Trade-Size and Price Clustering: The Case of Short Sales

Transcription

1 Trade-Size and Price Clustering: The Case of Short Sales Benjamin M. Blau Department of Economics and Finance Huntsman School of Business Utah State University Bonnie F. Van Ness Department of Finance School of Business University of Mississippi Robert A. Van Ness Department of Finance School of Business University of Mississippi First version: November 15 th, 2007 Current version: August 17 th, 2009 The authors would like to thank Kathleen Fuller, Andriy Shkilko, Mark Van Boening and seminar participants at the University of Mississippi, Mississippi State University, and the 2009 Eastern Finance Association for their comments.

2 Trade-Size and Price Clustering: The Case of Short Sales Abstract: This paper compares the clustering of short sales and regular (non-short) trades on round prices and round trade sizes. Our findings show that short sellers prefer round sizes and round prices less than regular (non-short) traders. Further, we find evidence suggesting that size and price rounding decisions are not correlated for short sales on the NYSE and are negatively correlated for our Nasdaq sample. Combined, the results in this study support the idea that short sellers are less concerned with negotiation costs, cognitive processing costs, and the costs of revealing information to the market and more concerned with exploiting their private information.

3 I. Introduction After showing that traders prefer round trade sizes and round prices, Alexander and Peterson (2007) contend that three hypotheses best explain the observed trade-size and price clustering. First, the behavioral hypothesis posits that traders think in round numbers and therefore choose round sizes and prices to minimize cognitive processing costs (Wyckoff, 1963; Niederhoffer and Osborne 1966; and Ikenberry and Weston 2003). Second, clustering is consistent with the negotiations hypothesis, which suggests that buyers and sellers of assets attempt to minimize the costs of continuing negotiations by settling on round prices and round sizes (Ball, Torous, and Tschoegl, 1985 and Harris, 1991). Third, the stealth trading hypothesis argues that informed traders will attempt to disguise their information by breaking up larger trades into medium-sized trades not too large to reveal their information to other sophisticated traders and not too small because of transactions costs (Kyle, 1985; Foster and Vishwanathan, 1990; and Barclay and Warner, 1993). Results in Alexander and Peterson (2007) are consistent with the idea that sophisticated traders may attempt to disguise their trades using round sizes as they show that the price impact of round trades is greater than the price impact of unrounded trades, particularly for the medium trade-size category. In a separate stream of literature, Diamond and Verrecchia (1987) present theory showing that short sellers are more informed that other traders. Empirical research confirms this prediction as short sellers are shown to consistently predict negative returns (Dechow et al., 2001; Desai et al., 2002; Diether, Lee, and Werner, 2009; Senchack and Starks, 1993; Aitken et al., 1998; Desai et al., 2002; and Christophe, Ferri, and Angel, 2004). Recently, Boehmer, Jones, and Zhang (2008) show that larger short sales contain 1

4 more information than smaller short sales indicating that short sellers do not stealth trade, which is used to partially explain clustering on round trade sizes. Further, Diether, Lee, and Werner (2009) show that short sellers target stocks that become temporarily overvalued and are successful in predicting price reversals. Boehmer and Wu (2008) show that daily short activity adds to the informational efficiency in stock prices by shorting overvalued stocks and thus reducing pricing errors. If informed short sellers do not wish to disguise their trades and their tradable information depends on temporary pricing inefficiencies, then short sellers are likely to be less concerned with cognitive processing costs and negotiations costs and more concerned with exploiting their information. This assertion motivates the need to compare the preferences of short sellers and non-short traders for round trade sizes and round prices. This paper provides this comparison. We hypothesize that short sales will cluster less on round trades sizes and round prices than regular (non-short) trades. Results in this paper show that the percentage of short sales that execute at round sizes is significantly less than the percentage of non-short trades that execute at round sizes, particularly for the larger trade-size category, which likely contains more informed short sales (Boehmer, Jones, and Zhang, 2008). These results are robust to a variety tests similar to those reported in Alexander and Peterson (2007) and substantiate our claim that short sellers prefer round trade sizes less than non-short traders. In unreported results, we examine the intraday return predictability of short sellers. First, we find consistency with the notion that larger short sales contain the most information about future stock price movements (Boehmer, Jones, and Zhang, 2008) as larger short sales are followed by the most negative intraday returns. After separating 2

5 short sales into rounded and unrounded trades, respectively, we find that large unrounded short sales are followed by greater negative returns than large rounded short sales. This result rejects the idea that short sellers attempt to disguise their private information by using round trade sizes. In additional tests, we find that the percentage of short sales that execute at multiples of $0.05, $0.10, $0.25, $0.50, and $1.00 is significantly lower than the percentage of non-short trades that execute at these round price fractions, thus supporting the idea that short sellers also prefer round prices less than non-short traders. Less preference for round prices indicates that short sellers are not as concerned about processing costs and the costs of further negotiations. To provide more robust tests of the behavioral and negotiations hypotheses, we follow Alexander and Peterson (2007) and examine the simultaneous occurrence of round short sales executing at round prices. Using a bivariate probit method, we model price rounding and trade-size rounding decisions simultaneously. After controlling for factors that affect price and trade-size rounding, we find no statistical correlation between the likelihood of a round short sale executing at a round price for NYSE stocks. The correlation is significantly negative for NASDAQ stocks. This result makes the case for the negotiations and behavioral hypotheses less compelling when examining short selling data. Combined, this study shows short sellers are less concerned about costs that arise from continuing negotiations, cognitive processing costs, and the costs of revealing their private information to other sophisticated market participants. Instead, short sellers are likely more concerned with exploiting their private information. 3

