the post-2000 period, unconditional contrarian profits are statistically zero, and we find evidence of risk-adjusted profits only among stocks that had declined in value in the previous quarter. For example, among the stocks in the loser quintile, the industry-adjusted reversal profit in the post-2000 period ranges from 0.63 to 1.83 percent per month for the large, small and microcap stocks. Our main findings are robust to alternative explanations. First, our findings are present when we exclude January months from the sample, indicating that the relation between reversals and institutional participation is not simply a consequence of tax loss selling but is driven by withdrawal of liquidity by institutions. Second, we use the Fama-MacBeth cross-sectional regression approach to examine the individual 4

7 stock level relation between reversals and declines in holdings of active institutions (and returns in the prior quarter). Again, we find that the monthly reversals are significantly stronger if the stock experienced a decline in active institutional ownership or had a negative returns in the prior quarter, consistent with our prediction of reduction in liquidity provision for these stocks. The latter evidence is unaffected when we control for other firm characteristics that have been shown to be related to cross-sectional differences in return reversals. These firm characteristics include illiquidity, turnover and volatility (see, Avramov, Chordia and Goyal (2006), Huang, Liu, Rhee and Zhang (2010), Nagel (2012)). Finally, we perform a series of tests to shed light on another possible explanation: that reversals are accentuated after low past returns owing to price-pressure inducing fire sales by institutions following a prolonged period of low returns. The notion here is that after incurring losses over three months, institutions sell stocks in the subsequent month, causing a further decline in that month, and a subsequent reversal. We show, however, that among three-month losers, turnover is not higher for one month losers relative to one month winners. Further, the profits to reversals do not solely or primarily emanate from one month losers. These tests indicate that while the fire sales hypothesis cannot be fully ruled out, the notion that lower institutional presence is associated with lower liquidity supply and greater reversals receives reliable support from the data. Our research is part of a large and growing literature that examines short-term return reversals. For example, in addition to Da, Liu and Schaumburg (2014) and Hameed and Mian (2014), there are a number of papers that refine the reversal strategy by subtracting out returns that are likely generated by fundamental information rather than liquidity trades. Other studies, like Avramov, Chordia and Goyal (2006), Da and Gao (2010), Hameed, Kang and Viswanathan (2010), and Nagel (2012) refine the strategy by identifying stocks (and times) where liquidity shocks are expected to 5

8 be especially strong. For example, Da and Gao (2010), who are primarily interested in explaining the abnormal high returns of distressed stocks, provide evidence that most of the abnormal returns are due to reversals of negative returns generated by price pressure when institutional investors sell these stocks. In contrast, our empirical analysis assumes that institutions are informed liquidity providers, and examines shocks to liquidity provision that occur as a result of exits by these informed institutions. There are also a number of papers that consider the role of informed investors in the provision of liquidity. Indeed, our model adapts Grossman and Stiglitz (1980) by taking the number of informed investors as exogenous and focusing attention on the endogenous entry of active uninformed investors who act as market makers. 4 Several more recent papers provide detailed analyses of how informed investors provide liquidity. 5 However, we are the first to explicitly look at how the interaction of informed traders with an endogenous supply of uninformed liquidity providers affects the magnitude of reversals. Our paper is also related to more recent work that explores the link between institutional investor holdings and liquidity during the crisis period. For example, Aragon and Strahan (2012) show a significant decline in the liquidity of stocks held by Lehman-connected hedge funds following the Lehman bankruptcy in September 2008 and Anand, Irvine, Puckett and Venkataraman (2013) show that withdrawal of liquidity-supplying institutional investors during financial crisis amplified the illiquidity of the stocks, particularly the riskier securities. Despite this evidence around the crisis, our paper suggests that perhaps because of the introduction of uninformed quantitative traders, the disruptions to liquidity supply following institutional exits has decreased over time, particularly for large firms. 4 Campbell, Grossman, and Wang (1993) also present a model of reversals caused by the risk aversion of market makers who absorb the order flow of outsiders. In contrast to their model, we allow for endogenous entry of market makers, and exogenous shifts in the mass of informed agents. 5 For example, Bloomfield, O Hara and Saar (2005), Kaniel and Liu (2006), Goettler, Parlour and Rajan (2009), Boulatov and George (2013) and Rosu (2014) examine the incentives of informed investors to use limit orders and thus supply liquidity. 6

