Signaling Pessimism: Short Sales, Information, and Unusual Trade Sizes

Transcription

1 Signaling Pessimism: Short Sales, Information, and Unusual Trade Sizes Benjamin M. Blau Department of Economics and Finance Huntsman School of Business Utah State University Comments Welcome

2 Signaling Pessimism: Short Sales, Information, and Unusual Trade Sizes Abstract: Past research argues that informed investors may strategically break up their larger trades into smaller sizes to disguise their information (Kyle, 1985, Barclay and Warner, 1993, and Alexander and Peterson, 2007). However, short sellers, while informed, may be motivated to signal their information to the market by using unusual trade sizes because the quicker the market reacts to their signal the sooner they can close their short position and forego additional borrowing costs. This study tests this assertion. While short sellers are shown to be contrarian in contemporaneous and past returns and able to predict negative returns at the daily level (Diether, Lee, and Werner, 2009), we show the these results are driven primarily by large unrounded short sales in stocks that are most likely to face higher equity borrowing costs. These results are consistent with the idea that short sellers use different trade sizes to signal pessimism to the rest of the market.

3 I. Introduction Theory in Kyle (1985) shows that informed investors can increase their profitability by spreading their trades over longer periods of time. This prediction and others in Admati and Pfleiderer (1988) and Foster and Viswanathan (1990) provide the framework for Barclay and Warner s (1993) stealth trading hypothesis, which states that informed investors will break up their larger trades into medium-sized trades. The purpose for doing so is that larger trades may reveal their information to other sophisticated investors while smaller trades are subject to higher relative transaction costs. Consistent with the stealth trading hypothesis, Barclay and Warner find that medium-sized trades indeed move prices more than larger or smaller trades. 1 While examining the information contained in short sales, Boehmer, Jones, and Zhang (2008) find that current short selling relates inversely with future returns at the daily level indicating that short sellers are informed investors (Diamond and Verrecchia, 1987; Senchack and Starks, 1993; Aitken et al., 1998; Dechow et al., 2001; Desai et al., 2002; and Christophe, Ferri, and Angel, 2004). However, Boehmer, Jones, and Zhang find that short sellers return predictability is driven by large short sales suggesting that short sellers have little intention of disguising the information in their trades. This novel result is largely unexplained. In this study, we contend that, instead of disguising their trades through the use of smaller trade sizes, short sellers may be motivated to signal their information to the market by using unusual trade sizes. Short sellers are likely motivated to signal their pessimism to the market for two reasons. The first reason is that the profitability of establishing short positions relates inversely to the equity borrowing costs that short sellers face. Equity borrowing costs are likely increasing in the length of the stock loan. Therefore, short sellers may be able to mitigate higher 1 Barclay and Warner s (1993) finding is much different from the prediction that larger trades contain more information (Hasbrouck, 1988). 1

4 equity borrowing costs by signaling their information to other sophisticated traders in the market with unusually large trade sizes. Other traders may respond to this type of signaling and assist in driving prices down thereby allowing short sellers to close out their positions sooner and reduce their borrowing costs. The second reason is related to the first reason and is based on the concept of synchronization risk, discussed in Abreu and Brunnermeier (2002). Abreu and Brunnermeier argue that there are limits to arbitrage when short sellers face uncertainty about when peer arbitrageurs will begin to sell off a particular overvalued stock. In other words, the timing of expected downward stock-price movements may not be synchronized among arbitrageurs. This study contends that short sellers may attempt to signal their pessimism to the market in order to align the beliefs among peer informed traders about when prices will begin to move. For exposition, we denote the signaling of pessimism to the market by the use of unusual short-sale sizes as the signaling hypothesis. This study provides tests of the signaling hypothesis by examining the trade sizes of short sellers that drive the short-term trading strategies documented in Diether, Lee, and Werner (2009). First, Diether, Lee, and Werner show that short sellers are contrarian in contemporaneous and past returns suggesting that short sellers target stocks that have deviated from their fundamental price and may be overvalued. Second, they document that short sellers can impressively predict price reversals as current daily short selling relates negatively to nextday returns. Consistency with the signaling hypothesis is found if large short sales drive both the positive relation with contemporaneous and past returns and the negative relation with future returns. Further, Alexander and Peterson (2007) examine trade-size rounding and find that rounded trades, or trades that are multiples of 500 shares, have a greater price impact than unrounded trades particularly in the medium trade-size category. Alexander and Peterson argue 2

5 that informed traders may not only attempt to disguise their information using medium-sized trades, but they may also use rounded trades as a possible disguise. Accordingly, our hypothesis predicts that signaling by short sellers should be driven by unrounded trade sizes. Initial results indicate first, that the contrarian behavior of short sellers, documented in Diether, Lee, and Werner (2009), is driven by large short sales. Second, the ability of short sellers to predict negative returns is stronger for short sales in the large trade-size category, which is consistent with Boehmer, Jones, and Zhang (2008). However, we also document that the return predictability of short sellers is driven by unrounded trade sizes, which contradicts the idea that informed investors prefer rounded sizes to disguise their information (Alexander and Peterson, 2007). Combined, these results support the idea that short sellers have a greater intention to signal their information than to disguise it. We perform additional tests to strengthen the claim that short sellers signal through the use of unusual trade sizes by examining the combination of large short sales that are unrounded. Interestingly, we show that the positive relation between current short selling and both contemporaneous and past returns is driven by large, unrounded trade sizes. The positive relation between large shorting volume and past returns is not statistically discernable when examining only rounded trades. Similarly, we show that return predictability found in larger short sales is driven by unrounded instead of rounded short sales. In fact, the ability of larger shorts to predict negative returns significantly better than smaller shorts is not apparent in rounded trade sizes. As an additional test of the signaling hypothesis, we examine whether our results are driven by stocks that are most likely to face binding short-sale constraints. Following Asquith, Pathak, and Ritter (2005), Nagel (2005), and Xu (2007), we use the percentage of shares 3