6 While our results, which are obtained using short-sale transactions data, differ from the findings in Alexander and Peterson (2007) who examine all trades, our study indirectly provide robustness for their findings. Because short-sale volume makes up nearly 25 percent of trade-volume on the NYSE and 31 percent of trade-volume on NASDAQ (Diether, Lee, and Werner, 2009), the conclusions in Alexander and Peterson would be even stronger when excluding short sales. The rest of this paper follows. Section II describes the data. Section III develops empirical predictions and presents the tests of our predictions. Section IV concludes. II. Data Description Short-sale transactions data that is available in response to Regulation SHO (January 2005) and Trades and Quotes (TAQ) data are used in order to distinguish between short sales and non-short trades. Following Alexander and Peterson (2007), we randomly choose 200 NYSE-listed stocks and 200 Nasdaq-listed stocks from a universe of NYSE and Nasdaq-listed stocks that trade every day of the third quarter in 2006 (July 1, 2006 to September 30, 2006) and have a price greater than $5. 1 We obtain daily returns, prices, and market capitalization from the Center for Research on Security Prices (CRSP). Using the daily returns, we calculate return volatility, which is defined as the standard deviation of returns from day t-10 to day t. Following Diether, Lee, and Werner (2009), we also use a measure of price volatility that is obtained by dividing the difference between the daily high price and the daily low price by the daily high price. 1 Each stock that trades every day of the third quarter 2006 and has price greater than $5 is assigned a randomly generated number, from which, we choose 200 NYSE and Nasdaq stocks with the lowest random numbers. The choice of random stocks follows the sample selection of Alexander and Peterson (2007). 4

7 When matching the short-sale transaction data to TAQ, there are occasions when short sales only make up part of the trade. We exclude these trades in attempt to isolate the difference between unique short sales and unique non-short trades. 2 Table 1 reports statistics that describe our random sample. Panel A reports the average daily price, return, market cap (in $ thousands), return volatility, price volatility, non-short, and short-sale volume for the NYSE sample while Panel B presents the statistics that describe the Nasdaq sample. The average NYSE-listed stock has a daily price of $32.72 and daily return of Panel B shows that the average stock in the Nasdaq sample has a price of $22.64, a return of , and higher returns and price volatility than NYSE-listed stocks. When comparing the short volume to the non-short volume, it appears that short volume relative to non-short volume is higher for the Nasdaq sample than for the NYSE sample, which is consistent with the findings of Diether, Lee, and Werner (2009). III. Empirical Tests and Results In this section, we develop empirical predictions using relevant theoretical and past empirical literature. We then test our hypotheses. First, we compare the degree of clustering on round trade sizes for short sales and non-short trades. Second, we examine the clustering of prices on round fractions for both types of trades. Third, we turn to the simultaneous occurrence of rounded sizes and prices (both short and non-short). IV.A Rounded Trade Sizes 2 We also exclude trades that execute on regional exchanges so that trades for stocks listed on the two primary exchanges are included. 5

8 Wyckoff (1963) and Niederhoffer and Osborne (1966) argue that individuals are behaviorally motivated by round numbers, therefore, buying and selling will occur in round numbers. Ikenberry and Weston (2003) contend that traders will prefer round numbers in attempt to minimize cognitive processing costs. Alexander and Peterson (2007) argue that a trader s preference for round trade sizes is consistent with, what they term, the behavioral hypothesis. Observing clustering on round sizes may also be consistent with the idea that traders settle on round numbers in order to mitigate further negotiations costs (Ball, Torous, and Tschoegl, 1985, and Harris, 1991). Denoted the negotiations hypothesis, Alexander and Peterson (2007) argue that clustering on round sizes is also consistent with this idea. Alexander and Peterson (2007) assert that round sizes may be used by informed traders in order to disguise their information. This argument parallels the stealth trading hypothesis presented in Barclay and Warner (1993). 3 Stealth trading is defined as the occurrence of informed traders breaking up larger trades into medium-sized trades in order to disguise their information. Medium trades are optimal because large trades can reveal the informed investors private information to other sophisticated market participants and small trades are subject to higher overall transaction costs. In the 3 Theory suggests that informed traders spread their trades over time (Kyle, 1985, Foster and Vishwanathan, 1990, and Admati and Pfleiderer, 1988). In their seminal study on stealth trading, Barclay and Warner (1993) document that approximately 90% of the cumulative price change is made up from medium-sized trades for their sample of stocks that are tender offer targets in the 1980s. Chakravarty (2001) argues that, if institutional traders are more informed than individual traders (Lo and MacKinlay, 1990; Meulbroek, 1992; Cornell and Sirri, 1992; Chakravarty and McConnell, 1997; and Koski and Scruggs, 1998), then institutions are more likely to engage in stealth trading strategies. Consistent with his conjecture, Chakravarty finds that approximately 80% of the cumulative price change is made up from medium-sized, institutional trades while virtually none of the cumulative price change is made up from medium-sized individual trades. 6

