Short-Selling Behavior Prior to Earnings Announcements
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Short-Selling and the Accrual Anomaly
By
Stephen E. Christophe George Mason University School of Management, MS5F5 Fairfax, VA 22030 Tel. (703) 993-1767, FAX (703) 993-1767 [email protected]
Michael G. Ferri George Mason University School of Management, MS5F5 Fairfax, VA 22030 Tel. (703) 993-1893, FAX (703) 993-1767 [email protected]
and
James J. Angel Georgetown University The McDonough School of Business Room G-4 Old North Washington, DC 20057 Tel. (202) 687-3765, FAX (202) 687-4031 [email protected]
February, 2005
______
Direct correspondence to: Stephen E. Christophe, George Mason University, School of Management, MS5F5, Fairfax, VA 22030, (703) 993-1767, [email protected]. We thank the Nasdaq Stock Market for providing the data. Angel and Ferri gratefully acknowledge financial support from the Nasdaq Educational Foundation. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Nasdaq Stock Market, Inc., the Nasdaq Educational Foundation, or anyone else. Short-Selling and the Accrual Anomaly
ABSTRACT
This study employs newly available information on the daily short-selling of Nasdaq stocks from September 2000 to July 2001 in an effort to analyze how short-sellers respond to the Form 10K disclosure of the accrual component of corporate earnings. Research by Sloan (1996) showed that accrual earnings are less persistent than cash earnings and that the market had failed to recognize that fact. Richardson (2003) found no evidence that short-sellers aggressively pursued high accrual firms. Unfortunately, he was constrained to work with the data of the stock exchanges’ monthly short interest report. The Nasdaq dataset we analyze is far more precise than the short interest and permits tests of daily patterns in short-selling. The test results support the view that investors are ready to use short-selling to exploit the market’s failure to adjust downward the share prices of firms that rely heavily on accrual-based earnings. Short-Selling and the Accrual Anomaly
I. Introduction
This study utilizes information on the daily short-selling of Nasdaq stocks to analyze how short-sellers respond to disclosure of the accrual component of corporate earnings. That disclosure takes place in the Form 10K, which the Securities and Exchange Act of 1934 requires companies with publicly traded securities to file annually with the Securities and Exchange
Commission (SEC). While the 10K releases data about many aspects of a firm’s financial situation and performance, it has the particularly important function of informing investors about the portion of the company’s reported earnings that takes the form of accruals.
The composition of earnings acquired special significance after Sloan (1996) found that
(1) earnings from accruals exhibit lower future persistence than earnings from cash flows, and
(2) this difference in persistence is not fully reflected in stock prices. This anomaly presents a potential arbitrage opportunity whereby investors could short the stocks of companies with high accruals as a portion of total earnings and establish long positions in the stocks of companies with high cash flow as a percentage of total earnings. In fact, Sloan demonstrated that such a strategy can generate positive abnormal returns, though he acknowledged that the strategy could entail substantial costs from both the acquisition of information and the price impact from the action of shorting targeted shares.
Richardson (2003), however, finds no empirical evidence that short-sellers have attempted to exploit the accrual anomaly. His research reveals that short interest (reported for companies once per month) is relatively invariant across quintiles that he based on his sampled
1 companies’ levels of accruals relative to earnings. He considered several explanations for this phenomenon: high accrual firms are more costly and/or difficult to short; high accrual firms are more risky to investors and therefore carry potentially high downside payoff potential; and investors may not be aware of the accrual anomaly.
Another possible explanation for Richardson’s empirical results is that the short interest data he utilizes in his study is limited in two important ways. First, it represents only a snap-shot of total shorted shares on one day during the month. Further, the exchange’s monthly short interest report aggregates the short positions of market participants as different in motivation and planning horizon as dealers, option-market arbitrageurs, and investors expecting price declines.
As a result of either or both limitations, the data-set Richardson worked with is probably much too coarse to capture the day-by-day activities of short-sellers who are engaging in investment strategies aimed at exploiting the accrual anomaly.
Recently, additional and far more detailed data on short-selling in Nasdaq stocks have become available, and these data allow a precise examination of daily short-selling specifically by investors who expect price declines.1 The purpose of our study is to analyze these data to examine shorting activity around SEC 10K filing dates to further explore how short-sellers react to the disclosure of the accrual versus cash component of earnings.
We uncover evidence that short-sellers establish positions consistent with an attempt to exploit the accrual anomaly. For example, we find significantly higher post 10K filing date short-selling for high versus low accrual firms. And, this result is robust to both the inclusion and exclusion of firm’s that did not file their 10K forms in a timely manner at the SEC. Further, we reconcile our results with Richardson’s (2003) by showing that although there is a
1 For example, our data makes it possible to separate from our short-selling measure those shares shorted either by dealers (who do so to manage inventory), or by option-market arbitrageurs.
2 statistically significant relationship between reported accruals and daily short selling, there is no significant relationship between reported accruals and monthly short interest. We provide first evidence that some of the component parts that are aggregated to obtain short interest are negatively correlated with one another and argue that this negative correlation makes a company’s reported short interest a rather crude statistic for examining whether short sellers establish investment positions in an attempt to exploit the accrual anomaly.
The paper proceeds as follows: Section II more fully describes prior research that examines different aspects of the accrual anomaly and short selling; Section III describes our short-selling data, and the sample of Nasdaq firms examined in our analysis; Section IV contains estimations and results including a reconciliation of our findings with prior research that looks at monthly short interest; and, the final Section presents our conclusions.
II. Background
In seminal work, Sloan (1996) finds that investors do not fully recognize the implications for future earnings contained in a company’s disclosure of the accrual and cash flow components that comprise its current earnings. Instead, investors act in a manner consistent with overestimating the persistence of earnings that arise from accruals, and underestimating the persistence of earnings that arise from cash flows. Sloan demonstrates that these mis-estimations lead to apparent stock pricing errors such that a trading strategy based upon establishing a long position in the stocks of companies which report high cash flows relative to earning and a short position in companies reporting high accruals relative to earnings can potentially result in arbitrage profits.
3 Lev and Nissim (2004) document that this anomaly continues to persist in recent years.
They also provide some evidence that institutional investors adjust their portfolio holdings in reaction to accrual disclosures. For example, they examine 13(f) filings and find a negative relationship between a firm’s reported accruals and the reported institutional ownership of that firm’s shares in the subsequent quarter.2 This suggests that institutions trade on accrual information during the quarter during which that information is released. In addition, they find that in recent years institutions have more intensely altered their share holdings in response to accrual disclosures. This increase in the intensity of the response is consistent with an increasing awareness of the accrual anomaly. However, they also report that extreme accrual firms tend to have characteristics that tend to make them unattractive to most institutional investors. For example, they tend to be small firms with a low stock price and book to market ratio.
