Does perceived information in short sales cause institutional herding? July 13, Chune Young Chung. Luke DeVault. Kainan Wang 1 ABSTRACT

Transcription

1 Does perceived information in short sales cause institutional herding? July 13, 2016 Chune Young Chung Luke DeVault Kainan Wang 1 ABSTRACT The institutional herding literature demonstrates, that institutional long equity demand in period t is dependent on their long equity demand in period t-1. We, test if institutions long positions also rely on perceived information contained in the trades of sophisticated arbitrageurs in the form of short interest. We test two hypotheses. First, institutions perceive changes in short interest as predicting future returns. In this case subsequent institutional demand should be negatively related to changes in short interest. Second, institutions perceive short interest as correcting mispricing. In this case short sale constrained institutions, underweight securities until short interest increases, they view prices as corrected, and subsequently purchase the security. We find that institutional demand is positively related to past changes in short interest, supporting the perceived price correction hypothesis. Keywords: short interest, institutional herding, short sale constrained institution, price correction 1 Chung is from the School of Business Administration, College of Business and Economics, Chung-Ang University, Seoul, Korea; bizfinance@cau.ac.kr. DeVault is from the Department of Finance, Clemson University, Clemson, South Carolina, 29634; ldevaul@clemson.edu. Wang is from the Department of Finance, College of Business and Innovation, University of Toledo, Toledo, OH, 43606; kainan.wang@utoledo.edu. 0

2 1. Introduction This work examines the relation between short sellers trading activity and institutional investors demand. While relatively few studies exist successfully predicting institutional demand, the fact that institutional demand is positively related to returns, makes predicting it economically valuable. One exception is the herding literature. Previous work extensively documents that institutional investors herd (Nofsinger and Sias (1999), Wermers (1999), Sias (2004), and Sias and Choi (2009)), meaning institutional demand in quarter q-1 predicts institutional demand in period q. Thus far, the studies on herding focus primarily on long equity transactions. The findings further support the hypothesis that herding is a result of reputational concerns and not necessarily perceived information gained from observing past trades. Our studies asks if a rich source of information--past arbitrage activity in the form of short interest--predicts institutional demand. 2 The goal is to better understand how institutions both interact and garner information when making investment decisions. There are two possible relations between past changes in short interest and institutional demand. These relations depend on how institutions interpret the impact of a change in short interest. First, institutions may view changes in short interest as correcting mispricing. This could impact institutional demand because the overwhelming majority of institutions are short-sale constrained and cannot directly profit from overpriced securities with their trading activity. When they view a security as overpriced their only option is to underweight the security in their portfolio until the mispricing is corrected. Under this perceived price correction hypothesis, an increase in 2 Short-sellers's trades should exclusively be about their expectations of future returns because short-sellers never sell short for liquidity reasons (e.g., Diamond and Verrechia (1987)). Further, empirical work suggests the majority of short positions are likely taken by hedge funds. For example, Boehmer, Jones, and Zhang (2008) estimate institutions make up about 75% of short sale transactions. This 75% is likely primarily from hedge funds since hedge funds make up the majority of non-short-sale constrained institutions. Given, hedge funds are often assumed to be the most sophisticated investor class (e.g., Brunnermeier and Nagel (2005), Sias, Turtle, and Zykaj (2014)) this makes their trading activity valuable. 1

3 short interest in the prior quarter should predict an increase in institutional demand the next quarter. Those institutions who can sell securities short should take advantage of the overpriced securities with short sales and do not need to rely on other arbitrageurs to correct the price. Further, given short-sale constrained institutions can profit from undervaluation, the herding behavior should be restricted to overpriced securities. Conversely, institutions may view short interest as a predictor of future returns. In this case an increase in short interest in the prior quarter should predict a decrease in institutional demand (i.e., institutional selling) the next period. In addition, because any institution should value future return indicators, the decrease in demand should not be restricted to short-sale constrained institutions. Finally, under this hypothesis, the relation should exist for both underpriced and overpriced securities and both a large increase and a large decrease in short interest should predict institutional demand. The empirical results support the perceived price correction hypothesis, we find an increase in short interest in the prior quarter predicts an increase in institutional demand (i.e., an increase in institutional ownership) in the contemporaneous quarter. The initial univariate analysis uses a portfolio sorting approach, sorting stocks into quintile portfolios by the change in short interest in quarter q-1, and measures the change in institutional ownership in quarter q within those portfolios. The results show the highest change in short interest quintile portfolio experiences institutional demand twice as large as the lowest quintile portfolio. We then extend the analysis to control for factors known to impact institutional trading. First, as previously mentioned institutional investors herd (Nofsinger and Sias (1999), Wermers (1999), Sias (2004), Sias and Choi (2009), Oehler and Chao (2000) and Kim and Nofsinger (2005)). Second, institutional demand is positively related to contemporaneous returns (e.g., Jones, Lee, and Weiss (1999), Bennett, Sias, and Starks (2003)). Third institutions are momentum traders (e.g., Grinblatt, 2

