Short selling and intraday price pressures.We study episodes of significant intraday downward price pressures in individual stocks and find that price declines during such episodes are driven mainly by liquidity demanding non-short volume. Although short sellers during these price pressure episodes are also active and somewhat exacerbate the magnitude of price declines, their influence on prices is secondary to that of nonshort sellers. As such, our findings are inconsistent with the recently reignited allegations of systematic trading abuses caused solely by short sellers and might shed light on the debate regarding the need to reinstitute short selling restrictions.
During the recent financial crisis, short selling became the focus of intense debate triggered by a rapid decline in stock prices. A number of commentators, including Charles Schwab, Chairman of the Charles Schwab Corporation, and John Mack, Chairman of the Board of Morgan Stanley, publicly urged the Securities and Exchange Commission (hereafter the SEC) to reinstitute short selling restrictions. Proponents of the restrictions cited bear raids, predatory trading, rumormongering, credit default swap market manipulation, and other vices among short sellers' abusive practices. (1)
Regulators seem to have taken the antishort sale arguments seriously. In 2008, in the midst of the crisis, the SEC instituted a temporary short selling ban and introduced a requirement for hedge funds to disclose their short positions. (2) In 2010, in the aftermath of the crisis, the SEC approved Rule 201 that restricts short selling once a stock price has declined by 10% or more in one day. (3) Subsequent to such a decline, short sales must execute above the highest current public bid until the end of the following trading day. Given that the SEC lifted short selling restrictions in July 2007, the new rule is viewed by many as a step back in the decades-long effort to relax short sale constraints in the United States stock market.
Despite widespread criticism, evidence of short selling abuses is, for the most part, anecdotal. In the meantime, extant empirical evidence is principally in favor of short sellers. A number of recent studies (Alexander and Peterson, 2008; Diether, Lee, and Werner, 2009b; Boehmer and Wu, 2010; Chakrabarty, Moulton, and Shkilko, 2011) find no evidence of systematically abusive short selling practices. On the contrary, they report that short selling enhances price discovery, improves market efficiency, and, as such, should be unrestricted. In addition, Boehmer, Jones, and Zhang (2009), Boulton and Braga-Alves (2010), and Beber and Pagano (2011) argue that even in the midst of the 2008 crisis, the ban on short selling caused substantial deterioration of market quality. Finally, the vast asset pricing literature holds that unrestricted short selling is an essential condition for efficient markets (Miller, 1977; Harrison and Kreps, 1978; Scheinkman and Xiong, 2003).
Given the disagreement between academic research and industry commentators, it is important to provide empirical evidence regarding the existence of price pressures caused by short sellers. In this study, we provide such evidence on an intraday basis. Our analysis indicates that during the price decline stages of large intraday price reversals, short selling often intensifies and short sellers switch from their usual role as liquidity providers to demanding liquidity. (4) As they demand liquidity, short sellers contribute to price declines. Our sample selection procedure identifies price reversals that are free of firm-specific news releases and of arbitrage opportunities. Thus, active short selling cannot be attributed to the workings of price discovery or to merger arbitrage and convertible arbitrage. (5) Given its liquidity demanding nature and the price reversals that it accompanies, short selling in our sample possesses some of the features that are widely criticized in the media.
Nonetheless, it is important to emphasize that short sellers are not the only drivers of price declines nor are they the main drivers. In fact, during large price reversals, the magnitude of abnormal short selling is markedly smaller than that of abnormal nonshort (long) selling. Long selling has a notably more significant downward effect on prices and is the main force behind the prerebound price declines.
Our focus on price reversals relies on the argument that in the absence of news and certain arbitrage opportunities, price declines that are followed by quick rebounds might suggest unjustified prerebound price pressure. Brunnermeier and Pedersen (2005) and Carlin, Lobo, and Viswanathan (2007) theorize that markets are susceptible to episodic liquidity crises caused by the weak capital positions of large investors. For instance, an ailing institution (or a group of institutions) might be compelled to sell out of a large stock position, creating downward pressure on the stock price. Market watchers with predatory intentions might then exacerbate the price decline by (short) selling alongside the institution. As the selling pressure subsides, the price quickly rebounds. Thus, after a predatory episode, a reversal price pattern emerges.