9 The paper is organized as follows: Section 2 presents the theoretical model that motivates our empirical tests. Section 3 describes our data and presents the empirical results, and Section 4 concludes the paper. All proofs, unless otherwise stated, appear in Appendix A. 2 The Model 2.1 The Stock Market We model the stock price of a single firm that is born at date 0; investors trade the stock at date 1, and the firm s cash flows, which are realized at date 2, are expressed as follows, F = θ + ɛ. (1) The variables θ and ɛ represent exogenous shocks; ɛ is not revealed until date 2, but θ can be observed by informed investors at date 1. These variables have zero mean and are mutually independent and normally distributed. We adopt a standard rational expectations model (e.g., Grossman and Stiglitz, 1980). There are masses m of informed agents and n of uninformed market-makers, each with negative exponential utility with risk aversion R. The first group can be viewed as hedge funds, mutual funds and other investors that actively collect fundamental information about firm cash flows. These investors learn the realization of the shock θ perfectly after date 0 and prior to trade at date 1. The second group can be viewed as high frequency traders and other quantitative hedge funds that do not have access to fundamental information but try to make money from short-term price movements. We assume that the shares that active investors trade are in zero net supply on average. One interpretation is that the market portfolio is held by relatively passive investors, generally hold the market portfolio, and trade only when they are subject to 7

10 exogenous liquidity shocks that affect the supply of shares available to the informed and uninformed investors that we model. We represent this additional demand of liquidity traders by z (or supply by z), which is normally distributed with mean zero, and independent of all other random variables. 6 Throughout the paper we denote the variance of any generic random variable, η, by v η. The number of active investors, both m and n, are initially assumed to be determined exogenously; however, we will later relax this assumption and consider a case where the mass of market-makers is endogenous. One interpretation is that we will be considering conditions under which formerly passive investors choose to expend resources to actively monitor market conditions. 2.2 Reversals The rational expectations equilibrium of the model is derived in the Appendix A. Note that the date 0 price is not stochastic since the information and participation shocks are realized only at date 1. The serial covariance of price changes can therefore be expressed as cov(f P, P ). We denote the corresponding serial correlation by ρ. Straightforward calculations lead to the following proposition: Proposition 1 1. The serial covariance of price changes is always negative. 2. The absolute magnitude of the serial correlation in price changes, ρ, is decreasing in m, and n, the masses of informed agents and market makers, respectively. 3. The serial correlation ρ goes to zero as n or as m. The negative serial covariance of price changes is a standard result; an unanticipated increase (decrease) in liquidity trades reduces (increases) the stock s risk premium since the change in holdings by these traders must be held by risk averse active traders who demand risk premiums. An increase (decrease) in the risk premium 6 The analysis is unchanged if we model z as an shock to the informed agents endowment. 8

11 decreases (increases) the date 1 price, thereby decreasing (increasing) the expected date 2 return. The magnitude of these return reversals depends on both the risk aversion and the mass of the active investors. In particular, a decrease in the mass of either informed agents or market makers reduces the risk-bearing capacity of the market, thus increasing the magnitude of the reversal in asset returns. If the mass of either of these agents increases arbitrarily, in the limit, risk-bearing capacity of the market goes to infinity and the serial correlation goes to zero. 2.3 Entry of Market Makers Up to now, the number of active investors has been exogenous. We now relax this assumption and allow market makers to freely enter the market. In particular, uninformed passive investors can pay a cost c to monitor market conditions and become an active market maker. Since the expected utility from market making decreases in n, the number of market makers (as shown in Appendix A), n is decreasing in c. Thus, Part 2 of Proposition 1 immediately yields the following proposition: Proposition 2 A decrease in the cost of market making reduces the magnitude of reversals in asset returns. The above proposition suggests that changes in technology and regulations that make it less costly for investors to actively monitor market prices and trade will reduce the magnitude of return reversals. The observed decline in return reversals in more recent times is thus consistent with this proposition. It should also be noted that a change in the number of informed investors, m, can influence price patterns very differently when the number of market makers endogenously respond to these changes. As we showed in Proposition 1, an exogenous change in m alters the serial correlation in price changes when the number of market makers n is held constant. However, as we will show, when market makers can enter 9