9 framework of round trade-size clustering, Alexander and Peterson argue that round sizes may act as an additional disguise for the information contained in certain trades. The recent consensus in the literature is that short sales contain information about future stock prices (Diamond and Verrecchia, 1987; Aitken et al., 1998; Christophe, Ferri, and Angel, 2004; Boehmer, Jones, and Zhang, 2008). Further, evidence indicates that short sellers are contrarian traders (Diether, Lee, and Werner, 2009) and add to the informational efficiency in prices by reducing pricing errors when stocks become temporarily overvalued (Boehmer and Wu, 2008). We hypothesize that because short sellers are informed about the true value of stocks and their information about overvalued stocks is based on differences between the trading price and the true price, short sellers will likely be less concerned about costs that arise from additional negotiations, cognitive processing, and costs of revealing information to the market. Instead, short sellers are likely more concerned with exploiting their information. Therefore, trade-size clustering on round sizes should occur less frequently for short sales than for non-short sales. An important caveat should be made as the data used in the analysis consists of the trade size at execution as opposed to the order size of the trade. Because of the lack of availability of order data, we use trade data, similar to those used in Alexander and Peterson (2007). Alexander and Peterson do use order data for a portion of their analysis and find that the results for the trade data and order data during the same time period are qualitatively similar and therefore argue that using trade data to extend their time period is justified. 7

10 Because of this argument, we follow previous research and use trade data as an approximation of trader s order preferences when examining clustering. 4 Figures 1.A through 1.D show the clustering of trades on certain sizes for both non-short trades and short sales of NYSE and Nasdaq-listed stocks. In figures 1.A and 1.B, trades on the NYSE tend to cluster on multiples of 1,000 shares and multiples of 5,000 shares. Also, the figures show some evidence of clustering on multiples of 500 shares. When comparing the two figures, it appears that non-short trades have a slightly more distinct clustering pattern than short sales. Figures 1.C and 1.D show the clustering of trades on certain sizes for the Nasdaq sample. Clustering on round sizes appears to be more prevalent in the Nasdaq sample than in the NYSE sample, which is consistent with findings in Alexander and Peterson (2007). 5 In order to test for a difference in the trade-size choice of short sellers and nonshort traders, we calculate the percentage of trades that execute on multiples of 500 shares, 1,000 shares, and 5,000 shares. Using standard t-tests, we determine whether there is a significant difference between trade-size rounding of short sales and non-short trades. Table 2 reports the percentage of non-short trades that occur on multiples of 500, 1,000, and 5,000 shares for the two samples. Panel A presents the results for the NYSE sample while Panel B report the results for the Nasdaq sample. In Panel A, we see that 4 The empirical predictions are based on the comparison of the non-short trades and short sales. If there is a systematic bias between trade and order data, it will probably exist for both short sales and non-short trades. 5 While the figures appear to show more clustering on Nasdaq, we do not know if there is more/less clustering on Nasdaq than the NYSE as do not directly compare the two exchanges, and that is outside the scope of this study (the NYSE and Nasdaq samples are not matched). 8

11 the percentage of non-short trades that occur at round sizes is significantly higher for multiples of 500 shares, 1,000 shares, and 5,000 shares. Indeed, clustering on round multiples of 500 shares tends to occur 10.5 percent ([ ]/ ) more often for non-short trades than for short sales while clustering on round multiples of 1,000 shares is 15.3 percent higher for non-short trades. Results in column (3) are pervasive as the percentage of non-short trades that execute on round multiples of 5,000 shares ( percent) is nearly three times larger than the percentage of short sales that execute on similar round multiples ( percent). Results for the Nasdaq sample differ somewhat. In Panel B we observe that large Nasdaq trades (non-short) are more likely to cluster on round sizes than large Nasdaq short sales (column three). The evidence from Table 2 supports the notion that short sales cluster less on round sizes than non-short trades, particularly for large trades. This result is consistent with our hypothesis that information-motivated short sellers are less concerned with costs associated with foregoing rounded trades and is reconcilable with current literature. Boehmer, Jones, and Zhang (2008) contend that informed short sellers do not stealth trade and instead execute larger trade sizes. If short sellers informativeness decreases the likelihood of clustering on round sizes, then large short sales, which are found to contain the most information, should drive the observation of less overall clustering. Findings in Table 2 are consistent with this argument. We next follow Alexander and Peterson (2007) by attempting to determine whether traders prefer round trades to unrounded trades by examining the percentage of trades that are multiples of 500 shares relative to the proportion of trades that are plus 100 shares or minus 100 shares from the multiples. This method, which is used in Alexander 9