We use this theoretical argument as a basis for our identification procedure and study large intraday price reversals that are not accompanied by major corporate news announcements or merger/convertible arbitrage opportunities. Figure 1 describes the reversal pattern that we use for identification. The details of the identification procedure are described in a later section. We identify reversals during a one-year period from July 2005 to June 2006 and demonstrate that short sales contribute to the prerebound price declines.
[FIGURE 1 OMITTED]
The literature has argued that short sellers usually provide liquidity and enhance price discovery (Diether et al., 2009b; Boehmer and Wu, 2010). It is unlikely that the active short selling that we observe during the prerebound price declines performs either of these two functions. Generally, our findings are more consistent with Brunnermeier and Pedersen's (2005) line of reasoning, although our inability to identify short sellers' motives and covering strategies prevents us from labeling their activity as predatory. Whereas it is possible that short sellers could be purposefully putting excessive pressure on prices, alternatively, they might be pursuing less impious strategies.
Besides adding to the debate on abusive intraday short selling, our study expands the extant literature about the role of short selling in triggering price pressures. Prior studies (Bechmann, 2004; Mitchell et al., 2004; Henry and Koski, 2010) focus on price pressures in the context of corporate events such as convertible or merger arbitrage and seasoned equity offerings (SEOs). Our evidence is more general in that we study price pressure episodes that are not accompanied by corporate events. Although short selling activity increases during such episodes, the role of short selling is secondary to that of long selling in contributing to price declines. Thus, our results are not particularly supportive of the view that short sellers single-handedly destabilize prices.
The remainder of the paper is organized as follows. Section I summarizes theoretical and empirical evidence on short selling in relation to price pressures. Section II introduces data sources and describes the identification procedure. Section III examines the correlation between short selling and price reversals, the mechanics of such reversals, the role of long sales, and the determinants of pre- and postrebound returns. Section IV contains a discussion of the study's implications and our conclusions.
In the finance literature, short sellers are usually viewed as informed traders. Initially modeled by Diamond and Verrecchia (1987), short sellers' informedness is extensively tested. Dechow et al. (2001) discover that short sellers are able to identify firms that are overvalued based on their book-to-market ratios and short stock in these firms with subsequent covering after the ratios mean revert. Kot (2007) reports that short selling activity is positively related to arbitrage opportunities and hedging demand. Boehmer, Jones, and Zhang (2008) find that highly shorted stocks underperform lightly shorted stocks by as much as 15.6% on an annualized basis. Diether et al. (2009b) indicate that in addition to the ability to predict future stock performance, investors who choose to sell short are able to recognize transient market overreactions. Boehmer et al. (2009) and Diether et al. (2009b) suggest that short sellers tend to provide liquidity, whereas Akbas et al. (2008) and Boehmer and Wu (2010) argue that short sellers enhance price efficiency by facilitating price discovery and generating value relevant information.
In this study, we focus on a somewhat different phenomenon; namely, temporary intraday price pressures that involve short selling. Unlike in Diether et al. (2009b), short sellers in our sample often act as liquidity demanders and, unlike in Akbas et al. (2008) and Boehmer and Wu (2010), short sellers in our sample do not seem to enhance price discovery given the absence of news around our event days.