12 (and exit) the market, a change in the number of market makers more than offsets the change in informed investors. Specifically, tedious but straightforward calculations lead to the following proposition: Proposition 3 With endogenous entry of market makers, the magnitude of the serial correlation is increasing in the total mass of informed agents, m. Essentially, all else held constant, an increase in the mass of informed investors decreases reversals. However, the expected change in reversals leads to a decrease in the number of market makers, which, in turn, increases reversals. The latter effect more than offsets the former because of the effect of the number of informed investors on the risk borne by the market makers. Our numerical simulations, however, indicate that the magnitude of the net effect is quite small. In general, across a wide range of parameter values, a proportional change in m of 10% results in a proportional change of less than 1% in the serial correlation. In other words, we do not expect a change in informed investors to have a material effect on the magnitude of return reversals when their effect can be offset by the entry of uninformed market makers. 2.4 The Case Where the Mass of Informed Traders is Uncertain The discussion in the last subsection assumes that uninformed investors decide on whether or not to become market makers after observing the number of informed investors. We now consider a scenario where the mass of informed agents, m, is random, and market makers make their entry decision prior to observing the mass of informed traders. As a result, shocks to the number of informed traders are not immediately offset by changes in the number of market makers. To keep our analysis simple we assume that m can take on one of two possible values: m l with probability p and and m u with probability 1 p, with m u > m l. We then have the following proposition. 10

13 Proposition 4 Suppose that market makers enter based on a distribution of m without observing the realization of m. Then reversals are greater when the realization of m is m l rather than m u. Moreover, the magnitude of the reversals are greater in this case than they would be if market makers enter after observing that m = m l. Similarly, the magnitude of the reversals are lower when m=m u is unanticipated, relative to the magnitude for the case when m = m u is known prior to the entry choice. To illustrate and quantify the relation between the entry of market makers and the magnitude of reversals consider the parameter values v θ = v ɛ = v z = R = m l = 1, m h = 2, p = 0.5, and c = Suppose that market makers know that m l = 1. With these parameters, and the assumption that market makers enter knowing the mass of informed traders, the equilibrium number of market makers, is 4, and the serial correlation is Now consider a scenario where market makers do not know the realization of m, and hence enter based on the two-point distribution of m. In this case, the equilibrium mass of market makers is 2.5, and when m is revealed to be equal to m l, the serial correlation is Thus, reversals are stronger when market makers do not respond to a drop in the mass of active investors. [An analogous example can be constructed for the case where the realization of m = m h = 2.] In summary, the model presented in this section suggests that in a setting where market makers enter based on the expected number of informed traders, return reversals will be stronger following a negative shock to the number of informed investors. Secondarily, it suggests the intuitive notion that any secular innovation that reduces the costs of entry to market making will reduce reversals. In the next section, we test these implications. 11