6 outstanding that are held by institutions as an inverse proxy for the severity of short-sale constraints. Because institutions are the primary lenders of shares to short sellers, stocks with higher institutional holdings are more likely to have a greater equity loan supply and subsequently lower borrowing costs. Results in D Avolio (2002) indicate that a stock s equity loan supply relates positively to the proportion of shares outstanding held by institutions. The signaling hypothesis predicts that short sellers will signal their information to the market through the use of unusual trade sizes in order to forego longer open short positions and subsequently greater equity borrowing costs. Further, Abreu and Brunnermeier (2002) argue that synchronization risk is increasing in the costliness of borrowing shares. Therefore, our preliminary results supporting the signaling hypothesis should be driven by stocks that are most likely to face higher borrowing costs. Interestingly, we find that the positive relation between large short-sale volume and both contemporaneous and past returns is stronger for stocks that are more likely constrained. Further, this result in only found when examining unrounded short sales. Observing greater contrarian behavior by short sellers that use large unrounded trade sizes in stocks that are more likely constrained provides strong support for the signaling hypothesis. When examining the negative relation between current short selling and future returns, we find that the ability of larger short sales to predict negative returns better than smaller short sales is driven by constrained stocks, which supports the idea that short sellers are more motivated to signal pessimism in stocks that are most likely constrained. Again, this result is markedly higher for unrounded trade sizes when compared to rounded trade sizes. This latter result supports the idea that pessimistic signaling by short sellers is more apparent in stocks that 4

7 are most likely constrained and indicates that the severity of borrowing costs may indeed motivate short sellers to signal. The rest of this paper follows. Section II discusses the data used in the analysis. Section III presents the empirical tests while Section IV concludes. II. Data Description The short-sale data used in this analysis are obtained from the NYSE in response to the Securities and Exchange Commission s Regulation SHO. Short-sale transactions that are timestamped to the second are provided. We aggregate this intraday short-sale data to the daily level. One limitation of the Reg SHO data is that it is only available from January 2005 to beginning of Therefore, we restrict our sample time period to the calendar years of 2005 and From the Center for Research on Security Prices (CRSP), we obtain daily volume, returns, prices, shares outstanding, and market capitalization. To approximate short-sale constraints, we obtain quarterly institutional holdings from the 13F filings on the Thompsons Spectrum database. We require our sample of ordinary common stocks (CRSP share code 10 or 11) to trade everyday of the sample time period and have a price greater than $2. After merging the data and imposing our restrictions, we are left with 1,140 stocks. Of the 1,140 stocks, 367 are stocks that are part of the SEC s pilot program that temporarily suspended the uptick rule. Because Boehmer, Jones, and Zhang (2008) and Diether, Lee, and Werner (2009b) argue that the uptick rule may affect the trade sizes used by short sellers we further exclude these pilot stocks. 2 Therefore, our final sample includes 773 NYSE-listed stocks and 388,819 stock-day observations. 2 We perform the analysis separately for pilot stocks and find that the results are generally consistent with the nonpilot stocks. 5

8 Table 1 presents statistics that describe our sample. Panel A reports different stock characteristics while Panel B describes our different short-selling measures. Panel C introduces our short-selling ratios used to test the signaling hypothesis. Panel A shows that the average stock in our sample has a market cap (size) of nearly $9.5 billion and a price of $37. We calculate two measures of volatility. R_volt is the return volatility, which is defined as the standard deviation of daily returns from day t-10 to t, where day t is the current trading day. P_volt is calculated similar to Diether, Lee, and Werner (2009) and is defined as the difference between the daily high price and the daily low price divided by the daily high price. The average return volatility is while the average price volatility is Turn is the share turnover, which is the daily CRSP volume relative to shares outstanding (in percent). Nearly 0.82 percent of shares outstanding are traded daily for the average stock in our sample. InstOwn is the number of shares outstanding held by institutions, which is approximately 76 percent. Panel B reports the different measures of short-selling activity used in the analysis. Sh_turn is the short turnover, which is the daily short volume relative to shares outstanding (in percent). We partition the daily short-sale data into three different trade sizes similar to Boehmer, Jones, and Zhang (2008). Small short sales are short sales that are less than 2,000 shares while medium short sales are short sales that are between 2,000 and 4,999 shares. Short sales are classified as large if the short sale is greater than or equal to 5,000 shares. 3,4 Similar to Alexander and Peterson (2007), we define a short sale to be round if the short sale is a multiple 3 Boehmer, Jones, and Zhang (2008) use even a finer small trade size category of short sales less than 500 shares. However, we also examine round short sales (multiples of 500 shares) which would leave us without round short sales in the small trade-size category. 4 Our hypothesis that short sellers will choose to signal through their trade-size choice is based on the important assumption that the executed trades in the Reg SHO data represent the choices of the short sellers. While we would prefer to analyze order data as opposed to trade data, short sale orders are not publicly available. Alexander and Peterson (2007), who face similar data limitations when examining traders preferences for round sizes, overcome this limitation by comparing order data from the TORQ that is only available for a small period of time to trade data from TAQ. They find that order data and trade data produce nearly identical results and argue that using trade data to analyze traders preferences for particular trade sizes is justified. 6