12 and Peterson (2007), analyzes trades that are 400, 500, 600, 900, 1,000, 1,100, 1,400, 1,500, 1,600 shares; etc.. If traders are indifferent between round sizes and unrounded sizes, then the percentage of trades at multiples of 500 shares will be approximately 33 percent. If traders prefer round sizes, the percentage of trades at multiples of 500 shares will be significantly greater than 33 percent. Similar intuition applies when examining the percentage of trades that occur at multiples of 1,000 shares relative to trades that occur at plus or minus 500 shares from the multiple. Hence, we include trades of 500, 1,000, 1,500, 2,000, 2,500, 3,000 shares, etc. If traders prefer multiples of 1,000 shares, then the percentage of rounded trades will be significantly greater than 33%. A binomial z-statistic tests the following hypothesis, H H 0 A 1 :Z 3 1 :Z 3 where Z is the percentage of trades (both short and non-short) that are multiples of 500 and 1,000 shares, respectively. Since research finds that non-short traders break up larger trades into smaller trades in order to disguise their information to other market participants (Barclay and Warner, 1993; Chakravarty, 2001; and Alexander and Peterson, 2007) but short selling research finds that informed short sellers prefer larger trade sizes (Boehmer, Jones, and Zhang, 2008), the differences between the percentage of trades at round sizes should be a function of the size of the trade. Since our hypothesis suggests that informed short sellers are less concerned with negotiations costs, cognitive processing costs, and the costs of revealing their information to market, large short sales, which contain the most information, are less likely to be rounded than large non-short trades. 10

13 We expect the difference between trade-size rounding for non-short trades and short sales to be increasing across trade sizes. 6 Trades are separated into three categories similar to Boehmer, Jones, and Zhang (2008). Small trades are trades less than 2,000 shares, medium-sized trades are trades between 2,000 and 5,000 shares while large trades are trades greater than or equal to 5,000 shares. 7 Table 3 Panel A reports the percentages of small non-short trades and small short sales that are rounded along with a p-value that is obtained from the binomial z-test. First, we find that non-short traders of small sizes prefer round multiples of 500 shares to unrounded sizes across each trade-size category as the percentage of round trades is significantly greater than 33%. Small non-short traders do not prefer multiples of 1,000 shares for the small trade-size category as the percentage of rounded non-short trades is significantly less than 33 percent, suggesting that small non-short traders prefer trades of 500 shares or 1,500 shares to trades of 1,000 shares. The rounding preference is similar between samples. Second, we find that short sellers of small sizes may also prefer round sizes to unrounded sizes as results for short sales are quite similar to the results for non-short trades. Because our objective in this section is to compare the trade-size preferences of non-short traders and short sellers, we examine the difference between the percentages of rounding for non-short trades and the percentages of rounding for short sales. Interestingly, the difference between non-short percentages and short sale percentages in Panel A shows that short sellers of small sizes prefer rounded trades more than non-short traders as evidenced by 500 share multiples on 6 For this reason, we do not examine the percentage of trades at rounded multiples of 5,000 shares because these multiples are all categorized as large trades and our hypothesis argues that the rounding decision is based on these trade-size categories. 7 Boehmer, Jones, and Zhang (2008) separates short sales into small trade sizes (< 500), medium-small trade sizes (500 to 1,999), medium-large trade sizes (2,000 to 4,999), and large trade sizes (5,000). The small size group is extended to 2,000 shares in order to test if smaller short sales are executed on a multiple of 500 shares. 11

14 the NYSE and 1,000 share multiples for the Nasdaq sample. A similar examination of Panel B shows that medium-sized short sales and medium-sized non-short trades are similarly rounded. The only exception is for multiples of 1,000 shares as the NYSE short sales cluster less on round sizes while Nasdaq short sales tend to cluster more on round sizes. Comparing the preferences of round multiples in Panel C reveals that nearly systematically, clustering on round multiples is much lower for short sales than for nonshort trades as the reported differences are positive in each column (the difference in [3] is insignificant). These results support the notion that large short sales are motivated by information and informed short sellers are less concerned with negotiations costs and cognitive processing costs. Short sellers of large sizes may be more concerned with the information contained in the transaction, not necessarily the terms of the transaction. Additional tests of the hypothesis that clustering depends on trade sizes are provided in a regression framework. Similar to Alexander and Peterson (2007), the following equation is estimated: ln perc i = δ 0 + δ 1 D 500 _ Si + δ 2 D 500 _ Mi + δ 3 D 500 _ Li + δ 4 D 1000 _ Si + δ 5 D 1000 _ Mi + δ 6 D 1000 _ Li + δ 7 D 5000i + ε i (1) The dependent variable is the natural log of the percentage of trades that occur at size i. The independent variables are seven dummy variables that capture whether or not size i is a round trade size while accounting for the size of the trade. D 500_S is equal to one if size i is 500, 1,000, or 1,500 shares. D 500_M is equal to one if size i is 2,000, 2,500, 3,000, 3,500, 4,000, or 4,500 shares. Likewise, D 500_L is equal to one if size i is equal to multiples of 500 greater than or equal to 5,000 shares. The other dummy variables are 12