We believe that an investigation of short selling during significant intraday price fluctuations is warranted given the recently renewed pressure on regulators to reinstitute short selling restrictions. We note that extant research (Bechmann, 2004; Mitchell et al., 2004; Henry and Koski, 2010) already demonstrates that short selling occasionally causes price pressures. Specifically, Bechmann (2004) and Mitchell et al. (2004) find evidence of price pressures from short selling associated with convertible bond arbitrage and merger arbitrage, respectively. In addition, Henry and Koski (2010) present evidence consistent with manipulative short selling around SEOs. Although the evidence in these studies might seem similar to ours, we believe that the short selling pressures discussed in this paper are of a different nature because our sample contains no arbitrage events, no SEOs, and no corporate news. As such, we might be closer than previous research to identifying episodes of a potentially predatory nature. (6)
Several theoretical models (Attari, Mello, and Ruckes, 2005; Brunnermeier and Pedersen, 2005; Carlin et al., 2007) describe market conditions that might lead to predatory trading defined as "trading that induces and/or exploits the need of other investors to reduce their positions." Brunnermeier and Pedersen (2005, p. 1825). If one or more large investors need to sell, others might also engage in selling (or short selling) and then profit by buying the stock back at a lower price. Such sellers actively open new positions at the beginning of a predatory episode and push prices below equilibrium levels. Prices rebound once predatory activity ceases. (7)
The theoretical suggestion that a predatory trading episode might be triggered by an institution's attempt to unload a sizeable stock position could seem unrealistic. A healthy institution is unlikely to subject itself to the possibility of predation by attempting to quickly sell out of a large position. Indeed, Chiyachantana et al. (2004) and Lipson and Puckett (2006) indicate that institutions usually spread their sales and purchases over several consecutive days. Nonetheless, if an institution is financially constrained, it might have to sell quickly. It is estimated that nearly 600 hedge funds failed in 2005 alone suggesting that predatory episodes triggered by rushed institutional selling might be a relatively abundant phenomenon during our sample period. (8)
Theoretical models of predation discount the fact that large orders may be routed to the upstairs market to mitigate, or entirely avoid, manipulative trading. Meanwhile, studies of block trading provide evidence that upstairs markets periodically facilitate executions of large blocks. Grossman (1992) suggests that many large investors do not express their trading interests publicly, and that upstairs brokers collect information on such interests, occasionally drawing on this information to provide additional liquidity to block orders. Bessembinder and Venkataraman (2004) confirm Grossman's (1992) suggestion and report that upstairs brokers on the Paris Bourse are able to tap into pools of unexpressed liquidity. Nonetheless, only 67% of the block volume on the Bourse executes upstairs. Similarly, Madhavan and Cheng (1997) investigate upstairs trading in 30 Dow Jones stocks and discover that as much as 80% of block dollar volume executes downstairs. Thus, although upstairs markets regularly facilitate large executions, there might still exist sufficient opportunities for price pressures in the downstairs market.
Two studies of mutual funds shed some light on the possibility and the profitability of trading against constrained institutions. Coval and Stafford (2007) find that selling pressure originated by distressed mutual funds can create profitable front-running opportunities. Chen et al. (2008) link such opportunities to hedge fund profits and find that hedge fund returns increase when the number of distressed mutual funds is large. Our data do not allow us to identify the type of institutions involved in price reversals, but we are able to describe reversal mechanics and define the role of short sales in their development.
II. Sample Selection and Identification of Reversals
Our sample consists of all trades and quotes in the NYSE and NASDAQ securities from July 2005 to June 2006. (9) Trade and quote data are derived from the Trade and Quote (TAQ) database. Trades that involve shorted shares are identified using the Regulation SHO database. (10) We apply conventional filters to TAQ data and exclude trades and quotes that are reported out of time sequence and are coded as involving an error or a correction. We also exclude trades with a nonstandard settlement. Quotes are omitted if either the ask or bid price is nonpositive. We also exclude quotes with bids equal to or greater than asks and quotes (trades) with zero depths (sizes). To reduce the influence of opening and closing calls, we exclude the largest trades at the opening and at the close.