Consequently, even though institutions appear to adjust holdings in recognition of the accrual anomaly, lack of institutional ownership of many extreme accrual firms may help explain why the anomaly persists.
Consistent with Richardson’s (2003) finding, Mashruwala, Rajgopal, and Shevlin (2004) argue that arbitrageurs may not eliminate the accrual anomaly because the trades required to exploit the anomaly can be risky and/or costly. They find that there is a 49% chance that pursuit of the strategy could be unprofitable in any given year, and that the strategy shows negative profits during 5 months of the median year. In addition, they report that extreme accrual firms lack close substitutes against which to lay-off risk. If arbitrageurs only want to pursue a limited number of perceived mispriced investment opportunities (Shleifer and Vishny (1997)), they may be wary of employing an accrual anomaly-based strategy due to the common occurrence of
2 Note that 13(f) institutional share ownership data is reported in the Thomson Financial Securities database utilized by Lev and Nissim (2004) on a quarterly basis
4 losses during certain years and/or months during the year (either of which could induce fund investors to withdraw their investments in the fund).
A number of other studies have begun to examine how institutional ownership can lead generally to constraints on short-selling (though these studies do not necessarily focus specifically on short-selling constraints and the accrual anomaly). For example, Chen, Hong and
Stein (2002), and Nagel (2004) both suggest that low institutional is a likely indicator of a stock that may be short sale constrained (due to a general unavailability of lendable shares). Nagel suggest that a limited supply of shares may help explain why some types of return predictability are not arbitraged away. For example, consistent with this argument, he reports that return predictability increases sharply for stocks with low institutional ownership. Asquith, Pathak, and
Ritter (2005) report that although short sales constraints are not binding for most companies, stocks that exhibit both high short interest and low institutional ownership (which together imply the existence of short sale constraints) exhibit significantly negative abnormal returns when measured from a four-factor model regression with the stocks placed in an equally-weighted portfolio.
Short sales constraints of high accrual firms could help explain Richardson’s (2003) finding that four months after company fiscal year-ends, there is no statistically significant difference between the short interest of high accrual versus other firms. Instead, he finds that short interest across accrual quintiles is relatively constant at about 1.2% to 1.25% of shares outstanding. He concludes that short sellers apparently do not utilize the information contained in accrual disclosures, and are therefore foregoing a potential profit opportunity. However,
Richardson’s (2003) utilization of the monthly report of a stock’s short interest as his dependent variable in empirical estimation potentially represents the choice of a very noisy statistic. As
5 described in substantial detail below, short interest is an aggregation of share sold short by many different types of investors/dealers. Therefore, it is worthwhile to further examine the relationship between disaggregated daily short-selling and accruals to provide additional insights into the behavior of investors.
III. Data and Sample
The source of our short-selling data is Nasdaq’s Automated Confirmation Transactions
Service (ACT), which processed the vast preponderance of trades in stocks listed on Nasdaq’s
National Market System (NMS). Market participants in Nasdaq-listed stocks are required to report their trades to ACT within 90 seconds of execution.3 In addition to price and volume statistics, each ACT record contains a code which indicates whether the seller is engaged in short selling. From the Nasdaq, we received all ACT records for more than 3,000 NMS stocks on the 207 trading days between September 13, 2000, and July 10, 2001. We aggregated the records of each stock’s trades within each day and conduct our analysis on daily short-selling data.
The ACT records allow us to separate short sales into several different categories. For example, we are able to identify short sales that are exempt from the bid test because the trade represents such activities as options arbitrage.4 We can also identify the shorting activities of dealers, who short sell mostly to manage their inventories and carry out their normal function of market-making. Finally, we can identify short sales that are designated “customer short” which
3 ACT reporting is not required for odd lots, although some odd lots are reported anyway to ACT because they need to use the clearing services of DTCC. Also, ACT reporting is not required for trades conducted completely outside the United States and for informal trades between individuals that do not involve the use of a broker/dealer. We believe the total volume of these unreported trades to be very small. 4 For a more complete description of the types of short trades that qualify for the “exempt” designation, see the NASD Special Notice to Members 94-68, titled “SEC Approves Short-Sale Rule For The Nasdaq Stock Market.”
6 represent investors establishing short positions (we believe) in anticipation of stock price declines (or relative underperformance)
This final group of short sales (“customer short”) and the associated shares that are shorted represent the focal point of our analysis. Specifically, we examine the data on customer behavior for evidence that short-selling around 10K filings is different from other times and that the difference does indicate a response to the accrual information disclosed in the filings. Thus, a rise in short-selling from a typical to a high level around a filing that reveals high accruals is evidence that investors expect the price decline that Sloan (1996) uncovered. By contrast, if short-selling around the filing is basically the same as at other times and the same for firms of varying amounts of reported accruals, this would tend to undermine the view that investors pursue accrual-based strategies.
We restricted our initial sample from ACT to the stocks that traded every day over the
207 day sample period and averaged at least 50 trades each day. In our view, this criterion mitigates the possibility of making improper inferences that reflect peculiar features of infrequently traded stocks. This initial sample consists of a total of 1,312 stocks for which we obtained daily return data from CRSP.5
We next merged this initial sample with financial statement data obtained from Compust where we imposed the additional restriction that Compustat contain sufficient information to estimate each company’s operating accruals for year-end 2000. Following Richardson (2003), we define operating accruals (OA) in this way:
OA = (Earnings before extraordinary items – Cash flow from operations)/Average Assets6
5 We were able to obtain CRSP return data for all 1312 stocks. 6 The Compustat mnemonics corresponding to earnings before extraordinary items, cash flow from operations, and assets are IB, OANCF, and AT, respectively.
7 The sample obtained from this merging of data in ACT, CRSP, and Compustat consists of 1,217 stocks.
Although the Compustat database contains a record of each company’s earnings announcement date, it is appropriate for our analysis to identify the firm’s 10K filing date because this date is typically the first point in time when investors can definitively discern the composition of the firm’s earnings (accrual versus cash components). To obtain 10K filing dates, we conducted an online search of the records in www.search-sec.com. That search provided filing dates for 1,101 stocks in our sample.
The next set of restrictions to the sample included eliminating 24 financial services companies (SICs 6000-6999) and 475 companies whose stock prices were less than $10 on the
10K filing date. The latter criterion derives from evidence presented by D’Avolio (2002) that companies with low stock prices may be difficult to short. This restricted sample, then, consists of 602 stocks which we posit represents the opportunity set of Nasdaq stocks from which investors could have chosen, following fiscal year-end 2000 accounting disclosures, if they had attempted to implement an investment strategy based upon accruals.