14 3 Empirical Results The focus of the rest of the paper is on examining the change in the magnitude of return reversals that arises from changes in the number of informed investors, and we examine the pre- and post-2000 periods separately to explore the effect of innovations that occurred after 2000, which may have reduced the costs associated with market making. 3.1 Data and Methodology Our sample consists of all NYSE/AMEX/Nasdaq common stocks with share code 10 or 11, obtained from the Center for Research in Security Prices (CRSP). The full sample period starts in January 1980 and ends in December Our sample begins in 1980 as some of the firm specific variables we consider are only available from the 1980s. In order to minimize microstructure biases emanating from low priced stocks, we exclude penny stocks whose prices are below $5 at the end of each month. Our primary methodology involves sorting into quintiles based on stock returns in month t and evaluating returns in month t + 1. We implement the conventional contrarian strategy by taking long positions in the bottom quintile of stocks (loser portfolio) in the past month and shorting the stocks in the top quintile (winner portfolio). The zero-investment contrarian profit (Jegadeesh, 1990) is computed as the loser minus winner portfolio returns in month t + 1. The contrarian profits represent the returns to supplying liquidity (Stoll, 1978; Grossman and Miller, 1988; Nagel, 2012; and others). More recently, Hameed and Mian (2014) show that the monthly price reversal, and, in turn, the return to providing liquidity, is better identified using industry-adjusted returns, which presumably, contain less noise arising from price reactions to public information and thus increase the signal coming from order imbalances (or liquidity demand). Specifically, they 12

15 use deviations of monthly stock returns from the average return on the corresponding industry portfolio to sort stocks into winner and loser portfolios. Thus, as an alternative approach, we construct industry-adjusted contrarian portfolios by sorting stocks into loser and winner quintiles based on the industry-adjusted stock returns. Following Hameed and Mian (2014), we rely on the Fama and French (1997) system of classifying firms into 48 industries based on the four-digit SIC codes. We report the contrarian portfolio returns in month t + 1 for all stocks as well as stocks sorted into size groups. The analysis across size groups is motivated by recent findings in Fama and French (2008), who show that equal-weighted long-short portfolios may be dominated by stocks that are plentiful but tiny in size. On the other hand, value-weighted portfolios are dominated by a few large firms, and hence, the resulting portfolio returns are not representative of the profitability of the strategy. Thus, following Fama and French (2008), we group stocks into three categories based on the beginning of period market capitalization: microcaps (defined as stocks with size less than the 20th NYSE size percentile); small firms (stocks that are between the 20th and 50th NYSE size percentiles) and big firms (stocks that are above the 50th NYSE size percentile). In addition to the equal-weighted raw contrarian portfolio returns for each category of stocks, we report alphas from a four-factor model that consists of the three Fama and French (1993) factors: the market factor (excess return on the valueweighted CRSP market index over the one month T-bill rate), the size factor (small minus big firm return premium, SM B), the book-to-market factor (high book-tomarket minus low book-to-market return premium, HM L), as well as the Pástor and Stambaugh (2003) liquidity factor. The alphas we report in the paper are robust to the addition of the momentum factor in a five-factor model, suggesting an insignificant exposure to the factor (results are available upon request). The standard errors in all the estimations are corrected for autocorrelation with three lags using 13

16 the Newey and West (1987) method. Information about institutional investors is extracted from Thomson-Reuters Institutional Holdings (13F) database. 7 We break down the institutional investors into informed and uninformed types following Abarbanell, Bushee and Raedy (2003) (ABR), where the informed institutions are defined as investment companies and independent investment advisors, which are generally considered to be active investors. We exclude other institutions, such as bank trusts, insurance companies, corporate/private pension funds, public pension funds, university and foundation endowments, who have longer investment horizons and trade less actively. 8 We compute the percentage of shares held by informed institutional investors in a firm at the end of each quarter, labeled as Informed IO and denote a change in the holdings of informed institutional investors over the quarter as Informed IO. Details on the construction of all variables are provided in Appendix B. Since our theory focuses on the liquidity provided by informed investors, it is natural to ask whether active institutions, such as those defined in ABR, are actually informed. The existing evidence suggests that short-term active institutional investors are likely to be informed. For example, Ke and Petroni (2004) show that transient institutional investors are able to predict a break in a string of consecutive quarterly earnings increases. Yan and Zhang (2009) find that changes in the holdings of short-term institutional investors predict one quarter ahead stock returns. Consistent with the notion that the active institutional investors are informed, we find a significant positive relation between Informed IO for stock i in quarter q and the return on stock i in the subsequent quarter. As shown in Appendix C, Table C1, in (Fama-MacBeth) cross-sectional regressions of quarterly returns of individual stocks, 7 The institutional ownership data come from quarterly 13F filings of money managers to the U.S. Securities and Exchange (SEC). The database contains the positions of all the institutional investment managers with more than $100 million U.S. dollars under discretionary management. All holdings worth more than $200,000 U.S. dollars or 10,000 shares are reported in the database. 8 We thank Brian Bushee for making the institutional investor classification data available at this website: 14