We follow Bessembinder (2003) and do not lag quote time stamps when merging quotes and trades. We restrict the analysis to regular trading hours (9:30 a.m. to 4:00 p.m.) and divide each trading day into 78 five-minute intervalsj. For each interval j, we use volume-weighted withininterval prices to compute continuously compounded five-minute returns, [ret.sub.j]. Securities with prices lower than $5 per share and those with fewer than 60 traded intervals on a given day are omitted. (11)
B. Identification of Large Price Reversals
To identify a trading day d in a stock i as a day with a large price reversal (hereafter an event day), we first assess stock i's historical intraday volatility by computing the average standard deviation of its five-minute cumulative returns during 20 trading days preceding day d, [[sigma].sub.i]. Subsequently, we define day d as an event day, if stock i's price declines by two or more [[sigma].sub.i]s and subsequently rebounds by 90% to 110% of the initial decline by the end of the day. For instance, for a stock with [[sigma].sub.i] = 1%, day d would be identified as an event day if 1) the minimum cumulative intraday return is -2% and 2) the cumulative return at the end of the day is greater than or equal to -0.2% (= [1 - 0.9] x [-2%]) and is lower than or equal to 0.2% (= [1 - 1.1] x [-2%]). An illustration of event day identification is provided in Figure 1.
We set the recovery range to 90% to 110% in an attempt to filter out the reversals that might be triggered by the arrival of new information. As new information is likely to result in a new price level at the end of the day, we restrict the sample to days when prices almost fully recover. This procedure identifies 10,118 reversals in 3,588 stocks. In Panel A of Table I, we report summary statistics for the stocks subject to large intraday reversals, the sample stocks. For comparison purposes, we provide similar statistics for the universe of the NYSE and NASDAQ stocks with prices at or higher than $5 per share.
The data reveal that the sample firms are somewhat larger and more actively traded than the universe. This is, most likely, because of the 60 intraday trading intervals requirement. The standard deviation of intraday cumulative returns, [sigma], is somewhat smaller for the sample stocks than it is for the universe. Although, the requirement that a stock must have at least 60 intraday trading intervals tilts the sample toward larger, more actively traded and less volatile firms, we believe that it makes our estimates more conservative, as small firms' stock prices are likely to be more susceptible to manipulation. We provide support for this claim in the subsequent sections.
Market valuation statistics provide mixed results. Although the mean price-to-earnings ratio implies that the sample stocks might be slightly overvalued, the mean market-to-book ratio suggests the opposite. Yet, it is clear that an average reversal prone stock is not significantly overvalued, consistent with our suggestion that, in our setting, the motives behind short sales might differ from those discussed in the prior literature (Dechow et al., 2001).
A sample stock becomes subject to a reversal about 2.82 times during the sample year. Seventynine percent of Pilot stocks (the stocks for which short selling restrictions were lifted by Regulation SHO during our sample period) undergo reversals; yet, reversals in Pilot stocks comprise only 20.40% of all reversals. In addition, 51.84% of reversals occur in the NYSE-listed stocks. The remaining reversals occur in NASDAQ stocks.
C. Elimination of Confounding Events
As our goal is to identify information-free reversals, we seek to further eliminate information effects by searching Compustat, Center for Research in Security Prices (CRSP), and LexisNexis databases for corporate announcements and other news on and around price reversal days. Specifically, we eliminate reversals that occur within a [-5; +5]-day window surrounding an earning or a dividend announcement as reported by Compustat and CRSP, respectively, and reversals that occur within a [-1; +1]-day window surrounding other corporate news events transmitted by major business news outlets as reported in LexisNexis.
Finally, to reduce the possibility that sample reversals are caused by ongoing convertible arbitrage, merger arbitrage, or SEO announcements like those described in Bechmann (2004), Mitchell et al. (2004), and Henry and Koski (2010), we drop reversals that happen in close proximity to convertible calls, merger, and SEO announcements as reported in LexisNexis. Specifically, based on the findings in the aforementioned studies, we eliminate reversals that occur within three months preceding and one month following a convertible call, reversals that occur within one month preceding and three months following a merger announcement, and reversals that occur within a [-5; +5]-day window around an SEO announcement. These filters leave 72.25% of the original reversals, for a sample of 7,310 reversals.