Our empirical methodology (described in more detail below), however, limit us to examining the short-selling characteristics for a sub-set consisting of 437 of these companies.
To examine how a company’s short-selling differs during the 10K filing period compared to its typical amount of short-selling we construct a measure of each company’s normal daily short- selling and normal daily volume. To estimate these variables, we rely on the trading and short- selling of a company’s stock that occurs over the six calendar weeks (approximately 30 trading days) ending one week prior to the company’s earnings announcement. In addition, to minimize the possibility that empirical findings are due to the short-selling effects surrounding the earnings
8 announcement rather than the 10K filing, we also restrict the sample to only those firms with a
10K filing date at least 7 calendar days after their earnings announcement date (as reported on
Compustat).7
Because the starting point of our short-selling data is September 13, 2000, these restrictions entail that the 10K filing date must be at least (6+1+1) eight weeks after September
13, 2000. Finally, to enable an examination of a stock’s short-selling subsequent to the 10K filing, we require that the filing date is at least 10 days prior to July 10, 2001 (the last day of our short-selling sample data). The imposition of these methodological restrictions results in a final sample of 437 companies.
Similar to Richardson (2003), we classify stocks into quintiles based on their level of OA at fiscal year-end 2000. We have chosen to form those quintiles on the basis of the distribution of OA for the full set of 602 stocks because, as mentioned above, we assume these stocks represent the opportunity set from which investors could have chosen if they were pursuing an investment strategy focused on accruals. The lowest quintile (Q1) consists of firms with OA <=
-0.1407; the second lowest quintile (Q2) contains firms with -0.1407 < OA <= -0.0766; the middle quintile (Q3) is comprised of firms with -0.0766 < OA <= -0.0316; the second highest quintile (Q4) consists of firms with -0.0316 < OA <= .0241; and, the highest quintile (Q5) contains all firms with .0241 < OA.
Table 1 presents information about the final sample of 437 companies for which we examine short-selling, and for sub-samples of these 437 companies after assigning them to their respective accrual quintile. Note that there are not an equal number of companies in each quintile because the accrual quintile breakpoints are based upon the opportunity set of 602 firms.
7 Christophe, Ferri, and Angel (2004) have reported already that short-sellers engage in informed trading prior to earnings announcements.
9 For the final sample of 437 firms, the mean (median) book value of year-end 2000 assets is
$1,379.8 million ($378.3 million). Companies in operating accrual quintiles 1 and 5 tend to have a lower median book value of assets and slightly lower median market capitalization at the 10K filing date by comparison with those in the other quintiles. The filing dates for the 10K reports are rather similar across the quintiles, with the median filing date for quintiles 1 through 4 being
March 29, 2001 and the median for quintile 5 being March 30.
Firms in quintiles 1 and 5 exhibit the highest mean values for the ratio of average daily shorted shares to shares outstanding, both for the interval of day 0 to day 3, and of day 1 to day 3 relative to the firm’s 10K filing date. If short-sellers are investing in an attempt to exploit the accrual anomaly, a high level of short-selling for quintile 5 firms is to be expected. In contrast, however, the results for quintile 1 are a bit surprising, and indicate that there are other firm- specific issues beyond accruals that are (not surprisingly) responsible for short-selling. A potential explanation is revealed by the mean and median earnings per share for Q1 firms which are both negative. Although all of the Q1 companies have low accruals relative to total earnings, the poor financial and operating health of some may induce short-selling activity.8
IV. Estimations and Results
A. Modeling the Linkage between Accruals and Short-Selling
To examine how short-sellers respond to the 10K filing and its disclosure of information about a firm’s accruals and operating cash flow, we estimate a specification that considers the linkage between a company’s operating accrual quintile and post-filing short-selling, while
8 Fifty-eight of the Q1 firms report negative earnings per share, and 27 report positive earnings per share for year 2000.
10 controlling for other factors that may impact short sales. More specifically the model we consider has the following form:
SS AbVol NormSS 0 1Ret 2 3Price(0) 4 5 EPS 1Q 2 2Q 3 3Q 4 4Q5 (1) Shr Shr Shr
SS Here, represents the average daily number of a company’s shares that are sold short Shr following the firm’s 10K filing, normalized by the firm’s total number of shares outstanding. To mitigate the concern that our findings are an artifact of the metric chosen to measure post-filing
SS short-selling, we conduct estimations for measured over two intervals: days 1 to 3, which Shr are the three days after the filing date; and days 0 to 3, which are the filing date and the subsequent 3 days.9 We choose to look at the days just after the filing because Collins and
Hribar (2000) report that the abnormal returns associated with the accrual anomaly begin accruing shortly after the company discloses its earnings information. Consequently, an investor attempting to earn arbitrage profits from exploiting the anomaly would likely move quickly when establishing their long and short positions.
Ret represents the company’s stock return during the days following the filing date. Ret is included in the specification to control for any association between contemporaneous return and short-selling. For example, the 10K filing might release information that is not related to accruals and that spurs negative stock returns and a corresponding increase in short-selling, or positive returns and a decrease in short-selling. In estimations using three-day average short- selling, RET is also measured over days 1 to 3; in estimations using four-day average short- selling, RET is measured over days 0 to 3. Consequently, the number of days over which RET is
9 Hereafter, we refer to the day 1 to 3 measure as three-day average short-selling, and the day 0 to 3 measure as four- day average short-selling.
11 computed – either 3 or 4—corresponds to the number of days used for the computation of the
SS independent variable . Shr
AbVol Abnormal volume, , is the difference between the company’s average daily Shr volume during the days following its filing and its normal daily volume, normalized by the
AbVol firm’s total number of shares outstanding. The role of in the specification is to control Shr for the impact of the correlation between short-selling and spikes in volume in the post-filing days. This variable also accounts for the possibility that stocks experiencing unusual increases
(decreases) in volume might thereby become easier (more difficult) to sell short. In estimations
AbVol using either the three-day (four-day) average short-selling, , is also computed over three Shr
(four) days. We report results from estimations that use two different measures of the normal
AbVol daily volume component of . The first measure is based upon the firm’s mean daily Shr volume during the six calendar weeks (approximately 30 trading days) that end one week prior to its earnings announcement. The second measure is based upon the firm’s median daily volume during the same six weeks.