17 we find that Informed IO in the past quarter (or a dummy variable indicating increases in Informed IO) significantly predicts future stock returns. On the other hand, similar increases in the holdings of other institutions defined by Abarbanell, Bushee and Raedy (2003) as inactive investors (which we denote as Uninformed IO) are not related to subsequent stock returns. These findings account for the predictive effects of other firm characteristics such as firm size, book-to-market ratio and past returns. Following the work by Gaspar, Massa and Matos (2005) and Yan and Zhang (2009), we also consider an alternative definition of active institutional investors based on institutions portfolio turnover. Intuitively, short-term investors buy and sell the stocks in their portfolios frequently. Each institutional investor s quarterly churn (or turnover) rate is measured based on the purchase and sale of stocks in their portfolio. We classify those institutions with turnover rates above the median turnover ratio of all institutions in the past four quarters as short term investors or Short- Term IO, while the remaining institutions are labelled as Long-Term IO. Using a similar definition, Yan and Zhang (2009) find that short-term institutional investors are better informed. 3.2 Short-Term Reversals and Institutional Exits Table 1 contains the returns to the monthly contrarian investment portfolios. In Panel A, we report the returns to the contrarian portfolio strategy formed using unadjusted stock returns. Over the sample period, the (equal-weighted) average contrarian return across all stocks is a significant 0.54 percent per month (t-statistic=2.86). We also obtain significant raw profits in each of the three groups of microcaps, small, and big firms. The profits weaken considerably after adjusting for risk exposures using the four-factor model and become insignificant, except for microcaps. Our model predicts that the magnitude of reversals is affected by the presence of 15

18 informed investors. Ceteris paribus, an increase (decrease) in the number of informed investors should decrease (increase) the magnitude of the stock s return reversals. For our initial test of this proposition, we examine changes in the percentage of shares held by informed institutional investors for each stock, proxied by Informed IO. Specifically, we separately examine the return patterns for two groups of stocks: those that experienced a decline in informed investor holdings over the quarter prior to month t 1, and those that did not. As Figure 1 illustrates, we measure the change in institutional ownership over months t 3 to t 1, and evaluate contrarian profits across the portfolio formation month t, and the holding period, month t + 1. Panel A of Table 1 shows that return reversals are stronger following a decrease in informed institutions. For the sample of all stocks, the risk-adjusted contrarian strategy yields a significant 0.51 percent per month when there is a decline in informed institutions, while the returns are insignificant at 0.10 percent for firms that had an increase in informed institutional investors. The risk-adjusted contrarian profit is significantly higher for the group of stocks that experience a drop in informed institutional ownership compared to the stocks that had an increase in institutional ownership. We obtain the same findings for stocks grouped into large firms, small firms and microcaps. Consistent with Hameed and Mian (2014), the reversal profits reported in Panel B of Table 1 are larger in each size category when the portfolios are formed using industry-adjusted returns. For instance, the contrarian profit for all firms increases to 1.02 percent (t-statistic=7.27), with a risk-adjusted return of 0.84 percent (t-statistic=5.93). The industry-adjusted contrarian profits are significant in each of the size groups, with risk-adjusted returns ranging from 0.46 percent (big firms) to 1.04 percent (microcaps). More importantly, we find that the industry-adjusted reversals are stronger for stocks that had a drop in institutional ownership in the previous quarter. For all firms, the risk-adjusted contrarian profits is 0.97 percent 16