9 of 500 shares. Using the different trade-size and rounding categories, we calculate the percentage of shares outstanding that are shorted using small short sales (S_sh_turn), medium short sales (M_sh_turn), large short sales (L_sh_turn), round short sales (R_sh_turn), and unrounded short sales (U_sh_turn). Panel B shows that 0.17 percent of shares outstanding are shorted daily for the average stock, which is made up of mostly small short sales (S_sh_turn = ) and unrounded short sales (U_sh_turn = ). The other descriptive statistics for the short-selling measures are also reported in Panel B. Panel C reports three different ratios that use throughout the paper to test the signaling hypothesis. L_Rat is the ratio of large short volume relative to the sum of both small and medium short volume (L_sh_turn/(S_sh_turn+M_sh_turn)). L_Rat* is the ratio of large short volume relative to the only small short volume (L_sh_turn/S_sh_turn). Finally, U_Rat is the ratio of unrounded short volume relative to rounded short volume (U_sh_turn/R_sh_turn). The panel reports that the average stock has a daily L_Rat of , a L_Rat* of , and the U_Rat of III. Results In this section, we first determine which types of short sales drive the positive relation between current short selling and both contemporaneous and past returns. Consistency with the signaling hypothesis is found if large shorts and unrounded shorts (or some combination of the two types of short sales) drive the contrarian behavior of short sellers. Second, we focus on the common negative relation between current short selling and future returns. While Boehmer, Jones, and Zhang (2008) show that larger short sales are better at predicting negative returns than smaller short sales, our analysis also focuses on unrounded and rounded short sales. 7

10 III.A. Contrarian Short Selling Diether, Lee, and Werner (2009) show that short sellers are contrarian in contemporaneous and past returns as the relation between current short selling and both current and past returns is significantly positive. Here, we attempt to determine which trade sizes drive the contrarian behavior of short sellers. We begin by examining the relation between current short selling and both contemporaneous and past returns in a multivariate framework similar to Diether, Lee, and Werner (2009). Table 2 provides the results from estimating the following equation using pooled data. Sh_turn i,t or SignalRatio i,t = β 0 + β 1 ret i,t + β 2 ret i,t-5,t-1 + β 3 sh_turn i,t + β 4 turn i,t + β 5 r_volt i,t + β 6 p_volt i,t + β 7 sh_turn,t-5,t-1 + β 8 turn i,t-5,t-1 + β 9 r_volt i,t-5,t-1 + β 10 p_volt i,t-5,t-1 + ε i,t (1) The dependent variable is short turnover (Sh_turn i,t ) or the signaling ratio (SignalRatio i,t ) for stock i on day t. SignalRatio is specified as L_Rat i,t, L_Rat* i,t, and U_Rat i,t which have been defined in Table 1. The independent variables include the contemporaneous return (ret i,t ), lagged return (ret i,t-5,t-1 ), the contemporaneous short turnover (sh_turn i,t ), turnover (turn i,t ), return volatility (r_volt i,t ), and price volatility (p_volt i,t ). We also include lagged short turnover, lagged turnover, lagged return volatility and lagged price volatility as additional control variables. These control variables are similar to those used in past research (Arnold et al., 2005; Boehmer, Jones, and Zhang, 2008; and Diether, Lee, and Werner, 2009). The variables of interest are the contemporaneous return (ret i,t ) and past returns (ret i,t-5,t-1 ). A Hausman test reveals observed differences across stocks and days so we report twoway fixed-effects estimates. Results obtained from pooled OLS regressions while controlling for conditional heteroskedasticity and clustering in the error terms are qualitatively similar. 8

11 Consistent with the results in Diether, Lee, and Werner (2009), column [1] shows that short selling is positively related to both contemporaneous (estimate = , p-value = 0.000) and past returns (estimate = , p-value = 0.000). Column [2] reports the results after controlling for a variety of other independent variables. Again, we see that the short turnover relates positively to both contemporaneous (estimate = , p-value = 0.000) and past returns (estimate = , p-value = 0.000). Similar to Diether, Lee, and Werner (2009) we find that contemporaneous shorting activity is positively related lagged shorting activity and negatively related to lagged turnover and contemporaneous price volatility. In columns [3] and [4], we report the results when the dependent variable is defined as L_Rat. Again, our hypothesis predicts that the estimates for ret i,t and ret i,t-5,t-1 will be increasing in the signaling ratio L_Rat. Consistent with this idea, we find that the estimate for ret i,t is (p-value = 0.000) in column [3] and (p-value = 0.000) in column [4]. A similar comparison shows that the estimates for ret i,t-5,t-1 are also positive in columns [3] and [4]. These results are consistent with the notion that larger trade sizes drive the contrarian behavior of short sellers and are consistent with the hypothesis that short sellers may be signaling that stocks are overvalued through the choice of their trade sizes. Columns [5] and [6] report the results for L_Rat*. Again, we show that the estimates for both ret i,t and ret i,t-5,t-1 are positive and significant. Interestingly, we show that estimate for ret i,t in column [5] is nearly 60 percent larger than the estimate in column [3]. Similarly, the estimate for ret i,t in column [6] is also 60 percent larger than the estimate for ret i,t in column [4]. A F- statistic, testing for equality between columns, rejects the null hypothesis that the estimates for ret i,t are equal suggesting that when excluding medium short volume in the denominator of the L_Rat, the positive relation between contemporaneous returns and large shorting activity is 9