Price(0) is the natural log of the company’s stock price on the filing date. We include this variable to control for the potential linkage between the level of the stock price and investors’ willingness to short sell it. For example, investors might be more inclined to short higher priced stocks than those with low prices, because establishing reasonably-sized short
12 positions in the higher priced stocks requires fewer shares and is therefore less likely to be affected by a company’s number of actively traded shares (its “float”).
NormSS Normal short-selling, , is the company’s normal daily short-selling normalized SHR by shares outstanding. We include this variable in the specification to cross-sectionally control for each firm’s typical ratio of short-selling to total outstanding shares.10 Similar to our estimation approach for the normal daily volume component of abnormal volume, we report
NormSS results from estimations using two different ways of computing . The first computation SHR uses the firm’s mean daily short-selling during the six calendar weeks one week prior to its earnings announcement. The second measure uses the firm’s median short-selling during the same period.11
EPS is the company’s earnings per share for the year 2000 and is measured as income before extraordinary items divided by total shares outstanding. We include EPS in the specification to control for the impact a company’s reported earnings may have on short-selling.
For example, if a company reports very low (or negative) earnings, but in its 10K filing reports that operating accruals are a very low portion of earnings, short-sellers may choose not to lower their short-selling of that stock because of the firm’s poor financial prospects.
Finally, Q2, Q3, Q4 and Q5 are dummy variables equal to one if the company is in the second lowest, middle, second highest, or highest operating accrual quintile based upon their
10 Our objective is to examine how a company’s short-selling differs during the 10K filing period compared to its typical amount of short-selling. 11 Note that in estimations when mean (median) daily volume is used to estimate normal daily volume, mean (median) daily short-selling is used to estimate normal short-selling. In addition, although not reported, we find results similar to those reported herein while using a variety of other methods for estimating normal short-selling – For example, we estimate normal short-selling over the period -45 to -7 days prior to the earnings announcement and +7 to +45 days after the filing date; over the period -30 to -7 days prior to the earnings announcement and +7 to +30 days after the filing date; and over the period -42 to -7 days prior to the earnings announcement. Results from these estimations are available from the authors upon request.
13 10K filing. These dummy variables allow us to examine the relationship between short-selling in a firm’s stock after its 10K filing and the accrual quintile into which that filing places the firm.
Our specification suppresses Q1 and makes those firms, which have relatively low accruals, the base case. Therefore, the estimates of the parameters of Q2, Q3, Q4, and Q5 represent the difference (positive or negative) in post-filing short-selling between the firms of each quintile and those of the Q1 stocks. Of course, these estimates should be free of any influence of a firm’s post-filing return, abnormal volume, price, normal short-selling and earnings per share.
Accordingly, if short-sellers employ an accrual-based short-selling strategy, we expect the parameter estimates associated with Q2, Q3, Q4 and Q5 to be monotonically increasing, and expect the estimate associated with Q5 (high accrual firms) to be significant greater than zero.
B. Results of Estimations
Results from estimating equation 1 appear in table 2. Panel A contains estimation results where the means of daily short-selling and volume over the six-week period ending one week prior to the firm’s earnings announcement are used to estimate NormSS and the normal volume
AbVol component of , respectively; panel B contains estimation results where the medians of Shr daily short-selling and volume over that six-week period are used, respectively. In both panels, results are presented for model estimations with and without the variable, EPS.
The results of panel A indicate that average daily short-selling in the days following the company’s 10K filing is significantly affected by contemporaneous stock return, abnormal volume, the company’s normal level of short-selling, and in some estimations filing date stock
NormSS price. In addition, although the parameter estimate associated with is significantly SHR
14 different from zero, it is not different from unity at normally accepted levels of statistical significance. Most importantly, however, in all four estimations, the highest accrual quintile firms experienced significantly higher short-selling than the firms in the lowest quintile. In the two model estimations where EPS is not included, the β4 parameter estimates are positive and statistically significant at a 10% level of significance. In the two model estimations where EPS is included as an independent variable in the model estimation, β4 parameter estimates are positive and statistically significant at a 1% level of significance. Consequently, the results presented in table 2 give strong indication that in the days just after a company’s 10K filing, short-sellers act in a manner consistent with attempting to exploit the accrual anomaly.
The results of panel B are similar, although the adjusted r2 in each model is higher than for the corresponding model of panel A. Average daily short-selling in the days following the company’s 10K filing is significantly affected by abnormal volume, filing date stock price, and the company’s normal level of short-selling. And in all four estimations, the β4 parameter estimates associated with firms in the highest accrual quintile are significantly positive.
C. An Alternative Approach
SS A potential criticism, of the empirical specification is that the dependent variable, , is Shr bounded at zero. Thus, the residuals obtained from the estimation of specification 1 might deviate from normality, thereby rendering the statistical significance of the association between short-selling and accruals uncertain. To address this issue, we next examine a modification of
SS specification 1 whereby we redefine the dependent variable as the difference - NormSS. Shr
15 Consequently the new dependent variable in the estimation is a measure of a firm’s abnormal short-selling, and the model specification we estimate is:
SS NormSS AbVol 0 1Ret 2 3 Price(0) 5 EPS 1Q 2 2Q 3 3Q 4 4Q5 (2) Shr Shr Shr
Results from estimating equation 2 where the mean daily short selling and volume of the firm are used to measure NormSS and normal volume are presented in table 3. We choose to do the estimation using the mean values for these variables because the prior results reported above
NormSS show that the parameter estimate associated with when the firm’s mean daily short- SHR selling is used to estimate NormSS is significantly different from zero, but not significantly
SS different from unity. The implication of this result is that is not significantly different from Shr
NormSS SS after controlling for the impact on of the other independent variables. SHR Shr
The results show that the conclusions presented above are robust to the using abnormal short-selling as the dependent variable. Abnormal short-selling is significantly affected by contemporaneous return, abnormal volume, and filing date stock price. More importantly, in all four model estimations presented in the table, there is a significantly positive association between abnormal short-selling and accrual quintile, with the most significant results obtained when estimating the specifications that include EPS.
D. Dropping the cases where the firms file a 10K-405
16 All results presented so far are based upon a sample of firms that filed both 10K and
10K-405 reports at the SEC. A 10K-405 designation is attached to a company’s report whenever it is filed after the standard time period. A possible concern is that our results could be influenced substantially by including such firms in the sample. To examine the impact of the inclusion of 10K-405 filings, equation 1 is next re-estimated after eliminating firms that filed
10K-405s. This restriction reduces the sample by 126 stocks, resulting in a sample of 311 firms.
Results from these estimations, where NormSS and normal volume are measured by both the mean and the median are presented table 4.