4 Titman, and Wermers (1995), Wermers (1999), Wermers (2000), Nofsinger and Sias (1999)), they buy past winners and sell past losers. There are also several factors related to institutional ownership levels. First, institutions provide the supply of loanable shares to short-sellers (e.g., D'Avolio (2002) and Nagel (2005)) meaning the change in short interest should be positively related to the institutional ownership level. Second, institutions prefer certain firm characteristics such as size, age, price, and turnover (e.g., Gompers and Metrick (2001) and Yan and Zhang (2009)). We perform a regression analysis testing the relation between past changes in short interest and institutional demand while controlling for all known factors impacting institutional demand and ownership levels. We control for the factors related to ownership levels in an effort to be as careful as possible when identifying the effect of past changes in short interest on institutional demand. The results show a one standard deviation increase in short interest in quarter q-1 leads to a 6% standard deviation increase in institutional demand in quarter q. Next, recall the hypothesis that institutions rely on arbitrageurs to correct mispricing focuses on short-sale constrained institutions. Therefore, we test if the predictive power of short interest on institutional demand is concentrated in those institutions most likely to be short-sale constrained. To do this we separate institutions into transient institutions (those institutions with the highest portfolio turnover) and non-transient institutions. We hypothesize that institutions with the highest turnover are more likely to be short-term focused and therefore unconstrained. We also perform a more direct test using a sample of hedge funds compared to non-hedge funds. Hedge funds have the most freedom in their security selection decisions and are very unlikely short-sale constrained. Consistent with the price correction hypothesis, the demand from transient institutions and hedge funds is not related to past changes in short interest. 3

5 The price-correction hypothesis, even more specifically, focuses on securities viewed as overpriced. To test this empirically we again analyze the short interest herding behavior when examining portfolios formed on a proxy for mispricing. We use the short interest level as a measure of the mispricing level. Our hypothesis is if institutions use the change in short interest as an indicator of the change in mispricing, then the short interest level should serve as an indicator of the level of mispricing (e.g., stocks with high short interest levels are more likely viewed as overpriced). The results show that the herding behavior exists prominently in those securities with high short interest levels and are more likely viewed as overpriced. The hypothesis of systematic herding on changes in short-interest requires short-sale constrained institutions to systematically view a stock price as being overpriced and then have its price 'corrected.' This is most likely to occur when the information uncertainty of a firm is low (i.e., institutions are more likely to agree a stock is overvalued if the stock is easier to price). To evaluate a stocks information uncertainty we use three measures; size, liquidity, and idiosyncratic volatility. We find the short interest-herding behavior is concentrated in those stocks with the lowest information uncertainty. Therefore, we find that in the situation in which the hypothesized relation--that institutions systematically use changes in short interest as a mispricing correction indicator and increase their demand for securities following the price correction--is strongest is the situation where the herding behavior is concentrated. Finally, we test if institutions are benefitting from this herding behavior, by examining if changes in short interest actually corrects mispricing. To do so, we examine returns, to portfolios sorted by changes in short interest, in the period of the short interest change and the subsequent quarters. The results show that arbitrageurs increase their short interest positions in those stocks with large price increases. Following the increase, the stocks with the largest increase in short interest earn 4

6 negative risk adjusted returns, supporting the finding in the literature that short-sellers are informed (e.g., Boehmer, Jones, and Zhang (2008)). When examining the securities where the herding behavior is concentrated--those with high mispricing, large increases in short-interest and low information uncertainty--the results show no abnormal returns. We cannot reject the hypothesis that these stocks earn returns equivalent to their respective DGTW-portfolio return. It appears that institutions earn a fair return on their investment, in a risk-adjusted sense, by herding on short interest. Assuming institutions value the increase in portfolio diversification gained by purchasing these securities, the behavior appears rational. The paper makes several contributions to the literature. We are the first to study institutional herding on arbitrage trading activity, where arbitrage trading is measured by changes in short interest. The evidence is consistent with institutions using short interest as an indicator of the change in mispricing. Short-sale constrained institutions appear to use the perceived information signal to purchase securities whose prices they view as corrected. These findings help explain not only how institutions gain information when making investment decisions, but also suggests that institutional investment constraints (i.e., short-sale constraints) lead to predictability in their decisions. Finally, the finding that stocks where short-interesting herding is prevalent earn returns statistically indifferent from their respective risk portfolios, suggests institutions place a high premium on portfolio diversification. 2. Data/Methodology: The primary data in the study come from three sources. The institutional holding data are from Thompson's 13(F) filings database. The data cover each quarter between March 1981 and December According to SEC, all institutions with more than $100 million in equity ownership must report their equity holdings (both owned and loaned to another party) consisting of either more than 10,000 5