12 stronger. A similar comparison for the estimates for ret i,t-5,t-1 yields the same conclusion. In unreported tests, we estimate equation (1) but specify the dependent variable as L_sh_turn, M_sh_turn, and S_sh_turn and find that the estimates for ret i,t and ret i,t-5, t-1 increase monotonically across the different trade-size dependent variable specifications, which is again consistent with the signaling hypothesis. Next, we estimate equation (1) for U_Rat. While we find that U_Rat relates positively to both ret i,t and ret i,t-5,t-1, we find that the latter relation is not statistically significant in either column [7] or column [8]. This result provides some additional evidence for the signaling hypothesis. To provide additional robustness to tests in Table 2, we next partition the data into round and unrounded short sales. In other words, we recalculate L_Rat and L_Rat* separately using rounded short sales and unrounded short sales, respectively. Table 3 reports the results of these tests. Columns [1] through [4] show the results using rounded short sales while columns [5] through [8] report the findings using unrounded short sales. Consistency with the signaling hypothesis is found if the contrarian behavior of short sellers, which is driven by larger short sales (Table 2), is more pronounced for the unrounded sample rather than the rounded sample. Columns [1] and [2] report the results examining rounded short sales and show that while the relation between L_Rat and contemporaneous returns is positive and significant, the relation between L_Rat and lagged returns (ret i,t-5,t-1 ) is not significant. Columns [3] and [4] show that L_Rat* is unrelated to lagged returns in column [3]. Columns [5] through [8] show that estimates for ret i,t and ret i,t-5,t-1 are positive and significant in each specification when analyzing unrounded shorts separately. Combined, these results suggest that the contrarian behavior of short sellers, which is driven by short sellers of larger trade sizes (Table 2), is predominantly 10

13 found in unrounded short sales and consistent with the idea that short sellers attempt to signal that a particular stock is deviating from its fundamental value by using some combination of large unrounded trade sizes. III.B. Contrarian Short Selling The Case of Short-Sale Constraints This subsection repeats the analysis in Tables 2 and 3 while conditioning on the likelihood of facing binding short-sale constraints. We begin by estimating the following equation using panel data. SignalRatio i,t = β 0 + β 1 ret i,t + β 2 ret i,t-5,t-1 + β 3 CONST i,t + β 4 ret i,t CONST i,t + β 5 ret i,t-5,t-1 CONST i,t + β 6 sh_turn i,t + β 7 turn i,t + β 8 r_volt i,t + β 9 p_volt i,t + β 10 sh_turn,t-5,t-1 + β 11 turn i,t-5,t-1 + β 12 r_volt i,t-5,t-1 + β 13 p_volt i,t-5,t-1 + ε i,t (2) Equation (2) is similar to equation (1) with the exception of the dummy variable CONST, which is equal to one if stock i is in the lowest institutional ownership quartile during a particular quarter; zero otherwise. Prior research argues that stocks with the lowest level of institutional ownership are most likely to face high equity borrowing costs (Asquith, Pathak, and Ritter, 2005; Nagel, 2005; and Xu, 2007). D Avolio (2002) shows that the equity loan supply is positively related to a stock s institutional ownership. With a more constrained loan supply, stocks with less institutional ownership are more likely to have higher borrowing costs. The variables of interest are the two interaction variables (ret i,t CONST i,t and ret i,t-5,t-1 CONST i,t ). If higher equity borrowing costs are driving the results showing that the contrarian behavior of short sellers is markedly higher for short sellers that use larger trade sizes, then the interaction estimates are expected to be positive. Positive interaction estimates indicate that the positive 11

14 relation between L_Rat (or L_Rat*) and both contemporaneous and past returns is stronger for stocks that are most likely to face a constrained equity loan supply. 5 Table 4 reports the two-way fixed effects estimates for estimating equation (2). Columns [1] through [4] present the results for L_Rat while columns [5] through [8] show the results for L_Rat*. Results in columns [1] through [4] show that the dummy variable CONST produces negative estimates indicating that short selling is lower in stocks that are most likely to face severe borrowing costs. Interestingly, the interaction estimates are positive and significant in columns [2] through [4] suggesting that the contrarian behavior of short sellers of large sizes is driven by stocks that are most likely to face severe borrowing costs. Similar conclusions are drawn in columns [5] through [8] as the interaction estimates are consistently positive. Combined with the results in Tables 2 and 3, results in Table 4 provide strong evidence supporting the signaling hypothesis, which is based on the idea that short sellers will be motivated to signal pessimism to reduce borrowing costs. Stocks with lower equity loan supplies are likely to have higher borrowing costs and subsequently more signaling with unusual trade sizes by short sellers. Similarly, Abreu and Brunnermeier (2002) argue that synchronization risk is increasing in borrowing costs, therefore, short sellers may also be more prone to signal pessimism in constrained stocks to reduce the amount of synchronization risk they face. Table 5 continues this analysis to estimating equation (2) while examining rounded and unrounded short sales separately. Columns [1] and [2] report the results for rounded short sales while columns [3] and [4] show the results for unrounded short sales. The variables of interest 5 To obtain the dummy variable CONST, we sort stock-quarter observations into quartiles based on the level of institutional ownership. We resort these portfolios each quarter. The purpose in doing so is to allow the variable CONST to vary across the time series so that the sufficient conditions for consistent fixed-effects estimates are not violated. In unreported tests, we obtain the average level of institutional ownership during the 2-year sample time period and estimate equation (3) using pooled OLS. Conclusions from these tests are similar to the conclusions we draw in this paper. Furthermore, the results are similar whether we control for conditional heteroskedasticity or clustering in the error terms. 12