19 following institutional exits, which is significantly higher than the contrarian profits for firms that had an increase in institutional presence. Similar findings hold for the contrarian investment strategy implemented within each of the three size groups, although the additional profits for stocks that have fewer institutional investors are not statistically significant for the big firms. Our findings are robust to defining informed investors as those institutions that generate higher turnover, or Short-Term IO. As shown in Panel C of Table 1, decreases in the holdings by Short-Term IO in months t 3 to t 1 are associated with significant reversals of stock returns from t to t + 1. We obtain significant contrarian profits based on the unadjusted stock returns in Panel C1, in each of the size groups and in the full sample of all stocks. These risk-adjusted profits for large firms, small firms and microcaps range from 0.46 percent to 0.63 percent per month. On the other hand, none of the size groups display return reversals when there are increases in the holdings by Short-Term IO. The risk-adjusted profits for stocks with decreases in Short-Term IO are significantly higher than the profits for stocks with increases in Short-Term IO. We obtain similar findings for contrarian profits constructed using industry-adjusted contrarian investment strategies, and across all size groupings. The findings in Table 1 strongly indicate that exits by informed institutions affect the supply of liquidity and, hence, contribute materially to short-term return reversals. 3.3 The Effect of Institutional Exits on Reversals: Sub-Period Results The U.S. equity market underwent substantial structural changes in the past decade, which eroded the barriers to entry in the business of supplying liquidity. These structural changes (see, e.g., Chordia, Roll and Subrahmanyam (2011) and Chordia, Subrahmanyam and Tong (2014)) include the introduction of decimalization, greater participation of hedge funds and other informed institutional investors, and a sharp 17

20 increase in high frequency traders who have largely replaced the traditional liquidity providers such as NYSE specialists and Nasdaq market makers. To examine the impact of these changes on the return reversals, we split our sample into two sub-periods: and We expect the increase in the competition for liquidity provision to have a negative impact on contrarian profits and possibly attenuate the effect of exits by informed institutions. As shown in Panel A of Table 2, when we split the sample into the pre- and post time periods, the risk-adjusted contrarian profits are significant only for the sub-group of microcaps. We do not find significant return reversal profits for small and big firms in either sub-period. However, when the strategy is conditioned on exits by informed institutions, significant risk-adjusted profits emerges for each size group in the pre-2000 sub-period. Stocks with decreases in informed institutions register significant risk-adjusted profits for each of the three size groups, ranging from 0.51 percent to 0.81 percent per month. Similar to the findings for the full-sample period in Table 1, we do not observe return reversals for stocks with increases in informed institutions in both sub-periods. Decreases in informed institutional ownership are associated with higher risk-adjusted reversal profits for small firms and microcaps in both sub-periods. The effect of institutional exits on return reversals across the two sub-periods is different for the large firms. The risk-adjusted contrarian profit for large firms with decrease in Informed IO drops from 0.59 percent (t-statistic=2.42) in , to an insignificant 0.16 percent (t-statistic=0.36) in the recent decade. 9 The contrarian profits based on industry-adjusted returns for the two sub-periods are presented in Panel B, Table 2. The industry-based (risk-adjusted) contrarian profits are large and significant in the sub-period in all size groups, ranging from 0.82 percent to 1.03 percent. Similar to the findings in Panel A of Table 2, 9 Our results are also consistent with recent findings in Anand, Irvine, Puckett and Venkataraman (2013) who report that liquidity-supplying institutional investors decreased trading (i.e., withdrew liquidity supply) in riskier (small) stocks during the recent financial crisis period. 18