7 shares or $200,000 in value. The short interest and firm characteristic data are obtained from COMPUSTAT. The return data are provided by the Center for Research in Security Prices (CRSP). We define the change in institutional ownership as, ddddddddcc kk,qq = End of quarter institutional shares qq total shares outstanding qq End of quarter institutional shares qq 1 total shares outstanding qq 1 We define the change in short interest as, ddddhoooott kk,qq = short interest qq total shares outstanding qq short interest qq 1 total shares outstanding qq 1 From 1981 through September of 2007 short interest is reported on the fifteenth of the month and thus the change in quarterly short interest is calculated using the short interest reported on the fifteenth of the last month of the quarter minus the quarterly short interest reported on the fifteenth of the first month of the quarter. Beginning in 2008 the change in short interest is calculated using the short interest reported on the last day of the quarter minus the short interest reported on the last day of the previous quarter. Table 1 presents time-series summary statistics of the cross-sectional averages of the key variables used in this study. The average institutional ownership is 25% with a standard deviation of 9%. The average change in institutional ownership is 0.6%, despite the differences in sample period, these values are consistent with the existing literature (e.g., Yan and Zhang (2009) and Sias and Whidbee (2010)). The average short interest ratio is 1.9% and the average quarterly change in short interest is 0.1%. Both the level of and the change in short interest ratio have larger means than medians, reflecting the familiar right skewness in these variables (e.g., Asquith, Pathak, and Ritter (2005)). The quarterly raw returns have a mean of 3.7%, a minimum of -29% and a maximum of 35%. 6

8 [Insert Table 1 about here] 3. Empirical Results 3.1 Do changes in short interest predict institutional demand? Univariate analysis The focus of the paper is to test if institutions rely on past arbitrage trading activity when making their investment decisions. To test this empirically, we focus on the relation between changes in short interest in quarter q on institutional demand in quarter q+1. When testing this relation it is important to control for other previously found relations documented in the literature. First, institutions provide the loanable supply of shares to short sellers, meaning institutional demand is positively related to the contemporaneous change in short interest (D'Avolio (2002) and Nagel (2005)). Further, institutional demand is positively related to contemporaneous returns (Jones, Lee, and Weiss (1999), Wermers (1999), Wermers (2000), and Bennett, Sias, and Starks (2003)). We start our analysis by testing our primary question in a univariate portfolio sorting approach as well as confirming these previous results. At the beginning of each quarter, we sort stocks into quintile portfolios based on their changes in short interest over quarter q. We then compute the average demand from institutions (dfrac q)the demand from short sellers (dshort q), and the quarterly raw returns (ret q), for the current (quarter q) and future quarter (quarter q+1), for each quintile portfolio. The results are reported in Table 2. [Insert Table 2 about here] We find a clear relation between changes in short interest and contemporaneous institutional demand. For example, the average institutional demand (dfrac q) for the highest short interest portfolio is 1.8%, which is more than four times larger than the corresponding value for the lowest short interest portfolio (difference significant at above the 1% level). This result is consistent with D Avolio (2002) 7

9 who finds that institutional ownership explains up to 64% of the cross-sectional variation in loanable shares. Further, when examining contemporaneous returns, we find that the return difference in raw returns between the highest and lowest short interest portfolios is about 6% (analogously institutional demand is also positively related to contemporaneous returns), and the differences is statistically significant at the 1% level. This finding has two implications. First, it is consistent with the evidence of intra-quarter momentum trading by institutions. Moreover, it suggests that short sellers are contrarians and sell short firms with recent price increases. Table 2 also examines the relationship between changes in short interest in the current quarter and institutional demand in the future quarter. We find strong evidence that changes in short interest positively predict future institutional demand. For instance, institutional demand in the highest short interest portfolio is two times larger than that in the lowest short interest portfolio (.866% versus.433%). The difference is statistically significant at the 1% level. In addition, we find that stocks favored by short sellers in the prior quarter remain highly shorted in the current quarter, suggesting changes in short interest are persistent. This result is consistent with Asquith, Pathak, and Ritter (2005) who show that highly shorted stocks tend to have high short interest for several consecutive months. Moreover, we find that the portfolio with the highest change in short interest earns the lowest post one-quarter raw returns. In sum, our Table 2 results confirm several of the existing empirical findings regarding short interest, institutional demand, and returns. More importantly, we find that institutions not only provide liquidity to short sellers within the same quarter, but they also increase their demand for stocks with large increases in short interest the following quarter. This supports the perceived mispricing correction hypothesis, implying that institutions may perceive changes in short interest as correcting mispricing indicator and purchasing shares once they believe the mispricing is corrected in the next 8