III. Short Selling During Price Reversals
A. Abnormal Short Selling
Short volume, naturally, differs across stocks. Thus, to proceed, we define a standardized short selling measure that allows for a proper cross-sectional comparison. The literature usually standardizes short volume by either: 1) shares outstanding (Christophe, Ferri, and Hsieh, 2010), or 2) total volume (Diether et al., 2009b). The former metric performs well in capturing deviations in unconditional short volume, whereas the latter metric relates fluctuations in short volume to long volume. If both short and long volumes are relatively high during the reversals, the two metrics will provide different insights into short selling activity. We choose to use both standardization techniques. Thus, we compute the following two short ratios for stock i on day d during the five-minute interval j as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)
where [SHRAT1.sub.i.j,d] and [SHRAT2.sub.i,j,d] are short sale ratios; [SHVOL.sub.i,j,d] is short volume (the quantity of shorted shares); SHOUT,.,d is the number of shares outstanding; and [VOL.sub.i,j,d] is total volume. In Panel B of Table I, we provide summary statistics on the two ratios for the sample and for the universe of stocks. Short selling in sample stocks is somewhat more active than in the universe, with the sample and the universe SHRAT1 averaging, respectively, 0.046 and 0.039 and SHRAT2 averaging 33.1% and 31.5%, respectively.
Although the ratios defined in Equations (1) and (2) standardize short volume across stocks, they do not allow us to determine whether short selling activity during the price reversal episodes is abnormal. To draw inferences regarding the relative magnitude of short selling, we compare shorting activity during the reversals to shorting during benchmark events. Thus, defining such benchmark events becomes an imperative task.
We rely on the extant short selling literature for benchmarking ideas. Diether et al. (2009b) indicate that short volume is a positive function of same day returns. Given the significance of intraday returns during our reversal episodes, we benchmark pre- and postrebound metrics (1) and (2) against their equivalents computed on days of comparably negative or positive returns that are not followed by reversals:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)
where [ASHRAT.sub.i,j,d,m] is the abnormal short ratio computed during a reversal of m x [[sigma].sub.i] magnitude in stock i during a five-minute periodj on day d and where [MSHRAT1.sub.i,m] and [MSHRAT2.sub.i,m] are the benchmark five-minute averages computed on days with negative and positive price changes of m x [[sigma].sub.i] magnitudes that are not followed by same day reversals. (12) The benchmarks are computed during the six months preceding day d. We are able to find suitable benchmarks for 6,281 reversal episodes.
Next, we divide each event day d into two stages: 1) [[ret.sub.max,pre]; [ret.sub.min] and 2) ([ret.sub.min]; [ret.sub.max,post]], where retmax,pre is the maximum [ret.sub.j] during the prerebound stage; [ret.sub.max,post] is the maximum [ret.sub.j] during the postrebound stage; and [ret.sub.min] is the minimum [ret.sub.j]. Each of the two stages is further divided into 10 periods for a total of 20 time periods per event day. (13) This adjustment benefits subsequent analysis as it allows for standardization across price reversals that naturally vary in length. However, it restricts the sample to event days with pre- and postrebound stages lasting at least 50 minutes each. This restriction does not significantly reduce the number of event days, as the majority of large reversals take longer than 50 minutes to unfold.
As mentioned above, we subdivide event days into four groups based on the magnitude of the prerebound price decline, m x [[sigma].sub.i], with m varying among the following intervals: [2; 3), [3; 4), [4; 5), and [5; [infinity]). In Table II, we report period-by-period returns for each group. The magnitude of the prerebound price decline varies from -1.42% for the smallest reversals to -2.02% for the largest reversals (Panel A of Table II). The number of observed reversals declines with magnitude from 2,242 for the smallest to 1,067 for the largest reversals (Panel B). Prerebound price declines are larger on NASDAQ than on the NYSE, varying from -1.74% to -2.45% on the former and from -1.09% to -1.59% on the latter (Panel C). Finally, price declines are more pronounced in low priced and relatively illiquid stocks, varying from -1.65% to -2.52%. In comparison, in the high priced and relatively liquid stocks, price declines vary from -1.13% to -1.64% (Panel D). (14) This result is notable as the regulators are particularly concerned with short sellers' influence on prices in the former stock category.