15 are the interaction variables (ret i,t CONST i,t and ret i,t-5,t-1 CONST i,t ). Results show that the interaction estimate for ret i,t CONST i,t is not statistically different from zero in columns [1] or [2]. Furthermore, the interaction estimate for ret i,t-5,t-1 CONST i,t is not statistically significant in column [1] and only marginally significant in column [2] (p-value = 0.085). To the contrary, both interaction variables produce reliably positive estimates in columns [3] and [4]. Observing the positive (insignificant) interaction estimates in the sample of unrounded (rounded) short sales is consistent with the idea that short sellers of stocks that are most likely to face severe borrowing costs execute larger, unrounded short sales in an effort to signal pessimism to other sophisticated investors. III.C. Return Predictability Thus far, results in this study support the signaling hypothesis as the contrarian behavior of short sellers appears to be driven by short sellers of larger unrounded trade sizes in stocks that are most likely to face higher borrowing costs. Next, we examine the common negative relation between current short selling and future returns to determine if the return predictability of short sellers is driven by large unrounded short sales particularly in stocks that are most likely constrained. We begin by estimating the following equation using pooled data. adj-ret i,t+1, t+d = β 0 + β 1 SignalRatio i,t + β 2 sh_turn i,t + β 3 turn i,t + β 4 r_volt i,t + β 5 p_volt i,t + β 6 ret i,t-5,t-1 +ε i,t+1,t+d (3) The dependent variable is the four-factor risk-adjusted return from day t+1, t+d, where d = 3. Other dependent variable specifications (d = 1,2, 4 and 5) produce qualitatively similar results. 6 The independent variables include the signaling ratio (SignalRatio i,t ) for stock i on day t. We also include short turnover (sh_turn i,t ), turnover (turn i,t ), return volatility (r_volt i,t ), and price 6 We also estimate equation (3) using three-factor risk-adjusted returns, market-adjusted returns using either the CRSP value weighted or CRSP equally-weighted index, and CRSP raw returns. In each case, results are quantitatively similar to those reported in this study. 13

16 volatility (p_volt i,t ) for stock i on day t. Further, we include lagged returns (ret i,t-5,t-1 ). Equation (3) is similar to specifications in Diether, Lee, and Werner (2009). Since Diamond and Verrecchia s (1987) hypothesis that unanticipated increases in short selling will be followed by negative returns, others have found that short selling relates negatively to future returns at the daily level (Christophe, Ferri, and Angel, 2004; Boehmer, Jones, and Zhang, 2008; and Diether, Lee, and Werner, 2009). The objective in this subsection is to determine if large unrounded short sales drive the return predictability of short sellers. Therefore, we expect the estimate for sh_turn to be negative indicating that current short selling predicts future negative returns. After controlling for the return predictability of short selling, we expect SignalRatio (which is defined as L_Rat, L_Rat*, and U_Rat) to produce negative estimates. Table 6 reports the results from estimating equation (3). In response to a Hausman test, we estimate equation (3) using two-way fixed effects although similar results are obtained using pooled OLS while controlling for heteroskedasticity and clustering in the error terms. Column [1] shows that after controlling for other independent factors, the estimate for sh_turn is negative and significant (estimate = , p-value = 0.000) indicating that current short selling relates negatively to next-day returns. Columns [2] and [3] show that the estimate for L_Rat is negative and significant whether or not we control explicitly for sh_turn. The negative estimate for L_Rat suggests that larger short volume drives the return predictability and is consistent with findings in Boehmer, Jones, and Zhang (2008). In columns [4] and [5], we define SignalRatio as L_Rat* and find that L_Rat* produces reliably negative estimates again supporting the idea that the return predictability by short sellers is driven by larger short sales. Finally, columns [6] and [7] show that U_Rat relates negatively to future next-day returns. This new result indicates that 14

17 unrounded short sales also drive the return predictability thus providing additional support for the signaling hypothesis. Next, we provide additional tests in attempt to strengthen our results in Table 6. Table 7 reports the results from estimating equation (3) separately for rounded short sales and unrounded short sales. That is, L_Rat and L_Rat* are calculated first by using only rounded short sales, and second by using unrounded short sales. Columns [1] through [4] report the results for rounded short sales while columns [5] through [8] show the results for unrounded short sales. SignalRatio is defined as L_Rat in columns [1], [2], [5] and [6] and L_Rat* in columns [3], [4], [7] and [8]. Consistency with the signaling hypothesis is found if the negative relation between L_Rat (or L_Rat*) is predominantly stronger when examining the unrounded sizes compared to the rounded sizes. Table 7 columns [1] through [4] show that future next-day returns are unrelated to L_Rat and L_Rat* when examining rounded trades. Interestingly, columns [5] through [8] show that in each specification, L_Rat and L_Rat* produce reliably negative estimates. We again compare the estimates for L_Rat in columns [1] and [5] and in columns [2] and [6] and find that an F-statistic is sufficiently large enough to reject that the two estimates are equal indicating that the return predictability of short sellers that is driven by short sellers of larger trade sizes (Table 6), is particularly stronger in unrounded sizes. A comparison of the estimates for L_Rat* allows us to draw similar conclusions. Combined with Table 6, results in Table 7 provide adequate support for the signaling hypothesis. III.D. Return Predictability The Case of Short-Sale Constraints Similar to Section III.B, we next examine which trades drive the return predictability of short sellers while conditioning on the severity of equity borrowing costs. The signaling hypothesis predicts that short sellers will be more motivated to signal through the use of unusual 15