For each of the eight estimations reported in the table, the parameter estimate associated with accrual quintile 5 is statistically significant with at least a 10% level of confidence. In addition, for the two estimations where EPS is included in the specification, and mean values are used to measure normal short-selling and normal daily volume, the parameter estimate associated with accrual quintile 5 is statistically significant at a 1% level of confidence. These results confirm that the relationship between reported accruals and short-selling is independent of whether or not the company filed its 10K in a timely manner at the SEC.
E. Test results when short interest is used
As noted above, Richardson (2003) studies the relationship between short-selling and the accrual anomaly by examining monthly short interest, which is quite different from the data on daily short selling which we are analyzing. In an effort to maintain continuity with that previous research, we perform a set of tests that employ monthly short interest (rather than daily short selling) in our empirical specification for our sample of 437 stocks. We examine separate specifications that examine both the level of the firm’s short interest following its 10K filing, and
17 the change in the firm’s short interest after versus before its 10K filing. Because our specifications normalize short interest through division by the firm’s outstanding shares, the tests in effect employ the well-known “short interest ratio.” Table 5 presents selected statistics for the short interest ratio of the sampled companies in each of the accrual quintiles. The current short interest ratio is the firm’s nearest post-filing monthly short interest divided by its total shares outstanding; the prior short interest ratio represents the short interest in the most recent pre-filing month divided by shares outstanding. Finally, the change in short interest ratio equals a company’s current short interest ratio minus its prior short interest ratio.
During the time period analyzed in this research, Nasdaq stocks experienced a relatively high amount of short-selling. Indeed, Asquith, Pathak, and Ritter (2005) note that, since the early 1990s, the percentage of the Nasdaq sold short exceeds that of the NYSE and ASE.
Consequently, it is not surprising that the mean of the short interest ratio exceeds three percent of shares outstanding for all of the accrual quintiles. Although Q5 stocks have the highest mean and median current short interest, the mean and median change in short interest is highest for Q4 and Q3 stocks, respectively. This somewhat surprising result underscores the potential noise inherent in this aggregated, once-per-month data.
To explore the relationship between short interest and accrual quintiles, we estimate the following variation of equation 1:
CSI 0 1PSI 3Price(0) 5EPS 1Q2 2Q3 3Q4 4Q5 (3)
Here, CSI is the company’s current short interest ratio, PSI represents the company’s previous short interest ratio, and all other variables are as defined above. Results from estimating equation 3 are presented in table 6, panel A. The results indicate that PSI is a significant variable
18 for explaining CSI. The parameter estimate associated with PSI is 0.989, and it is significantly different from zero at a 1% level of significance. In addition, Price(0) is statistically significant
(at 10%) for explaining CSI. All other variables in the specification, however, including the four dummy variables for accrual quintiles, are insignificantly different from zero.
Since the parameter estimate associated with PSI is significantly different from zero, but not significantly different from unity, we also consider a specification where the dependent variable is the change in short interest, ∆SI:
SI 0 3Price(0) 5EPS 1Q 2 2Q3 3Q 4 4Q5 (4)
Results from estimating equation 4 are presented in table 6, panel B. Price(0) is still a statistically significant explanatory variable. However, the estimation generates a negative adjusted r2, and none of the parameter estimates associated with the four accrual quintiles is significantly different from zero. In sum, unlike the results based on daily short-selling data, these estimations with monthly short interest do not uncover any link between short-selling and accruals.
F. Exploring the components of short interest
The sharp contrast between the results obtained with daily short selling data versus short interest data suggests that monthly short interest is likely to be too coarse a metric to capture the activities of short-sellers around filing dates. It also raises the important question about the components of the monthly short interest and their potential variations from the day underlying one month’s report to the day of the next month’s report. As noted previously, a company’s short interest is the total number of its shares in all short positions on one day in the middle of the month (typically the 12th day of the month), and that total aggregates across the short
19 positions of Nasdaq dealers, investors who engaged in exempt trades (“short exempt”) linked to activities including options arbitrage, and customers anticipating price declines or relative stock price declines (“customer short”).12
To treat one month’s short interest just like another month’s short interest is to assume implicitly that the shares shorted by each group comprise the same percentage of all shorted shares from month to month. Unfortunately, this potentially untrue assumption was necessary due to the dearth of short-selling data. With the ACT daily transactions dataset, however, it is possible to identify the daily amount of short-selling by each type of short seller (dealer, “short exempt”, and “customer short”), their degrees of variability from day to day, and – even more importantly – the correlations among the types of daily short-selling. While interesting in themselves, these analyses can shed light on the failure of the short interest data to detect short- sellers’ possible reactions to announcements of accruals.
Table 7, panel A shows the component parts (and the variability of these component parts) of total shorted shares during our sample period for the 602 Nasdaq stocks described above. The table reveals that dealer-shorted shares comprise on average over 72% of all shorted shares, while customers and exempt trades account on average for only about 17% and 10% respectively. This fact might (though we cannot be certain) explain why researchers such as
Asquith and Meulbroek (1996), Dechow, Hutton, Meulbroek and Sloan (2001) and Desai,
Ramesh, Thiagarajan, and Balachandran (2002) restrict their various tests to cases in which a stock’s short interest was high or had changed a large amount from the previous month. Perhaps, many of those cases represented situations in which customers’ short-selling was large enough relative to dealer-shorting to uncover connections with investment-related phenomena. The table
12 Investors anticipating relative stock price declines would include hedge funds engaging in a strategy of going long one stock and short another in hopes of relative stock price underperformance of the shorted stock.
20 further shows that each percentage, however, is highly variable: dealer-shorted shares might comprise 79.89% on one day and only 61.89% of all shorted shares on another day, while customers might short as few as 11.68% and as many as 25.50% and the range for the percentage established in exempt trades is quite large at 24.09% less 5.83%. Figure 1, which graphs the daily composition, suggests a certain drift in the latter part of our sample period: the percentage of shares shorted by dealers and customers seems to fall somewhat while the percentage attributable to exempt trades grows larger. Whatever the cause of the later trend, it underscores the variability in the composition of daily values of shorted shares.
Another interesting way to examine the daily movements in the size of the types of short- selling is to consider each type of shorted shares as a percentage of daily total volume (or total of shares traded on the Nasdaq market). Table 7, panel B, presents a set of statistics about shares shorted by customers as a percentage of volume, shares shorted by dealers as a percentage of volume, and the percentage of volume for shares shorted in exempt trades. The table reveals some noteworthy facts. First, dealer-shorted shares amount to over 16% of total volume on average, while customer-shorted shares and shares shorted in exempt trades amount on average to only 4% and 2.4%, respectively. Further, all of the percentages vary to a considerable amount. For example, the percentage of volume represented by customer-shorted shares can be as low as 2.63% and as high as 6.15%. Finally and perhaps most interestingly, the panel contains some correlations and shows that the correlation between the percentage of volume for dealer-shorted shares and that for customer-shorted shares is significantly negative at -0.36. This negative co-movement is visible in Figure 2, which graphs the three volume-based percentages for the 602 Nasdaq stocks on a daily basis over our entire sample period.