10 period. This supports the idea that institutions rely on past arbitrage trading activity when making their portfolio allocation decisions Multivariate regression Our univariate results suggest that institutional investors investment decisions in quarter q depend on arbitrage trading activity in the form of changes in short interest in quarter q-1. While little work attempts to predict institutional demand one major exception is the institutional herding literature (e.g., Nofsinger and Sias (1999), Wermers (1999), Sias (2004), and Sias and Choi (2009)). Specifically, this literature finds institutional demand in the current quarter is positively related to the institutional demand in the prior quarter. Given that institutions provide the loanable supply of shares to be shorted, an increase in short interest is likely accompanied by a concurrent positive increase in institutional holdings. This relation implies that the observed positive relationship between past changes in short interest and institutional demand could be driven by institutions following their own past trades and not changes in short interest. In addition, the literature finds that institutions tend to buy past winners and sell past losers (e.g., Grinblatt, Titman, and Wermers (1995), Wermers (1999), Wermers (2000), Nofsinger and Sias (1999), Sias (2004), and Sias, Starks, and Titman (2006)). Given the positive contemporaneous relation between changes in short interest and returns, it is not surprising that institutions increase their demand for stocks with increased short interest in the prior quarter. Further, the literature suggests that institutions demonstrate preferences for certain firm characteristics such as size, age, price, and turnover (e.g., Gompers and Metrick (2001) and Yan and Zhang (2009)), if these characteristics are also related to mispricing they may also be correlated with changes in short interest. 3 Therefore, while the univariate results provide initial support for a 3 These characteristics are generally found to explain institutional ownership levels and not changes in ownership. However, we include them to reduce possible omitted variable concerns. 9

11 predictive relation between past short seller and concurrent institutional investor demand, to ensure that our univariate results are not driven by these previously found relations, in this section, we use a panel regression approach to control for factors that may cloud our findings. We start our analysis by confirming the role of institutions as liquidity providers to short sellers in the contemporaneous relationship. Our model setup is: ddddddddcc qq = ββ 0 + ββ 1 ddddhoooott qq + ββ 2 ddddddddcc qq 1 + ββ 3 rrrrrr qq + ββ 4 rrrrtt qq 4,qq 1 + XX qq BB + γγ qq + εε qq (1) where XX qq is a vector of firm characteristic controls; and γγ qq is the time fixed effect. We follow Sias (2004) and use lagged institutional demand to capture institutional herding. We include contemporaneous and one-year lagged returns to control for institutions momentum trading. We follow Gompers and Metrick (2001) and Yan and Zhang (2009) and consider the following firm characteristics as additional controls: share price, market capitalization, trading volume, book-tomarket, age, dividend yield, S&P 500 membership, turnover, and return volatility. In particular, market capitalization (MKTCAP) is stock price times the number of shares outstanding. Trading volume (VOL) is number of shares traded over a quarter. Book-to-market (BM) is book value at the fiscal year end before the most recent June 30 divided by market capitalization of December 31 during that fiscal year. Age (AGE) is the number of months since CRSP reported the first return. Dividend yield (DP) is annual cash dividend divided by share price. S&P 500 membership (SP500) is a dummy variable indicating whether the firm is included in the S&P 500 index. Turnover (TURN) is average monthly turnover within a quarter. Return volatility (RVOL) is standard deviation of monthly returns over the past two years. All characteristics except SP500 are in natural logarithms. The coefficient of interest is ββ 1 which measures the incremental effect of contemporaneous changes in short interest on institutional demand. 10

12 We follow Petersen (2009) and cluster standard errors in two dimensions, across time and across firms. Petersen (2009) shows that the Fama-Macbeth (Fama and Macbeth (1973)) standard errors are biased downward when they are correlated in the time-series; and the t-statistic when clustering standard errors on both time-series and cross-sectional dimensions are more robust. Nevertheless, to ensure that our results are robust, we also consider the Fama-Macbeth standard errors in all analysis. In these unreported results, we find that our results are not materially different. [Insert Table 3 about here] The first and second columns in Table 3 report the coefficient estimates without and with firm characteristic controls, respectively. We find that the coefficients for dshort q (the contemporaneous change in short interest) are positive and statistically significant in both cases, suggesting institutions increase their demand for stocks with simultaneous increases in short interest, consistent with the literature documenting that institutions provide the supply of loanable shares to short sellers. In addition, we show that conditioning on changes in short interest, institutions do not seem to herd. For example, when including firm characteristics, the coefficient on dfrac q-1 is a statistically insignificant These results contradict the widely-held notion that institutions engage in herding. With regard to returns, our results suggest that institutions increase their demand given positive contemporaneous and lagged returns, consistent with the momentum trading behavior of institutions documented in the literature. Comparing numbers in the first and second columns, we find that the coefficient estimates are similar in magnitude, suggesting that the institutional preferences for share characteristics either only explain ownership levels (consistent with previous work) or are unrelated to momentum trading, herding, and changes in short interest. We next examine the robustness of the predictability of lagged changes in short interest on institutional demand. Our primary interest is to investigate whether changes in short interest in the prior quarter 11