18 trade sizes in stocks that are more likely to face borrowing constraints. We again approximate borrowing constraints inversely with a stock s level of institutional ownership. To determine if our results in Tables 6 and 7 are driven by stocks that are most likely to face severe borrowing costs, we estimate the following equation. adj-ret i,t+1, t+d = β 0 + β 1 SignalRatio i,t + β 2 CONST i,t + β 3 SignalRatio i,t CONST i,t +β 4 sh_turn i,t + β 5 turn i,t + β 6 r_volt i,t + β 7 p_volt i,t + β 8 ret i,t-5,t-1 +ε i,t+1,t+d (4) The dependent variable and independent variables are similar to those reported in Table 7. We also include the dummy variable CONST which is equal to one if stock i is in the lowest institutional ownership quartile; zero otherwise. We interact CONST with the signaling ratio to determine if the negative relation between the signaling ratio and future returns is driven by stocks that are most likely to face binding short-sale constraints. A Hausman test again reveals differences across stocks and days so we estimate equation (4) using a two-way fixed effects regression. As before, we resort the institutional ownership portfolios each quarter to allow the dummy variable CONST to vary across the time series in order to avoid violating conditions for consistent fixed-effects estimates. Table 8 reports the results from estimating equation (4). Columns [1] and [2] report the results when including L_Rat while columns [3] and [4] present the results when including L_Rat*. Consistent with predictions of the signaling hypothesis, the interaction between L_Rat and CONST produces reliably negative estimates in both columns [1] and [2]. Similarly, the interaction between L_Rat* and CONST relates inversely with future next-day returns in both columns [3] and [4]. The negative interaction estimates indicate that the ability of large short sales to predict negative returns better than small short sales is markedly stronger in stocks that are more likely to face severe borrowing costs. In the framework of the signaling hypothesis, observing that the inverse relation between L_Rat (and L_Rat*) and future next-day returns is 16

19 stronger in stocks that are most likely constrained suggests that the propensity of short sellers to signal in increasing in the likelihood of higher equity borrowing costs. Our final test is in the same spirit as tests in Table 5. We estimate equation (4) separately for rounded short sales and unrounded short sales. In other words, the signaling ratios (L_Rat and L_Rat*) are calculated using rounded short sales and unrounded short sales. Table 9 reports the results from estimating equation (4) using a two-way fixed effects approach. Columns [1] through [4] report the results for rounded short sales while columns [5] through [8] present the results for unrounded short sales. Similar to Table 8, the variables of interest are the interaction variables. The signaling hypothesis predicts that the ability of larger short sales to predict negative returns better than smaller short sales should be driven by unrounded sizes in stocks that are most likely to face high borrowing costs. Therefore, the negative relation between the interaction of the L_Rat (or L_Rat*) and CONST should be driven by unrounded short sales in columns [5] through [8]. Table 9 columns [1] and [2] show that the interaction between L_Rat and CONST relates inversely with future next-day returns. We compare these estimates to the interaction estimates in columns [5] and [6]. Consistent with the predictions of the signaling hypothesis, the interaction estimates in columns [5] and [6] are approximately 1.65 times more negative than the interaction estimates in columns [1] and [2]. An F-statistic, testing for equality between columns [1] and [5] and columns [2] and [6], is sufficiently large (p-value = 0.000) thus rejecting the idea that the interaction estimates are equal and indicating that indeed the negative relation between the interaction of L_Rat and CONST and future next-day returns is driven by unrounded trade sizes. A similar comparison of columns [3] and [4] and columns [7] and [8] allow us to draw the same conclusions. In each comparison, the F-tests suggest that the interaction estimates for 17

20 unrounded shorts are more negative than the interaction estimates for rounded shorts. Combined, Tables 8 and 9 indicate that the return predictability of short sellers, which is shown in Tables 6 and 7 to be driven by larger sizes, is particularly stronger in the unrounded trade sizes and markedly higher in stocks that are most likely constrained, thus providing strong support for the signaling hypothesis. III.D. Unreported Tests Existing literature discusses how short selling can add to the informational efficiency in stock prices (Miller, 1977; Boehmer and Wu, 2009; and Diether, Lee, and Werner, 2009). Observing consistency with the notion that short sellers signal that particular stocks are overvalued through the use of unusual trade sizes is not tantamount to finding that the signaling by short sellers adds to price efficiency. In fact, the revenue from a short-sale transaction is the difference between the price at the time the short sale is executed and the price at when the short seller buys back the shares to return to the lender. If the price when the short position is closed is below the true price of the stock, the short seller s profitability is increasing, ceteris paribus. In unreported tests, we test whether short sellers use unusual trade sizes to destabilize prices by examining price reversals that occur after extreme negative returns. Following the methods of Boehmer and Wu (2009), we examine stock-day observations with extreme negative returns by identifying return observations that are two standard deviations below zero. We then define four different events based on returns the day after the extreme return day. Continuations are events when the return on day t+1 is negative. Small reversals are events when the return on day t+1 is positive but 20 percent less than the extreme return on day t in absolute value. Similarly, large reversals occur when returns on day t+1 are positive and between 20 percent and 100 percent of the extreme return on day t in absolute value. Over 18