21 In our view, the difference in estimation results between those based on daily short- selling and those based on the monthly short interest have a likely explanation. Short interest is not a completely reliable measure of the short-selling of investors who anticipate declines in price when new information is disclosed. It is unsuited precisely because of the variability in the daily composition of shorted shares, the variability in the volume-based percentages, and the negative correlation between the volume-based percentages for dealers and customers.
V. Conclusion
We present evidence that short-sellers establish positions consistent with an attempt to exploit the accrual anomaly. Using daily short-selling data, we show that companies that disclose high accruals relative to earnings in their 10K filings experience significantly above- normal amounts of short-selling. This result is robust across several modifications of the empirical specification and across various sub-samples which exclude companies that filed their form 10Ks late. We reconcile our results with prior research by showing that there is no statistically significant relationship between accruals and short-selling when short-selling is cross-sectionally measured as the firm’s monthly reported short interest. We present evidence that short interest is, in fact, a rather crude way to estimate customer short-selling. Short interest is constructed by combining the shorting activities of different market participants, and the dealer component and “customer short” component of short interest are negatively correlated across time when measured relative to volume.
Issues for further research include examining the subsequent stock return performance of high (low) accrual firms that experienced post 10K filing increases (decreases) in short-selling.
Prior research (Asquith, Pathak, and Ritter (2005)) has indicated that only a small subset of the
22 stocks of high accrual companies (which may be difficult to short-sell) consistently produce negative abnormal returns. Consequently, it would be interesting to examine whether short- sellers are able to consistently identify this subset and establish profitable short positions.
23 Table 1
Sample Characteristics
This table contains sample mean (top figure in each cell) and median (bottom figure in each cell) values for all firms, and firms split into quintiles based upon fiscal year-end 2000 operating accruals. Total Assets is the firm’s year-end 2000 book value of assets. Market capitalization at Filing Date is the firm’s stock price at the 10K filing date multiplied by shares outstanding. Operating Accruals/Average Assets is the firm’s income before extraordinary items minus cash flow from operations for fiscal year 2000 normalized by the average of year-end 1999 and 2000 book value of assets. Filing date is the date the firm filed its 10K at the Securities and Exchange Commission. Stock Price at Filing Date stock price is the firm’s stock price on its filing date. Earnings announcement date is the date the firm’s earnings per share is first publicly reported in the news media. Average Daily Shorted Shares From Day 1 to Day 3/Shares Outstanding is the average daily number of a firm’s shares sold short over the 3 days subsequent to the firm’s 10K filing date as a percentage of the firm’s total shares outstanding. Average Daily Shorted Shares From Day 0 to Day 3/Shares Outstanding is the average daily number of a firm’s shares sold short over the day of and 3 days subsequent to the firm’s 10K filing date as a percentage of the firm’s total shares outstanding. Normal Daily Volume is the firm’s average daily share volume during the six weeks that end one week prior to the firm’s earnings announcement. Normal Daily Short-selling, as % of Shares Outstanding is the firm’s average daily number of shorted shares during the six weeks that end one week prior to the firm’s earnings announcement as a percentage of the firm’s total shares outstanding. Market Value/Book Value is the firm’s market-to-book value at fiscal year-end 2000. Earnings per Share is the firm’s earnings per share during fiscal year 2000. Operating Accuals/Average Asset breakpoint for each quintile are: Quintile 1<-.1407; -.1407<=Quintile 2<-0.0766; -.0766<=Quintile 3<-.0316; -.0316 Table 2 SS AbVol NormSS Ret Price(0) EPS Q Q Q Q (1) Shr 0 1 2 Shr 3 4 Shr 5 1 2 2 3 3 4 4 5 SS The results of OLS estimation of this equation, as fitted to the sample of 437 firms. The variable represents the average daily number of a company’s shares that are sold Shr short following the firm’s 10K filing, normalized by the firm’s total number of shares outstanding. Estimations are conducted for where this independent variable is measured over two intervals: days 1 to 3, which are the three days after the filing date; and days 0 to 3, which are the filing date and the subsequent 3 days. Ret represents the firm’s stock return during the days following the 10K filing date. In estimations using three-day average short-selling, RET is also measured over days 1 to 3; in estimations AbVol using four-day average short-selling, RET is measured over days 0 to 3. Abnormal volume, is the difference between the company’s average daily volume during Shr days following its filing and the normal daily volume, normalized by total number of shares outstanding. In estimations using either the three-day (four-day) average short- selling, it is computed over three (four) days also. We report results from estimations that use two different measures of the normal daily volume component of abnormal. Panel A presents results based upon the firm’s mean daily volume during the six weeks that end one week prior to its earnings announcement. Panel B presents results based upon the firm’s median daily volume during the same six weeks. Price(0) is the natural log of the company’s stock price on the filing date. Normal short-selling NormSS is the company’s normal daily short-selling normalized by shares outstanding. Panel A presents results where normal daily short selling is measured as the SHR firm’s mean daily short-selling during the six weeks one week prior to its earnings announcement. Panel B presents results where it is measured as the firm’s median short- selling during the same six week period. EPS is the company’s earnings per share for the year 2000 and is measured as income before extraordinary items