15 similarly defined. All trade sizes that are multiples of 100 shares and less than or equal to 15,000 shares are included in the analysis. Equation (1) is estimated for non-short trades and for short sales and a comparison of the estimated parameters is discussed. If informed short sellers prefer round sizes less than non-short traders, then the estimates for δ 3, the coefficient for trades rounded to 500 shares in the large size category, and δ 6, the coefficient for trades rounded to 1,000 shares in the large size category, will be significantly larger for non-short trades than for short sales. The results estimating equation (1) using robust White (1980) standard errors are reported in Table 4. Panel A reports the regression results. Our first observation in the table is that clustering on round sizes is not robust to different trade sizes. The estimates for 1,000 share dummy variables (δ 1000_ S, δ 1000_M, and δ 1000_L ) are not significantly different from zero. When comparing the estimates for δ 500_S, δ 500_M, δ 500_L, and δ 5000 in columns (1) and (2), we see that each of the estimates in column (1) is larger than in column (2). 8 Again, the estimates for for δ 500_S, δ 500_M, δ 500_L, and δ 5000 in column (3) are larger than the same estimates in column (4). 9 There is no evidence of clustering on large multiples of 500 shares for NYSE or Nasdaq short sales while non-short trades appear to cluster on large multiples of 500 shares. This result is also consistent with the notion that short sellers of large sizes are not concerned with the terms of the transaction. The results of Table 4 provide some support for the notion that non-short traders prefer round sizes more than informed short sellers. 8 F-statistics comparing the estimates are 1.38 (p-value = 0.240) for δ 500_S, 2.92 (p-value = 0.088) for δ 500_M, (p-value = 0.000) for δ 500_L, and 1.00 (p-value = 0.318) for δ F-statistics comparing the estimates are 0.39 (p-value = 0.531) for δ 500_S, 0.51 (p-value = 0.476) for δ 500_M, 1.45 (p-value = 0.229) for δ 500_L, and 1.26 (p-value = 0.263) for δ

16 Thus far, we find evidence consistent with our hypothesis that short sales cluster less on round sizes than non-short trades because informed short sellers are less likely to be concerned with cognitive processing costs, negotiations costs, and the costs of revealing information to the market. This evidence appears to be driven by larger short sales, which likely contain the most information (Boehmer, Jones, and Zhang, 2008). Because our hypothesis is based on the informativeness of different sized short sales, we examine the ability of short sales to predict negative intraday returns. In unreported results, we examine 30-minute and 60-minute returns after rounded and unrounded short sales. 10 We also partition these tests by different trade sizes. For NYSE short sales we find that 60-minute returns following large short sales are nearly twice as negative as the 60-minute returns that follow small short sales. Consistent with Boehmer, Jones, and Zhang (2008), we find that returns are monotonically decreasing across increasing trade sizes, indicating that larger short sales contain more information than smaller short sales. We find similar results for Nasdaq short sales although returns following larger short sales are only slightly more negative than returns that follow small short sales. Both Boehmer, Jones, and Zhang (2008) and Diether, Lee, and Werner (2009b) suggest that stealth trading is more likely to occur in Nasdaq stocks than in NYSE stocks because of less restrictive price-tests, which may partially explain our results. In general, our untabulated results show that unrounded short sales, particularly in the larger trade-size category, are better at predicting negative intraday returns than rounded short sales. These results are consistent with the idea that short sellers do not attempt to disguise the information in their trades by using round trade sizes. 10 Results are available upon request. 14

17 IV.B Rounded Prices We now examine the preferences of short sellers and non-short traders for round prices. Alexander and Peterson (2007) argue that clustering on round prices may exist for the some of the same reasons that trade-size rounding exists, namely the behavioral and negotiations hypotheses. Figures 2.A to 2.D show the frequency of non-short trades and short sales at $0.01 increments for both the NYSE and Nasdaq samples. Similar to previous research, the figures show substantial clustering on round price fractions. Whole dollars appear to be more popular than half-dollars, which are more popular than quarters. Further, tenths (multiples of dimes) appear to be more popular than twentieths (multiples of nickels). In figures 2.A and 2.B, it appears that price clustering on the NYSE occurs more frequently for non-short trades than for short sales as the price increments between nickels are smoother for non-short trades than for short sales. In figures 2.C and 2.D, it is more difficult to determine if price clustering on Nasdaq differs between non-short trades and short sales. Similar to our initial analysis of trade-size rounding, we calculate the percentages of non-short trades and short sales that execute at round prices. We compare the percentages between non-short trades and short sales to determine if non-short trades execute at rounded prices more than short sales. Round prices are defined as multiples of $1.00, $0.50, $0.25, $0.10, and $0.05. Table 5 reports the results of the analysis. Panel A reports price rounding for both non-short trades and short sales as well as the difference between non-short and short trades for both the NYSE and the Nasdaq sample. 15

18 The NYSE results show that non-short trades execute at round prices significantly more than short sales. This result is consistent with the hypothesis that short sellers, who are more likely to be informed than non-short traders, are less concerned with negotiation and cognitive processing costs. Panels B through D show price rounding across the different trade sizes, where the different trade sizes are defined as before. The results hold for each trade size in the NYSE sample. However, the results are only significant for Nasdaq stocks in the small trade-size category although there is some evidence in support of our hypothesis in medium-sized trades. 11 This observation may be due to the lack of large Nasdaq short sales. IV.C Simultaneous Price and Trade-Size Rounding Following Alexander and Peterson (2007), we examine instances when both round short sales and round non-short trades execute at round price fractions. Alexander and Peterson argue that simultaneous trade-size rounding and price rounding provide a more robust test of the negotiation and behavioral hypotheses. Therefore, trades that are multiples of 500 shares and trades that are plus and minus 100 shares from the multiple are examined. The cross-sectional mean of the percentage of round trades that occur at round prices is estimated. We expect that informed short sellers will be less concerned with negotiations and cognitive processing costs, which will be manifested in fewer round short sales at round prices relative to non-short trades. 11 Figures 2.C and 2.D provide possible explanations. The results in Table 5, panels C and D may be a result of sparse short-selling activity in the larger trade-size categories for the Nasdaq sample. 16