21 reversals are events when returns on day t+1 are positive and greater, in absolute value, than extreme returns on day t. For instance, suppose on day t, the return for stock i is -2 percent, which we assume qualifies as an extreme return. If, on day t+1 the return for the same stock is +1 percent, then this occurrence is defined as a large reversal. If, on day t+1 the return for the same stock is +0.3 percent, then this event is categorized as a small reversal. A continuation would occur if the return on day t+1 is less than zero while an over reversal would be defined as the return on day t+1 being greater than +2 percent. Our first observation is that short turnover on the event day is decreasing in the size of the price reversal, which supports the notion that short sellers do not destabilize prices at the daily level. Our second observation is that percentage of short turnover made up from small (medium and large) short sales is increasing (decreasing) in the size of the price reversal. Third, these results are consistent for both round trade sizes and unrounded sizes. Combined, these observations indicate that the use of unusual trade sizes by short sellers do not generally destabilize prices on days with abnormally low returns. IV. Conclusion This study develops and tests the hypothesis that short sellers attempt to signal pessimism to the rest of the market through the use of different trade sizes. Because the cost of short selling is increasing in the length of the open short position, profit maximizing short sellers may be motivated to signal stocks are overvalued so the other market participants respond by helping correct temporary mispricing and thus reducing the length of the outstanding equity loan. Not only will signaling through unusual trade sizes potentially reduce equity borrowing costs, but signaling may also be a way that short sellers can mitigate help synchronization risk (Abreu and Brunnermeier, 2002). Using the assumption of previous research that argues that informed 19

22 traders will disguise their information by using smaller, rather than larger trades (Kyle, 1985; and Barclay and Warner, 1993) and round, rather than unrounded trades (Alexander and Peterson, 2007), we contend that short sellers will use large trades and unrounded trades to signal pessimism to the market. Consistent with this hypothesis, we find that while short sellers are contrarian in contemporaneous and past returns (Diether, Lee, and Werner, 2009), the level of their contrarian behavior is driven by larger trade sizes. Further, we find that this result is stronger for unrounded short sales than for rounded short sales. Interestingly, our findings are stronger in magnitude for stocks that are most likely to face higher borrowing costs. This latter result favorably supports the argument that short sellers are motivated to signal pessimism particularly for stocks that are most likely constrained. Next, we also examine the return predictability of short sellers. Both Boehmer, Jones, and Zhang (2008) and Diether, Lee, and Werner (2009) show that short sellers are able to predict negative returns at the daily level. Consistent with our hypothesis, we show that short sellers ability to predict negative returns is stronger in the large trade-size category. Furthermore, the ability of large unrounded short sales to predict negative returns is between 10 and 19 times stronger than the return predictability of large rounded short sales. Again, we find some evidence that these results are driven by stocks that are most likely constrained. The implications of this study are very different from other papers that analyze the behavior of informed traders (Kyle, 1985; Admati and Pfleiderer, 1988; Foster and Viswanathan, 1990; Barclay and Warner, 1993; Chakravarty, 2001; and Alexander and Peterson, 2007). Instead of disguising the information contained in their trades through the use of common trade sizes, our results are more consistent with the idea that informed short sellers can benefit 20

23 marginally from signaling their information. Further, our results provide a formal explanation for the findings in Boehmer, Jones, and Zhang (2008). 21

24 References: Abreu, D., and M.K. Brunnermeier, 2002, Synchronization Risk and Delayed Arbitrage. Journal of Financial Economics 66, Admati A. and P. Pfleiderer, 1988, A Theory of Intraday Patterns: Volume and Price Variability. Review of Financial Studies 1, Aitken, M., A. Frino, M. McCorry, and P. Swan, 1998, Short Sales are Almost Instantaneously Bad News: Evidence from the Australian Stock Exchange. Journal of Finance 53, Alexander, G.J. and M.A. Peterson, 2007, An Analysis of Trade-Size Clustering and its Relation to Stealth Trading. Journal of Financial Economics, Arnold, T., A.W. Butler, T.F. Crack, and Y. Zhang, 2005, The Information Content of Short Interest: A Natural Experiment. Journal of Business 78, Asquith, P., P.A. Pathak, and J.R. Ritter, 2005, Short Interest, Institutional Ownership, and Stock Returns. Journal of Financial Economics 78, Barclay, M.J. and J.B. Warner, 1993, Stealth Trading and Volatility: Which Trades Move Prices? Journal of Financial Economics, Boehmer E., C.M. Jones, and X. Zhang, 2008, Which Shorts are Informed? Journal of Finance 63, Boehmer, E., and J. Wu, 2008, Short Selling and the Informational Efficiency of Prices. Working Paper, University of Georgia. Chakravarty, S., 2001, Stealth Trading: Which Trader s Trades Move Prices? Journal of Financial Economics 61, Christophe, S., M. Ferri, and J. Angel, 2004, Short selling Prior to Earnings Announcements. Journal of Finance 59, D Avolio, G., 2002, The Market for Borrowing Stock. Journal of Financial Economics 66, Desai, H., K. Ramesh, S. Thiagarajan, and B. Balachandran, 2002, An Investigation of the - Information Role of Short Interest in the NASDAQ Market. Journal of Finance 52, Diamond, D. and R. Verrecchia, 1987, Constraints on Short Selling and Asset Price Adjustment to Private Information. Journal of Financial Economics 18,