divided by total shares outstanding. Q2, Q3, Q4 and Q5 are dummy variables equal to one if the company is in the second lowest, middle, second highest, or highest operating accrual quintile based upon their 10K filing. White’s (1980) heteroskedasticity-consistent standard errors in parentheses. α0 α1 α2 α3 α4 α5 β1 β2 β3 β4 Adj R2 Panel A: Mean used to estimate NormSS and AbVol SS -0.612* -1.073** 0.063*** 0.201 1.141*** 0.062 0.079 0.126 0.297* .629 measured over days 1 to 3 Shr (0.305) (0.518) (0.007) (0.103) (0.137) (0.130) (0.137) (0.128) (0.153) -0.775** -1.054** 0.063*** 0.245** 1.124*** -0.039 0.114 0.147 0.199 0.395*** .630 (0.322) (0.521) (0.007) (0.111) (0.139) (0.037) (0.120) (0.125) (0.123) (0.146) SS -0.547** -0.871* 0.063*** 0.184* 1.124*** 0.094 0.061 0.146 0.271* .623 measured over days 0 to 3 Shr (0.280) (0.458) (0.006) (0.095) (0.151) (0.122) (0.125) (0.129) (0.149) -0.689** -0.837* 0.062*** 0.217** 1.110*** -0.035 0.140 0.122 0.211* 0.358*** .623 (0.287) (0.464) (0.006) (0.101) (0.154) (0.033) (0.111) (0.112) (0.121) (0.137) Panel B: Median used to estimate NormSS and AbVol SS -0.564* -0.664 0.066*** 0.190* 1.368*** -0.001 0.068 0.076 0.282** .660 measured over days 1 to 3 Shr (0.306) (0.463) (0.007) (0.104) (0.144) (0.123) (0.136) (0.124) (0.140) -0.676** -0.667 0.065*** 0.218** 1.354*** -0.027 0.035 0.115 0.126 0.349** .660 (0.321) (0.467) (0.007) (0.110) (0.148) (0.036) (0.116) (0.126) (0.120) (0.139) SS -0.485* -0.610 0.065*** 0.162* 1.365*** 0.034 0.056 0.100 0.255* .659 measured over days 0 to 3 Shr (0.279) (0.409) (0.006) (0.095) (0.167) (0.116) (0.125) (0.126) (0.137) -0.575** -0.591 0.065*** 0.185* 1.352*** -0.022 0.063 0.094 0.141 0.310** .659 (0.286) (0.416) (0.007) (0.100) (0.171) (0.033) (0.107) (0.114) (0.119) (0.130) * = statistically significant at 10%, ** = statistically significant at 5%,*** = statistically significant at 1% Table 3 Abnormal Short-Selling SS NormSS AbVol Ret Price(0) EPS Q Q Q Q (1) Shr Shr 0 1 2 Shr 3 5 1 2 2 3 3 4 4 5 SS The results of OLS estimation of this equation, as fitted to the sample of 437 firms. The variable represents the average daily number of a company’s shares that are sold short following Shr the firm’s 10K filing, normalized by the firm’s total number of shares outstanding. Estimations are conducted for where this variable is measured over two intervals: days 1 to 3, which are the three days after the filing date; and days 0 to 3, which are the filing date and the subsequent 3 days. Ret represents the firm’s stock return during the days following the 10K filing date. In estimations using three-day average short-selling, RET is also measured over days 1 to 3; in estimations using four-day average short-selling, RET is measured over days 0 to 3. Abnormal AbVol volume, is the difference between the company’s average daily volume during days following its filing and the normal daily volume, normalized by total number of shares Shr outstanding. In estimations using either the three-day (four-day) average short-selling, it is computed over three (four) days also. We report results from estimations that use two different measures of the normal daily volume component of abnormal. Panel A presents results based upon the firm’s mean daily volume during the six weeks that end one week prior to its earnings announcement. Panel B presents results based upon the firm’s median daily volume during the same six weeks. Price(0) is the natural log of the company’s stock price on the filing date. NormSS Normal short-selling is the company’s normal daily short-selling normalized by shares outstanding. Panel A presents results where normal daily short selling is measured as the SHR firm’s mean daily short-selling during the six weeks one week prior to its earnings announcement. Panel B presents results where it is measured as the firm’s median short-selling during the same six week period. EPS is the company’s earnings per share for the year 2000 and is measured as income before extraordinary items divided by total shares outstanding. Q2, Q3, Q4 and Q5 are dummy variables equal to one if the company is in the second lowest, middle, second highest, or highest operating accrual quintile based upon their 10K filing. White’s (1980) heteroskedasticity-consistent standard errors in parentheses. White’s heteroskedasticity-consistent standard errors in parentheses. α0 α1 α2 α3 α5 β1 β2 β3 β4 Adj R2 Panel A: Mean used to estimate NormSS and AbVol SS -0.668** -1.134** 0.062*** 0.258*** 0.017 0.031 0.071 0.288* .426 measured over days 1 to 3 Shr (0.308) (0.538) (0.007) (0.097) (0.127) (0.133) (0.122) (0.154) -0.872*** -1.099** 0.061*** 0.303*** -0.051 0.092 0.127 0.175 0.417*** .430 (0.320) (0.540) (0.007) (0.102) (0.035) (0.117) (0.123) (0.118) (0.155) SS -0.611** -0.989* 0.061*** 0.235*** 0.056 0.021 0.100 0.267* .412 measured over days 0 to 3 Shr (0.291) (0.511) (0.006) (0.091) (0.116) (0.118) (0.120) (0.150) -0.783*** -0.928* 0.061*** 0.273*** -0.044 0.121 0.105 0.190 0.379** .415 (0.298) (0.512) (0.006) (0.094) (0.032) (0.108) (0.109) (0.116) (0.151) * = statistically significant at 10%, ** = statistically significant at 5%, *** = statistically significant at 1% Table 4 Restricted Sample Estimations SS AbVol NormSS Ret Price(0) EPS Q Q Q Q (1) Shr 0 1 2 Shr 3 4 Shr 5 1 2 2 3 3 4 4 5 SS The results of OLS estimation of this equation, as fitted to the sample of 311 firms obtained after dropping sample firms that did not file a timely 10K-405. The variable represents the Shr average daily number of a company’s shares that are sold short following the firm’s 10K filing, normalized by the firm’s total number of shares outstanding. Estimations are conducted for where this independent variable is measured over two intervals: days 1 to 3, which are the three days after the filing date; and days 0 to 3, which are the filing date and the subsequent 3 days. Ret represents the firm’s stock return during the days following the 10K filing date. In estimations using three-day average short-selling, RET AbVol is also measured over days 1 to 3; in estimations using four-day average short-selling, RET is measured over days 0 to 3. Abnormal volume, is the difference Shr between the company’s average daily volume during days following its filing and the normal daily volume, normalized by total number of shares outstanding. In estimations using either the three-day (four-day) average short-selling, it