19 Table 6 presents the results of the t-tests for both the NYSE and the Nasdaq samples. As previously, multiples of $1.00, $0.50, $0.25, $0.10, and $0.05 are shown. Panel A reports the results for trades (both non-short and short) of all sizes. Consistent with our expectations, round short sales occur less frequently at round prices and trade sizes than non-short trades. The results from these t-tests further strengthen earlier findings, which suggest that short sellers are less concerned with negotiations and cognitive processing costs. In Panel A, the analysis is performed across all trade sizes, while panel B is small, panel C is medium, and panel D is large trade sizes. If larger short sales contain more information (Boehmer, Jones, and Zhang, 2008) than smaller short sales, the difference between the percentage of round trades at round prices will increase across trade sizes because informed short sellers are less likely to be concerned with the terms of the transaction. Short sellers prefer round trade sizes at round prices significantly less than non-short traders for the NYSE sample. Further, the difference is increasing across increasing trade sizes for the NYSE sample. 12 A pooled bivariate probit regression provides additional tests of the simultaneous occurrence of round sizes and round prices. Alexander and Peterson (2007) use a bivariate probit model and show that, after controlling for other factors that influence the rounding decision, there is a positive correlation between the likelihood that a trade is rounded in size and the likelihood that a trade is rounded in price. Therefore, the following equations are estimated simultaneously. round size 1 = β 0 + β 1 return j,i,t-30 + β 2 shortsize j,i,d + β 3 volume j,i,d + β 4 size j,i,d + 12 While short sellers of Nasdaq stocks prefer round trade sizes at round prices less than non-short traders in the small trade-size category, we do not find significance in larger trade sizes, which may, again, be explained by fewer instances of short-selling activity in larger trade-size categories. 17

20 β 5 r_volt j,i,d + β 6 p_volt j,i,d + ε 1 (2) round price 2 = β 0 + β 1 return j,i,t-30 + β 2 shortsize j,i,d + β 3 volume j,i,d + β 4 size j,i,d + β 5 r_volt j,i,d + β 6 p_volt j,i,d + ε 2 (3) Rho = Cov(ε 1, ε 2 X 1, X 2 ) (4) where the dependent variable in equation (2) is binary and equal to one if short sale i is a multiple of 500 shares. Following Alexander and Peterson (2007), the dependent variable in equation (3) is equal to one if short sale i occurs on a round price, which is defined as a multiple of $0.05 or 1/20 th of a dollar. The past 30 minute return for trade i of stock j is included as a control. Other control variables include the size of the short sale, the daily volume, size (market cap), return volatility, and price volatility (defined before). Rho, in equation (4), is the estimated covariance of the error terms in equations (2) and (3) conditioned on the control variables used in the analysis. Alexander and Peterson find a positive estimate for Rho suggesting that, after controlling for other factors that influence the rounding decision, traders prefer round sizes and round prices simultaneously. If private information about the true value of stocks motivates short sellers to trade quickly and be less concerned with the transaction terms, then we expect the estimate for rho to be non-positive. Table 7 reports the results from the estimating equations (2) and (3) using only short sales. Consistent with the argument that information in short sales depends on past intraday returns, the estimate for β 1 is negative suggesting that after periods of high returns, short sellers do not prefer round sizes or round prices. Size rounding is positively related to the size of the short sale. Size and price rounding occur more on 18

21 high volume days. Return and price volatility are positively (negatively) related to the likelihood of trade-size (price) rounding for both samples. In general, price and size rounding occur more in lower cap stocks, which is consistent with the notion that smaller stocks have less of a following by analysts and the costs of negotiating for equilibrium prices are high, therefore, buyers and sellers settle on round sizes and round prices. The estimate of primary interest is rho, the conditional covariance of the error terms for the two equations. We observe non-positive estimates for both the NYSE and Nasdaq samples (the estimate for rho is virtually zero in the NYSE sample and negative in the Nasdaq sample), which suggest that, after controlling for other factors that influence rounding decisions, short sellers are indifferent to round sizes at round prices. These results differ from Alexander and Peterson (2007), whose findings are consistent with negotiations and behavioral hypotheses, that traders prefer round sizes at round prices. The results in our paper show that short sellers are, at least indifferent, suggesting that they are less concerned with negotiation and cognitive processing costs. Our results infer that short sellers trade-size choices are motivated differently than the trade-size choices of non-short traders. Short sellers, who are contrarian in past returns and add to the informational efficiency in prices, are arguably less concerned with costs of negotiations, cognitive processing costs, and the costs of revealing their information to the market. Since Boehmer and Wu (2008) finds that short sales reduce pricing errors as informed traders are able to execute short sales for stocks that become overvalued, short sellers likely view the timing of and the information contained in the transaction as more important than the terms of the transaction. 19