13 provide explanatory power to institutional demand this quarter controlling for the contemporaneous relationship between the two variables. Our model specification is: ddddddddcc qq = ββ 0 + ββ 1 ddddhoooott qq + ββ 2 ddddhoooott qq 1 + ββ 3 ddddddddcc qq 1 + ββ 4 rrrrrr qq + ββ 5 rrrrtt qq 4,qq 1 +XX qq BB + γγ qq + εε qq (2) The setup is identical to Equation (1) except that we include the lagged change in short interest as our variable of interest. The third and fourth columns in Table 3 report the coefficient estimates. We find that the coefficient for dshort q-1 without firm characteristic controls is 0.068, which is statistically significant at the 1% level. This means that a 10% increase in short interest in the prior quarter results in a 0.7% increase in institutional demand this quarter, above and beyond the demand due to institutions providing the necessary liquidity to short sellers. When including firm characteristic as controls, this coefficient decreases to.06 but remains positive and statistically significant (above the 1% level). Looking at the coefficient for Dfrac q-1, we again find no evidence of institutional herding when we control for both lagged and contemporaneous changes in short interest, while in both models institutions exhibit momentum trading. 4 In sum, these results support institutions reliance on arbitrage trading activity when making investment decisions independent of institutional herding, momentum trading, firm preferences, or institutions role as share suppliers to short sellers. 3.2 Do institutions of different types react to changes in short interest differently? So far, the empirical evidence shows that changes in short interest positively predict institutional demand. We interpret this result as evidence that institutions rely on short sellers for mispricing 4 When evaluating just the effect of institutional herding without the change in short interest variables, or firm characteristics, we find evidence of herding similar to that found in Sias (2004) when examining that studies sample period ( ). 12

14 correction and they increase demand once the mispricing is corrected. However, the mispricing correction hypothesis is about short-sale constrained institutions specifically. When short sale constrained institutions recognize that a stock is overvalued, they cannot directly profit from this information via short selling. Their only option is to unload their position and buy back the shares after the mispricing is corrected. By comparison, institutions that are not subject to short sale constraints, like hedge funds, can realize profits from overvalued stocks by selling short or using derivative positions. These institutions are unlikely to rely on past arbitrage activity, given they can make arbitrage trades themselves, and therefore their demand is unlikely to be related to past changes in short interest if the hypothesis is true. 5 Essentially the relation between past changes in short interest and institutional demand should only exist for those institutions who are short-sale constrained and cannot take advantage of observed overpricing. In this section, we empirically test this hypothesis by decomposing all institutions in our sample into short sale constrained and non-constrained institutions. We consider two methods to partition the institutions in our sample into short sale constrained and non-constrained groups. In the first method, we use the classification in Bushee (1998, 2001) and decompose institutions into transient and non-transient institutions. Non-transient institutions have long investment horizons and low portfolio turnovers, so they are more likely to be short sale constrained. Transient institutions, in contrast, exhibit high portfolio turnover, making them more likely to be able to sell short as a group (arbitrage traders likely trade quickly to take advantage of short-term mispricing leading to higher portfolio turnover). It is worth noting that separating institutions into transient and non-transient institutions does not give us a perfect divide between short sale constrained and non-constrained institutions. Thus, in the second decomposition method, we consider a cleaner measure of short sale constrained institutions. Specifically, we use the hedge 5 However, we are not able to empirically test this hypothesis because institutions disclose only long positions in their 13F report. 13

15 fund classification in Griffin and Xu (2009) and decompose our sample institutions into hedge funds and non-hedge-fund institutions. 6 To ensure non-hedge-fund institutions are composed of primarily short sale constrained institutions, we further constrain non-hedge-fund institutions to include only non-transient institutions. Because the classification data in Griffin and Xu (2009) end in December 2004, for this decomposition method, we limit our sample to the period from March 1981 to December We use the seemingly unrelated regression (SUR) approach to jointly estimate a system of two equations in which each equation takes the form given by Equation (2). The institutional demand variable in the first and second equation in the system corresponds to short sale non-constrained and constrained institutions, respectively. We use the SUR approach in this analysis because it allows for comparison of key coefficients between the two groups of institutions. [Insert Table 4 about here] The first two columns in Panel A report the results for transient and non-transient institutions. Consistent with our hypothesis, we find that changes in short interest only predict non-transient institutions demand. For example, the coefficient for dshort q-1 is for transient institutions. The related t-statistic indicates that this coefficient is statistically indifferent from zero. By comparison, the same coefficient for non-transient institutions is 0.061, statistically significant at above the 1% level. The last two columns in Panel A present analogous results for hedge funds and non-hedge-fund institutions. The demand from non-hedge-fund institutions is positively related to lagged changes in short interest. In contrast, we do not find any evidence that lagged changes in short interest predict institutional demand in hedge funds. Taken together, these results show that institutions not subject 6 The data is downloadable at 14