25 Diether, K., K. Lee, and I. Werner, 2009, Short-Sale Strategies and Return Predictability. Review of Financial Studies 22, Diether, K., K. Lee, and I. Werner, 2009b, It s SHO Time! Short-Sale Price Tests and Market Quaility. Journal of Finance 64, Foster, F.D., and S. Viswanathan, 1990, A Theory of the Intraday Variations in Volume, Variance, and Trading Costs in Securities Markets. The Review of Financial Studies 3, Hasbrouck, J., Trades, Quotes, Inventories and Information. Journal of Financial Economics 22, Kyle, A.S., 1985, Continuous Auctions and Insider Trading. Econometrica 53, Nagel, S., 2005, Short Sales, Institutional Investors and the Cross-Section of Stock Returns. Journal of Financial Economics 78, Senchak, A. J., and L.T. Starks, 1993, Short-sale Restrictions and Market Reaction to Short- Interest Announcements. Journal of Financial and Quantitative Analysis Xu, J., 2007, Price Convexity and Skewness. Journal of Finance 62,

26 Table 1 Summary Statistics The table reports stock characteristics (Panel A) and short selling characteristics (panel B) for the stocks used in our sample. The table also describes the signaling ratios used in the analysis. Size is the market capitalization in dollars. Price is the daily CRSP ending price. R_volt is the return volatility and is calculated as the standard deviation of the daily returns from day t-10 to t where day t is the current trading day. P_volt is the price volatility and is measured as the difference between the daily high price and the daily low price divided by the daily high price. Turn is the share turnover, which is the daily CRSP volume divided by the shares outstanding in percent. Sh_turn is the short turnover, which is defined as the daily short volume scaled by the number of shares outstanding in percent. Similarly, S_sh_turn is the daily short volume made up from the small short sales (less than 2,000 shares) divided by the number of shares outstanding. M_sh_turn is the medium short turnover where medium shorts are short sales between 2,000 and 5,000 shares. L_sh_turn is the large short turnover (greater than or equal to 5,000 shares). R_sh_turn is the round short turnover which is the daily short volume made up from the rounded, or multiples of 500 shares, divided by the shares outstanding while U_sh_turn is the unrounded short turnover. Panel C reports the signaling ratios. L_Rat is the L_sh_turn divided by the sum of M_sh_turn and S_sh_turn. L_Rat* is L_sh_turn divided by S_sh_turn. U_Rat is U_sh_turn scaled by R_sh_turn. Panel A. Stock Characteristics Mean Std. Deviation Min Max Size Price R_volt P_volt Turn InstOwn 9,472,905, ,836,219, ,488, ,142,805, Panel B. Short Selling Characteristics Sh_turn S_sh_turn M_sh_turn L_sh_turn R_sh_turn U_sh_turn Panel C. Signaling Ratios L_Rat L_Rat* U_Rat

27 Table 2 Panel Regressions The table reports the results from estimating the following equation using pooled data. Sh_turn i,t or SignalRatio i,t = β 0 + β 1 ret i,t + β 2 ret i,t-5,t-1 + β 3 sh_turn i,t + β 4 turn i,t + β 5 r_volt i,t + β 6 p_volt i,t + β 7 sh_turn,t-5,t-1 + β 8 turn i,t-5,t-1 + β 9 r_volt i,t-5,t-1 + β 10 p_volt i,t-5,t-1 + ε i,t The dependent variable is short turnover (Sh_turn i,t ) for stock i on day t or the signaling ratio (SignalRatio i,t ). SignalRatio is defined as L_Rat i,t, L_Rat* i,t, and U_Rat i,t. The independent variables include the contemporaneous return (ret i,t ), lagged returns (ret i,t-5,t-1 ), the contemporaneous short turnover (sh_turn i,t ), turnover (turn i,t ), return volatility (r_volt i,t ), and price volatility (p_volt i,t ). We also include lagged short turnover, lagged turnover, lagged return volatility and lagged price volatility. A Hausman test reveals observed differences across stocks and days so we report fixed effects estimates by stock and day. Similar results are found using pooled OLS while controlling for conditional heteroskedasticity and clustering in the errors. P-values are reported in parentheses while *,**,*** represent whether the correlation is significant at the 0.10, 0.05, or 0.01 levels. Full-Sample Regressions Trade-Size Regressions Round-Size Regressions Sh_turn t L_Rat t L*_Rat t U_Rat t [1] [2] [3] [4] [5] [6] [7] [8] Intercept Ret t Ret t-5,t-1 Sh_turn t Turn t R_volt t P_volt t Sh_turn t-5,t-1 Turn t-5,t-1 R_volt t-5,t-1 P_volt t-5,t (0.115) *** *** *** (0.215) *** *** *** *** *** *** *** *** *** ** (0.047) *** *** *** *** ** (0.021) *** *** *** *** *** *** *** *** ** (0.012) (0.129) (0.987) *** *** *** *** (0.924) *** *** *** *** *** *** (0.002) *** *** *** (0.295) 14.62*** *** (0.004) (0.337) *** *** *** ** (0.017) (0.357) *** (0.109) * (0.096) *** *** (0.002) *** *** *** Adj. R 2 Stock FE Day FE The insignificant estimate for ret_5_1 (ret) is drive by small trades. U_Rat for large trades is (5.3343), medium trades = (3.1270), small trades = p=0.155(3.1280)