21 decreases in the holdings of informed institutions in the previous quarter are associated with a larger magnitude of return reversals in each of the size groups. For the sample of all firms, stocks with decreases in informed institutions experience significantly greater reversals. However, exits by informed institutions have a weaker effect in the post-2000 sub-period. While decreases in Informed IO lead to a significantly higher reversals in the set of all firms, the effect is not significant for the size groups. In particular, for the portfolio of large firms, we do not observe significant reversals, independent of the change in informed institutions. As shown in Table 2, all the results remain similar when we define informed institutions as those with high turnover, Short-Term IO. For both the conventional and industry-adjusted reversal strategies, a decrease in the short-term institutional investors predicts larger reversals in both sub-periods. When we examine the sizebased portfolio results, exits by Short-Term IO have a weaker predictive effect on reversals in the post-2000 period, particularly for large firms. Overall, we find that declines in the percentage of informed investors accentuate the reversals significantly in the earlier sub-period and that the effect is weaker in the post 2000 sub-period. These results illustrate that the erosion of barriers to entry in the liquidity provision business (Hendershott, Jones and Menkveld (2011)) has attenuated the disruption to the efficacy of liquidity provision following exists by informed institutions, especially for the large stocks. 3.4 Stock Returns and Changes in Institutional Ownership As we just discussed, our findings in Table 2 are consistent with the predicted relation between changes in informed investors and return reversals. However, using changes in the presence of active institutional investors holding a stock as a proxy for active informed investors has several drawbacks. First, institutional holdings are measured only at a quarterly frequency. As a result, the time lag between the observed changes 19

22 in institutional holdings and the returns of the reversal strategy can be up to several months. Second, rather than the number of active traders that follow the stock, which is the variable suggested by our model, we are measuring the number of active institutions that hold the stock, which can be subject to endogeneity problems that can bias our inferences. For example, active institutions may steer away from stocks that are expected to become less liquid. Third, an increase in reversals in our model comes from shocks to the number of informed investors; however, the change in institutional investors we observe can be partially anticipated. To address these issues we use past stock returns (over the previous three months as shown in Figure 1) as a proxy for changes in the number of investors who actively participate in a stock. Past stock returns may influence the participation of active investors for several reasons. Active institutional investors holding stocks that performed badly in the past may face withdrawals, and as a result, may be forced to sell some of their stocks. Additionally, stocks may become less desirable for active insitutions when their market capitalization drops due to window dressing reasons (they do not want to be associated with losers). 10 Finally, part of the relation between the exit of active investors and past returns may be behavioral, and thus beyond the scope of our model. For example, active individuals as well as institutions can be susceptible to the extrapolation bias described in Barberis, Shleifer and Vishny (1998) and the Daniel, Hishleifer and Subrahmanyam (1998) self-attribution bias, which can lead them to sell losers. These arguments motivate our examination of the link between past returns and monthly reversal profits. We first document the relation between stock returns and institutional ownership 10 The stock s past return may also become a coordinating variable that causes investors exits. For example, within the context of the herding models of Froot, Scharfstein, and Stein (1992), and Hirshleifer, Subrahmanyam, and Titman (1994), there are situations where investors optimally choose to coordinate their choices of which stocks to evaluate. In this setting it is natural to have fewer active investors following stocks that show reductions in market capitalization, because of the belief that firms with low market capitalizations are less liquid, which becomes self-fulfilling because informed investors exit such firms. 20

23 by sorting stocks into quintiles based on the cumulative three-month stock returns from month t 3 to t 1 (3M). For the stocks in each of these quintiles, we compute the level and changes in the proportion of institutional investors, separately reporting the figures for those classified as informed institutional investors (Informed IO or Short- Term IO) as well as the remaining institutions (which are denoted as Uninformed IO or Long-Term IO). In each case, we report the level (in month t 1) and changes in these measures over the months t 3 to t 1 based on the latest information during the quarter. As shown in Panel A of Table 3, there appears to be fewer institutional investors holding loser stocks. We observe lower institional holdings for 3M loser stocks across most investor categories. More importantly, Panel B shows that informed institutional participation declines for 3M loser stocks. Indeed, we observe a fall in Informed IO and Short-Term IO only among the 3M losers. All other past 3M stocks groups have increases in institutional ownership. Moreover, we do not observe a similar decline in the ownership of inactive institutions for the 3M losers, consistent with a lower sensitivity of these investors to stock price movements. Hence, the numbers in Panel B of Table 3 indicate a strong positive relation between 3M stock returns and changes in the participation of informed institutions over the same quarter. 3.5 Monthly Return Reversals and Prior Quarterly Returns The results in Table 3 suggest that past stock returns provides a good proxy for changes in the number of informed investors, and our arguments suggest that low past returns may proxy for active investor exits better than institutional holdings data alone. Given this, we expect past returns to be associated with the magnitude of future return reversals. To examine the relation between return reversals and past returns, we sort stocks into twenty-five portfolios based on their return performance in the past one quarter 21