is computed over three (four) days also. We report results from estimations that use two different measures of the normal daily volume component of abnormal. Panel A presents results based upon the firm’s mean daily volume during the six weeks that end one week prior to its earnings announcement. Panel B presents results based upon the firm’s median daily volume during the same six weeks. Price(0) is the natural log of the company’s stock NormSS price on the filing date. Normal short-selling is the company’s normal daily short-selling normalized by shares outstanding. Panel A presents results where SHR normal daily short selling is measured as the firm’s mean daily short-selling during the six weeks one week prior to its earnings announcement. Panel B presents results where it is measured as the firm’s median short-selling during the same six week period. EPS is the company’s earnings per share for the year 2000 and is measured as income before extraordinary items divided by total shares outstanding. Q2, Q3, Q4 and Q5 are dummy variables equal to one if the company is in the second lowest, middle, second highest, or highest operating accrual quintile based upon their 10K filing. White’s (1980) heteroskedasticity-consistent standard errors in parentheses. α0 α1 α2 α3 α4 α5 β1 β2 β3 β4 Adj R2 Panel A: Mean used to estimate NormSS and AbVol SS -0.413 -0.666 0.066*** 0.104 1.257*** 0.096 0.097 0.182 0.329* .630 measured over days 1 to 3 (0.351) (0.553) (0.009) (0.116) (0.156) (0.162) (0.147) (0.171) (0.192) Shr -0.575 -0.672 0.065*** 0.146 1.233*** -0.038 0.145 0.157 0.250 0.422** .630 (0.365) (0.550) (0.009) (0.125) (0.164) (0.043) (0.150) (0.137) (0.159) (0.178) SS -0.403 -0.729 0.065*** 0.093 1.260*** 0.135 0.107 0.212 0.325* .611 measured over days 0 to 3 (0.339) (0.481) (0.008) (0.114) (0.179) (0.156) (0.142) (0.180) (0.194) Shr -0.514 -0.713 0.064*** 0.122 1.243*** -0.027 0.171 0.151 0.260 0.392*** .611 (0.346) (0.487) (0.009) (0.123) (0.189) (0.041) (0.143) (0.129) (0.164) (0.173) Panel B: Median used to estimate NormSS and AbVol SS -0.234 -0.424 0.067*** 0.069 1.402*** -0.018 0.055 0.113 0.317* .649 measured over days 1 to 3 (0.344) (0.539) (0.009) (0.115) (0.178) (0.154) (0.146) (0.166) (0.183) Shr -0.409 -0.430 0.066*** 0.114 1.375*** -0.041 0.072 0.120 0.186 0.416** .650 (0.347) (0.535) (0.009) (0.121) (0.186) (0.041) (0.142) (0.136) (0.154) (0.168) SS -0.202 -0.588 0.066*** 0.048 1.418*** 0.061 0.071 0.148 0.316* .635 measured over days 0 to 3 (0.332) (0.467) (0.008) (0.113) (0.205) (0.149) (0.141) (0.174) (0.185) Shr -0.325 -0.572 0.066*** 0.079 1.399*** -0.029 0.100 0.118 0.200 0.386** .635 (0.332) (0.472) (0.009) (0.119) (0.214) (0.039) (0.135) (0.127) (0.159) (0.163) * = statistically significant at 10%, ** = statistically significant at 5%,*** = statistically significant at 1% Table 5 Statistics for Data on the Monthly Short Interest of the Sample This table contains sample mean (top figure in each cell) and median (bottom figure in each cell) values for firms split into quintiles based upon fiscal year-end 2000 operating accruals. Current Short Interest Ratio is a firm’s short interest divided by shares outstanding in the month following the firm’s 10K filing date. Prior Short Interest Ratio is a firm’s short interest divided by shares outstanding in the month preceding the firm’s 10K filing date. Change in Short Interest Ratio is a firm’s Current Short Interest Ratio minus its Prior Short Interest Ratio. n represents number of firms. All numbers are percentages. Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 (n=85) (n=86) (n=86) (n=88) (n=92) Current Short Interest Ratio 4.582 4.645 4.041 3.847 5.924 3.563 3.132 2.728 2.947 4.113 Prior Short Interest Ratio 4.272 4.208 3.566 3.305 5.419 2.994 3.159 2.459 2.576 3.668 Change in Short Interest Ratio 0.310 0.436 0.475 0.541 0.505 0.073 0.176 0.216 0.196 0.085 Table 6 Short Interest Estimations CSI 0 1PSI 3Price(0) 5EPS 1Q2 2Q3 3Q4 4Q5 (3) SI 0 3 Price(0) 5 EPS 1Q2 2 Q3 3Q4 4 Q5 (4) The results of OLS estimation of these equations, as fitted to the sample of 437 firms. CSI (current short interest) represents the firm’s short interest reported in the month following the 10K filing date normalized by the firm’s total shares outstanding. PSI (prior short interest) represents the firm’s short interest reported in the month prior to the 10K filing date normalized by the firm’s total shares outstanding. SI (change in short interest) is measured for the firm as CSI-PSI. Price(0) is the natural log of the company’s stock price on the filing date. EPS is the company’s earnings per share for the year 2000 and is measured as income before extraordinary items divided by total shares outstanding. Q2, Q3, Q4, and Q5 are dummy variables equal to one if the company is in the second lowest, middle, second highest, or highest operating accrual quintile based upon their 10K filing. White’s (1980) heteroskedasticity-consistent standard errors in parentheses. α0 α1 α3 α5 β1 β2 β3 β4 Adj R2 CSI Model -0.0053 0.989*** 0.0026* -0.0007 0.0020 0.0027 0.0032 0.0038 0.924 (0.0045) (0.0139) (0.0015) (0.0004) (0.0018) (0.0021) (0.0022) (0.0027) SI Model -0.0052 0.0025* -0.0007 0.0020 0.0028 0.0033 0.0036 -0.002 (0.0045) (0.0015) (0.0004) (0.0018) (0.0021) (0.0022) (0.0026) * = statistically significant at 10%, ** = statistically significant at 5%,*** = statistically significant at 1% Table 7 Statistics for Classes of Shorted Shares as Percentages of All Shorted Shares and as Percentages of Total Volume: Daily Values for 602 Sampled Nasdaq Stocks from September 13, 2000, to July 10, 2001 All numbers are in percentages except for the cells containing estimated correlations. Shares Shorted by Shares Shorted Shares Shorted in Customers by Dealers Exempt Trades Panel A: As Percentage of All Shorted Shares Mean 17.21 72.60 10.19 Median 17.17 73.63 8.82 Standard Deviation 2.66 4.25 3.30 Minimum 11.86 61.89 5.83 Maximum 25.50 79.89 24.09 Panel B: As Percentage of Total Volume Mean 4.00 16.86 2.40 Median 3.95 16.81 1.99 Standard Deviation 0.67 1.05 0.88 Minimum 2.63 14.62 1.26 Maximum 6.15 19.58 6.09 Correlation of Customer Percentage with -- -0.36*** 0.26*** Percentages for Dealers and Exempt Trades Correlation of Dealer Percentage with -- -- -0.10 Percentage for Exempt Trades *** Statistically significant at 1% with indicated sign. Figure 1. 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