16 to short sale constraints (i.e., transient institutions and hedge funds) do not trade based on short sellers activity in the prior quarter. Short sale constrained institutions (i.e., non-transient and non-hedge-fund institutions) on the other hand, increase their demand after short interest increases in the prior quarter, supporting the perceived mispricing correction hypothesis. To gauge statistical significance of the difference in dshort q-1 between short sale constrained and non-constrained institutions, we use a Wald test. We report the results in Panel B of Table 4. We find that in both cases, the null hypothesis that the coefficient does not differ between the two groups of institutions is rejected, indicating that short sale constrained institutions react differently to lagged changes in short interest compared to short sale non-constrained institutions. Overall, the results in Table 4 support our hypothesis that the observed increase in institutional demand due to lagged increase in short interest is mostly attributed to institutions who are likely to be short sale constrained. 3.3 Institutions mispricing perceptions Level of short interest Our analysis indicates that short sale constrained institutions use information in past short sale transactions when making their investment decisions. If short sale constrained institutions use past short interest information to judge changes in firm mispricing, then the relation between lagged changes in short interest and future institutional demand should be stronger for firms that are more likely to be overpriced. So far, our analysis has focused on the change in short interest variable. The level of short interest, on the other hand, should reflect short sellers belief in the level of mispricing (i.e., a stock with a high short-interest level is viewed as highly overpriced). If this is true, we should expect to see that the predictability of changes in short interest on institutional demand exists only for 15

17 firms with a high level of short interest. To validate this hypothesis, we sort firms into quintile portfolios based on the level of short interest in the prior quarter. We then repeat the Table 4 analysis for the two extreme quintiles and report the results in Table 5. [Insert Table 5 about here] Panels A and B report the results for firms within the highest short interest quintile. We find very similar results to those in Table 4. For instance, the coefficients on dshort q-1 for short sale constrained institutions are positive and highly significant using both classification methods. By comparison, the same coefficients for short sale non-constrained institutions are statistically indifferent from zero. The Wald test results confirm the differences in trading behavior between short sale constrained and nonconstrained institutions. Panels C and D present analogous results for firms within the lowest short interest quintile. We find clear evidence that neither short sale constrained nor short sale nonconstrained institutions base their trading on lagged changes in short interest. These results imply that short sale constrained institutions infer information about firm mispricing from short sellers and that information includes both level and change in short interest. More importantly, Table 5 supports our hypothesis that the short sale constrained institutions rely on the perceived price correcting mechanism of short-sales because the herding behavior following changes in short interest is only present in the securities most likely to be overpriced Information uncertainty Our results in the previous section suggest that short sale constrained institutions herd on short interest only when the stock is most likely to be overpriced, i.e., in the situation when being short-sale constrained impacts their investment decisions. In this section, we attempt to further isolate the situations where institutions could most likely benefit from past arbitrage trading activity resulting in systematic herding. Our logic is straight forward. If short sale constrained institutions rely on short 16

18 sellers to correct mispricing, their herding should be concentrated most heavily in firms that are most clearly overvalued. If a firm is subject to a high level of information uncertainty, it may be difficult even for short sellers to assess its fundamental value and also leading to disagreement among shortsale constrained institutions about the stock's valuation. This disagreement should decrease the possibility of systematic herding. In this section, we empirically examine this hypothesis. Given that the positive relationship only exists for firms with high mispricing proxies, in this analysis, we restrict our sample to firms within the highest quintile of short interest. We follow the literature on firm-level information uncertainty and focus on three distinct measures: market capitalization, illiquidity, and idiosyncratic volatility (IV). 7 Specifically, market capitalization is calculated as the number of shares outstanding multiplied by the market price per share. Illiquidity is from Amihud (2002) and is defined as the quarterly average of daily ratios of absolute return to dollar value of trading volume. Following Ang et al. (2006), IV is measured using the Fama-French three-factor model. In particular, IV is obtained as the quarterly sum of the squared residuals of the regression of daily excess returns on the Fama-French three factors including market excess return, size, and book-to-market ratio. We start by sorting firms into quintile portfolios based on the level of short interest in the prior quarter. Within the highest quintile of short interest, we further sort firms into quintiles based on the level of information uncertainty. Firms with the largest size, lowest illiquidity, and lowest IV are considered as low uncertainty firms, whereas those with the smallest size, highest illiquidity, and highest IV are classified as high uncertainty firms. We replicate the analysis in Table 5 for each of these double-sorted portfolios and report the results in Table 6. To conserve space, we only report 7 See Park, Lee, and Song (2014) for a detailed discussion about these variables. 17