24 and past one month (see Figure 1 for the timeline used). Specifically, in each month t, we sort stocks into quintiles based on returns over the previous three months, that is, months t 3 to t 1. The stocks in the lowest quintile are labeled as 3M losers and those in the top quintile are 3M winners. We also independently sort all stocks into five equal groups using their returns in month t to produce 1M losers (stocks with lowest month t returns) and 1M winners (stocks with highest month t returns). Based on these independent sorts, we form twenty-five portfolios and calculate their mean holding period returns in month t + 1, which we report in Table 4. As shown in Table 4, the monthly contrarian profits increase dramatically when we move from the 3M winner quintile to the 3M loser quintile. In Panel A, the equal-weighted contrarian portfolio of all stocks produces the highest reversal return of 1.68 percent per month (t-statistic=7.80) for stocks that are 3M extreme losers. The reversal profits are virtually zero for the 3M winner stocks and the difference between the contrarian profits generated by the 3M loser stocks and 3M winner stocks is highly significant (t-statistic=7.46). The economic and statistical significance are similar when we adjust for exposure to the four common risk factors. Panel A of Table 4 reports additional tests that examine how these results relate to the market capitalizations of the stocks. As the Panel shows, the results are stronger for microcaps, but we find significant reversals among the 3M losers for small and big firms as well. In contrast, there is no evidence of contrarian profits for any of the size groups for stocks that are 3M winners. We next examine the returns of these portfolios in the pre- and post-2000 periods. As shown in Panels B and C of Table 4, the profitability of the contrarian strategy that employs all stocks is much lower in the post-2000 period, but is highest for 3M loser stocks in both sub-periods. For the 3M losers, the average risk-adjusted contrarian profit is 1.84 percent in the period, and declines to 1.25 percent in the recent period. The decline in return reversals is especially large for the big 22

25 firms, which realize an average reversal profit of 1.34 percent (t-statistic=4.96) in the earlier sub-period, but only 0.49 percent (t-statistic=1.13) in the recent decade. These findings are consistent with the increased competition in market making during the recent period. 11 Table 5 presents the profits for the industry-adjusted contrarian investment strategies, grouped by stock performance in the prior 3M period. Again, we find that the contrarian profits are strongest for stocks that are past 3M losers. Across all stocks and over the full sample period, the risk-adjusted profit for 3M losers is strikingly higher at 1.82 percent per month, compared to an insignificant 0.22 percent for 3M winners. The results are similar within each size sorted groups: the risk-adjusted profits are between 1.0 percent and 2.13 percent higher for 3M loser stocks when compared to 3M winners. Similar to the earlier findings, the effect of previous 3M returns on monthly reversals is weaker in the post-2000 period, particularly for the large firms. Overall, the evidence provides strong support for our contention that stock performance over the previous quarter proxies for exits by liquidity providers, which in turn predicts stronger return reversals. 3.6 Robustness Tests Return Reversals Excluding January Months There is strong evidence of return reversals in the month of January (Jegadeesh (1990)) and tax-loss selling contributes to this turn of the year effect (George and Hwang (2004)). To establish the robustness of our findings, we report the contrarian profits sorted on past 3M returns, excluding the January month holding period returns. As shown in Table 6, our main findings remain intact when we remove January 11 We also find that frictions in market prices, such as bid-ask bounce, do not drive our central findings. Specifically, when we skip a week between formation and holding months in the contrarian strategy we get qualitatively similar results. Specifically, all of the profit figures in Table 4 remain significant, except for big firms in the second sub-period. Results are available upon request. 23