22 IV. Conclusion Alexander and Peterson (2007) show that trades tend to cluster on round sizes and argue that this observed clustering is explained primarily by three hypotheses. The behavioral hypothesis suggests that traders think in round number and therefore prefer round trade sizes and round prices (Wyckoff, 1963; Niederhoffer and Osborne, 1966; and Ikenberry and Weston 2003). The negotiations hypothesis argues that traders will settle on round numbers to avoid the additional costs of continuing negotiations (Ball, Torous, and Tschoegl, 1985; Grossman et al., 1997; and Harris, 1991). The stealth trading hypothesis contends that informed traders are motivated to break up their larger trades into smaller trades to avoid revealing their information to other sophisticated market participants (Kyle, 1985; Admati and Pfleiderer, 1988; and Barclay and Warner, 1993). Alexander and Peterson argue and find some evidence that using round sizes may also disguise the information of informed traders. Following Alexander and Peterson (2007), this study examines the clustering of trades on round sizes and at round prices, but separates trades into two distinct categories, short sales and regular (non-short) trades. Our purpose in doing so is motivated by two streams of research. First, several papers document that short sellers are informed about the true value of stocks (Diamond and Verricchia, 1987; Senchack and Starks, 1993; Aitken et al., 1998; Desai et al., 2002; and Christophe, Ferri, and Angel, 2004) and that larger short sales contain more information about future firm performance than smaller short sales (Boehmer, Jones, and Zhang, 2008). The latter result indicates that short sellers do not stealth trade, which, in the framework of trade-size clustering, suggests that short sellers have less motivation to prefer round sizes. Second, Diether, Lee, and 20

23 Werner (2009) show that short sellers are contrarian in contemporaneous and past daily returns and are able to accurately predict price reversals while Boehmer and Wu (2008) show that daily short selling reduces pricing errors and add to the informational efficiency of stock prices. Combined, these studies indicate that short sellers are informed about the true value of stocks and tend to target stocks that become temporarily overvalued. If the profitability of short selling depends on information about temporary overvaluation, then short sellers are likely not willing to settle on round prices nor are they likely to be overly concerned about cognitive processing costs. For these reasons, we hypothesize that short sales will cluster less on both round trade sizes and round prices. Consistent with our contention, we first find that short sales generally cluster less on round trade sizes than non-short trades. This result is driven by larger short sales, which contain the most information (Boehmer, Jones, and Zhang, 2008) suggesting that short sellers are less concerned with minimizing negotiations costs and cognitive processing costs, and are more concerned with exploiting the information in their trades. Second, we show that short sales cluster less on round prices than non-short trades. Price rounding for short sales is driven by smaller cap stocks on days with high volume indicating that less known stocks during high levels of uncertainty motivate short sellers to prefer round prices. Third, using short sales transactions data, we find that price rounding and trade-size rounding is independent for the NYSE sample and negatively correlated for the Nasdaq sample. Alexander and Peterson (2007) argue that the simultaneous occurrence of price rounding and trade-size rounding is a robust test of the negotiations and behavioral hypothesis. Observing a non-positive correlation between 21

24 these two types of rounding indicates that short sellers are not concerned with the costs of negotiating and the cognitive processing costs. In unreported results, we find that large short sales predict larger negative returns than smaller short sales. Further we observe that large unrounded short sales predict negative returns better than large rounded short sales indicating that informed short sellers do not use round sizes to disguise the information in their trades. Combined, results from this study suggest that short sellers are more concerned with exploiting their private information. Further, our results provide additional robustness to the findings of Alexander and Peterson (2007). While short sales make up nearly 24 percent of trading volume on the NYSE and 31 percent on Nasdaq (Diether, Lee, and Werner, 2009), our findings suggest that the results in Alexander and Peterson would be stronger in magnitude than first documented if short sales were excluded. 22

25 References: 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, 84, Ball, C.A., W.A. Torous, and A.E. Tschoegl, 1985, The Degree of Price resolution: The Case of the Gold Market. Journal of Futures Markets 5, Barclay, M.J. and J.B. Warner, 1993, Stealth Trading and Volatility: Which Trades Move Prices?. Journal of Financial Economics, 34, Bessembinder, H., 2003, Trade Execution Costs and Market Quality after Decimalization. Journal of Financial and Quantitative Analysis, 38, pg 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, Texas A&M University. Chakravarty, S. and J.J. McConnell, 1997, An Analysis of Prices, Bid/Ask Spreads and Bid/Ask Depths Surrounding Ivan Boesky s Illegal Trading in Carnation s Stock. Financial Management, 26, 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, Cornell, B. and E. Sirri, 1992, The Reaction of Investors and Stock Prices to Insider Trading. Journal of Finance, 47, Dechow, P., A. Hutton, L. Meulbroek, and R. Sloan, 2001, Short-sellers, fundamental analysis, and stock returns, Journal of Financial Economics 61,