19 the coefficients on dshort q-1 in this table. We hypothesize that the short-interest herding behavior should be present in the stocks with the lowest valuation uncertainty. [Insert Table 6 about here] Panel A of Table 6 reports the analysis for firms that have high short interest and high information uncertainty. We find that for short sale constrained institutions, the coefficients on dshort q-1 are statistically indifferent from zero. The only exception occurs for non-transient institutions and when information uncertainty is measured by IV. In sum, the results suggest that when there is most likely disagreement about stock valuation herding greatly decreases. Panel B of Table 4 presents analogous results for firms with high short interest and low information uncertainty. Consistent with our hypothesis, we find that the positive relation between lagged changes in short interest and future institutional demand is concentrated in the securities where views about mispricing are most likely to be uniform and thus lead to systematic herding. In fact, the herding behavior appears using both classifications of short sale constrained institutions. When looking at non-transient institutions, we find significant predictability of changes in short interest on institutional demand when information uncertainty is measured by size and illiquidity. This suggests that in the cases when views of mispricing are most uniform even transient institutions purchase the securities following perceived mispricing correction. Comparing the coefficients between short sale constrained and non-constrained institutions, we find that in all cases short sale constrained institutions' demand is most reliant on changes in short interest, statistically significant at above the 1% level. In sum, the evidence suggests that in the situation when stocks should most systematically be viewed as overpriced the herding behavior following changes in short interest is the strongest. In other words, the herding behavior is concentrated in the situation most likely to produce systematic herding on arbitrage trading activity 18

20 3.4 Robustness test Our results in the previous sections provide strong support for the hypothesis that short sale constrained institutions herd on the past arbitrage activity, in the form of short interest, when a stock was likely mispriced in the previous period. In this section, we examine the robustness of those results. Specifically, we consider two factors that may cloud our findings. First of all, our hypothesis makes the prediction that when mispricing is a concern for short sale constrained institutions, they interpret large increases in short interest as an indicator of mispricing correction. Specifically, short sale constrained institutions believe that a stock s mispricing is more likely to be corrected this quarter if short sellers as a group increase the short selling activity in the prior quarter (i.e., increase in short interest). When short sellers cover their short positions in a quarter (i.e., decrease in short interest), mispricing is less likely a concern for short sale constrained institutions so they do not have to wait till the next quarter to trade. This means that the positive relationship between lagged changes in short interest and future institutional demand should be more pronounced for firms with a positive change in short interest than a negative change. Second, macroeconomic conditions may affect the reaction of institutional demand to past short interest information. For instance, during economic contractions, information uncertainty is escalated in the market as a whole, likely leading to less uniformity in agreement about mispricing and less systematic herding. In these periods the relation between past changes in short interest and short-sale constrained institutions may dissipate. To address the above two issues, we limit our sample to retain only positive changes in short interest and consider a model with additional controls for macroeconomic conditions: 19

21 ddddddddcc qq = ββ 0 + ββ 1 ddddhoooott qq +ββ 2 ddddhoooott qq 1 + ββ 3 ccccccccccccccccccccnn qq + ββ 4 ccccccccccccccccccccnn qq ddddhoooott qq + ββ 5 ccccccccccccccccccccnn qq ddddhoooott qq 1 + ββ 3 ddddddddcc qq 1 + ββ 4 rrrrrr qq + ββ 5 rrrrtt qq 4,qq 1 + XX qq BB + γγ qq + εε qq (3) where ccccccccccccccccccccnn qq is a dummy variable equal to one when at least one month of quarter q belongs to an economic contraction period and zero otherwise. The economic contraction periods are identified using the NBER business cycles. 8 The interaction terms ccccccccccccccccccccnn qq ddddhoooott qq and ccccccccccccccccccccnn qq ddddhoooott qq 1 capture the differential impact of bad economic conditions on the liquidity proving role of short sale constrained institutions and the perceived mispricing correction by short sale constrained institutions, respectively. Our hypothesis is that the relation between past changes in short interest and institutional demand will be smaller in contractionary periods. Our previous analysis suggests that the positive reaction of institutional demand to past changes in short interest is concentrated among short sale constrained institutions, in firms with high levels of short interest, and in firms with low information uncertainty. Thus we focus on only short sale constrained institutions and firms with the above characteristics. [Insert Table 7 about here] Table 7 presents the coefficient estimates for short sale constrained institutions proxied by nontransient or non-hedge-fund institutions, and for three firm-level uncertainty measures. Several interesting findings arise from this table. First, we find that the positive relation between lagged changes in short interest and future institutional demand holds under this new model specification, confirming the robustness of our hypothesis. Second, the coefficients on contemporaneous changes in short interest, dshort q, are either insignificantly different from zero or significantly negative at the 10% level, suggesting that when short interest increase in a quarter, short sale constrained institutions 8 Detailed information about the NBER business cycles can be found at: 20

22 sit out of the market until the perceived mispricing is corrected. Third, the coefficients on ccccccccccccccccccccnn qq ddddhoooott qq are positive and statistically significant for non-transient institutions, indicating that when the market-wide uncertainty is high, agreement about mispricing and mispricing correction is not uniform and herding ceases. Instead, they play a bigger role in providing the necessary liquidity to short sellers. Fourth, looking at the coefficients on ccccccccccccccccccccnn qq ddddhoooott qq 1, we show that they are negative and statistically significant for non-hedge-fund institutions, consistent with our hypothesis that short sale constrained institutions are less likely to interpret an increase in short interest as the correction of mispricing during economic contractions. In sum, Table 7 provides additional support to our hypothesis that short sale constrained institutions use information from short sellers to infer the correction of mispricing only when such information is trustworthy. When uncertainty is high and therefore stock valuation is most difficult, they are more likely to provide loanable shares to short sellers. 3.5 Institutions herding on the short interest information and subsequent returns The literature finds mixed evidence on the relationship between short interest levels and subsequent returns. Some papers show that the short interest ratio predicts negative future returns (Figlewski (1981)), while others find little or no relation between them (Woolridge and Dickinson (1994)). Recent papers on this topic incorporate supply of loanable shares to short sellers and find that short sale constrained stocks underperform (Asquith, Pathak, and Ritter (2005)). In this section, we examine the return implications of the short interest herding behavior of short sale constrained institutions. We begin by examining whether changes in short interest lead to negative subsequent riskadjusted returns. In our hypothesis, we suggest that short sale constrained institutions sit out of the 21

23 market till the perceived mispricing is corrected, and they use lagged changes in short interest as evidence of mispricing correction. If our hypothesis is correct, we expect securities earn positive or zero abnormal returns following quarters with large increases in short interest. At the beginning of each quarter, we sort stocks into five quintile portfolios based on changes in short interest in the prior quarter. We then report quarterly returns for two quarters before and four quarters after the portfolio formation date. We adopt the methodology in Daniel, Grinblat, Titman, and Wermers (DGTW, 1997) and compute the risk-adjusted return for each portfolio as the raw return minus the characteristic-based benchmark return based on 125 triple-sorted quintile portfolios on size, book-to-market, and momentum and therefore the DGTW-adjusted return controls for the size, book-to-market, and momentum effect. The DGTW-adjusted returns have the advantage of controlling for these dimensions, previously shown to impact the cross-section of returns, without having to make an exact assumption about the return generating process. [Insert Table 8 about here] Table 8 reports quarterly DGTW-adjusted returns for equal-weighted portfolios sorted by lagged changes in short interest. We find a clear monotonically increasing pattern in DGTW-adjusted returns during the quarter in which short interest portfolios are formed (i.e., second column), suggesting that short sellers tend to sell short stocks with high contemporaneous returns. Looking at the portfolio of stocks with the largest change in short interest (i.e., last row), we find that they earn the lowest returns in subsequent periods after the change in short interest is measured. The t-statistics suggest that these returns are all negative and statistically significant at the 5% level, indicating that besides short interest levels, changes in short interest also predict future returns and evidence contrary to the hypothesis that changes in short interest correct mispricing. This provides evidence that 22

24 institutions may actually be damaging their performance with their herding behavior. However, our findings in the previous sections indicate that short sale constrained institutions herd on the short interest information only when the firm is overvalued and the information uncertainty around the firm is low. Therefore the full sample of securities may not be representative of the returns earned by institutions herding on short interest. We next attempt to more directly examine the risk-adjusted returns realized by institutions herding on short interest, by focusing on the securities where the herding behavior is concentrated. Specifically, we use triple-sorted portfolios to retain high mispricing (overvalued firms) and low uncertainty firms. In particular, at the beginning of each quarter, we sort stocks into 3 equal-weighted portfolios based on the level of short interest in the prior quarter. Within the highest short interest tercile, we then sort stocks into 3 equal-weighted portfolios based on the level of information uncertainty measured by size, illiquidity, or IV. Lastly, within the lowest information uncertainty tercile, we then sort the stocks with increases in short interest (we only use stocks with increases in short interest because only increases in short interest should drive overvalued securities' price towards fundamentals) into 3 equal-weighted portfolios based on the magnitude of those changes. 9 We replicate Table 8 for each portfolio and report the results in Table 9. [Insert Table 9 about here] Panel A of Table 9 presents the DGTW-adjusted returns for low uncertainty stocks measured by market capitalization around portfolio formation. We find that again in the contemporaneous quarter when the change in short interest is measured, stocks that have the largest increase in short interest earn the highest returns. Looking at the returns after portfolio formation, we find no 9 We group stocks into terciles to allow for a reasonable number of stocks in each portfolio. 23