26 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, Diether, K., K.-H. Lee, and I. Werner, 2009, Short-sale strategies and return predictability. Review of Financial Studies 22, Diether, K., K.-H. Lee, and I. Werner, 2009b, It s SHO Time, Short-Sale Price Tests and Market Quality. Journal of Finance 64, Foster, F.D., and S. Viswanathan, 1993, A Theory of the Interday Variations in Volumn, Variance, and Trading Costs in Securities Markets. Review of Financial Studies 4, Grossman, S., M. Miller, K. Cone, D. Fischel, and D. Ross, Clustering and Competition in Asset Markets. Journal of Law and Economics, 40, Harris, L., 1991, Stock Price Clustering and Discreteness. Review of Financial Studies, 4, Ikenberry, D., and J.P. Weston, 2003, Clustering in US Stock Prices after Decimalization. Working paper, Rice University. Koski, J.L. and J.T. Scruggs, 1998, Who Trades on the Ex-Dividend Day? Evidence from the NYSE Audit File Data. Financial Management, 27, Kyle, A.S., 1985, Continuous Auctions and Insider Trading. Econometrica, 53, Lo, A. W. and A.C. MacKinlay, 1990, When are Contrarian Profits Due to Stock Market Overreaction?. Review of Financial Studies, 3, Meulbroek, L., 1992, An Empirical Analysis of Illegal Insider Trading. Journal of Finance, 47, Moulton, P., 2005, You Can t Always Get What You Want: Trade-size Clustering and Quantity Choice in Liquidity. Journal of Financial Economics, 78, Niederhoffer, V., and M.F.M. Osbourne, 1966, Market Making and Reveral on the Stock Exchange. Journal of the American Statistical Association, 61,

27 Senchack, A. J., and L.T. Starks, 1993, Short-sale Restrictions and Market Reaction to Short-Interest Announcements. Journal of Financial and Quantitative Analysis 28, Wyckoff, P., 1963, Psychology of Stock Market Timing. Prentice-Hall, Englewood Cliffs, NJ. 25

28 Table 1 Descriptive Statistics The table presents statistics that describe the sample of stocks used in the analysis. The sample includes 400 (200 from the NYSE and 200 from Nasdaq) randomly selected ordinary common stocks (share code 10 or 11), that trade every day of third quarter 2006, and have a price greater than $5. CRSP daily ending prices, returns, and market capitalization are included as well as two measures of volatility. Return volatility is defined as the standard deviation of daily returns from day t-10 to day t, where day t is the current trading day. Price volatility is defined and the daily high price less the daily low price divided by the daily high price. After matching the Reg SHO data to the TAQ data, we obtain which trades where short sales and which trades were non-short (or regular) trades. Panel A reports the statistics for the NYSE sample while panel B reports the results for the Nasdaq sample. Panel A. NYSE Sample Mean St. Dev Min Max N Panel B. Nasdaq Stocks Mean St. Dev Min Max N Price Return Market Cap Return Volatility Price Volatility ,795, ,126, , ,663, , ,105, , ,454, Non Short Sale Volume 374, , , ,431, , , , , Short Sale Volume 60, , , , , ,

29 Table 2 Trade Size Rounding The table reports the percentage of short sales that are executed on round trade sizes. Panel A reports the raw percentages of non-short trades and short sales that are rounded at multiples of 500 shares, 1,000 shares, and 5,000 shares with their differences for all stocks in our sample for the NYSE sample. Similarly, Panel B reports the results for the Nasdaq sample. We report t-statistics in parentheses. Panel A. NYSE Sample % 500 Shares [1] % 1,000 Shares [2] % 5,000 Shares [3] Non-short Trades % % % Short Sales Difference *** *** *** Panel B. Nasdaq Stocks Non-short Trades % Short Sales Difference (0.374) ** (0.011) *,**,*** Statistically significant at the 0.10, 0.05, and 0.01 levels ** (0.019) 27

30 Table 3 Rounding Preference The table reports the percentage of short sales and non-short trades that are executed on round trade sizes. The table shows the percentage of non-short trades and short sales that are rounded on multiples of 500 shares compared with non-short trades and short sales that are either 100 shares less than or greater than the multiple of 500 shares. Similarly, the percentage of non-short trades and short sales that are of multiples of 1,000 shares relative to non-short trades and short sales that are either 500 shares greater than or less than the multiple of 1,000 shares are reported. A binomial Z-statistic tests whether rounded short sales are preferred to the alternative. That is, *,**, and *** indicate that the percentage of short sales of 500 shares, for instance, is significantly greater than the percentage of short sales that are 400 shares and the percentage of short sales that are 600 shares. Panel A presents the results for small trades (less than 2,000 shares), while Panel B and Panel C report results for medium trades (between 2,000 and 5,000 shares) and large trades (greater than 5,000 shares), respectively. The results are reported separately for the NYSE sample and the Nasdaq sample. In each panel, we also calculate the difference between the percentages for non-short trades and short sales with a corresponding p-value. Panel A. Small Trade-size Category % Rounded 500 Shares [1] NYSE Stocks % Rounded 1,000 Shares [2] % Rounded 500 Shares [3] Nasdaq Stocks % Rounded 1,000 Shares [4] Non-Shorts Short Sales Difference *** *** ** (0.032) *** *** (0.732) *** *** (0.742) *** *** *** Panel B. Medium Trade-size Category Non-Shorts Short Sales Difference *** *** (0.107) *** *** ** (0.028) *** *** (0.783) *** *** * (0.052) Panel C. Large Trade-size Category Non-Shorts Short Sales Difference *** *** *** (0.003) *** *** *** *** *** (0.480) *** *** *** (0.005) 28