Table III contains abnormal short volume statistics computed for the reversals of different magnitudes. The data reveal that prerebound price declines are often accompanied by substantial increases in shorting activity. In particular, for the reversals of [3; 4), [4; 5), and [5; [infinity]) magnitudes, the average prerebound SHRAT1 is 10.90% to 51.22% higher than it is during the benchmark episodes (Panel A of Table III). Midway through the prerebound stage, SHRAT1 reaches 80.53% above the benchmark for reversals of [5; [infinity]) magnitudes (Panel B). Postrebound, SHRAT1 is virtually indistinguishable from the benchmarks. Increases in prerebound short volume differ between the NYSE-listed and NASDAQ stocks. The average ASHRAT1 for the former group is usually smaller than for the latter group (Panel C). Finally, short volume increases notably more for the low price liquidity category of stocks than for stocks with higher prices and liquidity (Panel D).
It is important to note that long volume also increases during the prerebound stages. Furthermore, as can be inferred from the ASHRAT2 statistics in Table III, the increase in long volume surpasses the increase in short volume in most periods. Specifically, prerebound ASHRAT2 statistics are often negative implying that prerebound short volume as a fraction of total volume is lower than that during the benchmark periods (Panel A of Table III). Given that ASHRAT1 statistics imply a significant increase in short volume, we surmise that long volume increases even more than short volume. Although the direction of long volume is not clear from this test, given the price declines during the prerebound stage, we infer that the majority of long volume is seller-initiated.
The literature has argued that short sellers usually provide liquidity and enhance price discovery. It is unlikely that the active short selling that we observe during the prerebound price declines performs either of these two functions. Selling during market declines is more likely to consume liquidity than to provide it, whereas the absence of news in our sample (in addition to the fact that prices almost completely reverse) suggests that price discovery is not the most likely explanation of abnormal short selling activity. (15)
Generally, our findings are more consistent with Brunnermeier and Pedersen's (2005) line of reasoning, although our inability to identify short sellers' motives prevents us from labeling their activity as predatory. Although it is possible that short sellers could be purposefully putting excessive pressure on prices, they might be pursuing less impious market neutral long-short strategies.
B. Demand for Liquidity
Given that during price declines, short sellers must compete for immediacy with long sellers, we expect that a significant share of prerebound short sales are liquidity demanding. To confirm this expectation, we use the trade direction identification algorithm proposed by Chakrabarty, Li, Nguyen, and Van Ness (2007), who argue that post-decimalization, their procedure performs better than the conventional algorithms of Lee and Ready (1991) and Ellis, Michaely, and O'Hara (2000). The algorithm developed by Chakrabarty et al. (2007) divides the spread into deciles and uses the quote rule if the transaction price is in the top three deciles or in the bottom three deciles. Alternatively, if the transaction price is in the two deciles above the midpoint or the two deciles below the midpoint, the algorithm uses the tick rule. For trades at the quotes, the quote rule is used. To measure short (long) sellers' demand for liquidity, we compute, similarly to Chordia and Subrahmanayam (2004), order imbalance metrics, SHIMB (LIMB), as the difference between the buyer- and the seller-initiated short (long) volume scaled by total short (long) volume. (16)
In Table IV, we report order imbalance statistics for short and long sales that execute during reversals of four previously defined magnitudes. We caution that the reliability of the Chakrabarty et al. (2007) algorithm (or that of any trade direction identification algorithm) has not been tested under the conditions of significant and rapid price changes. Thus, the results in Table IV must be interpreted with caution.
Generally, the data confirm our expectations that as reversals unfold, sellers dominate. In Panel A of Table IV, we demonstrate that the prerebound SHIMB averages -17% for the smallest reversals and -24% for the largest reversals. In the meantime, prerebound LIMB averages -27% for the smallest reversals and -35% for the largest reversals. During the postrebound stages, both short and long imbalances are, as expected, positive. In Panel B, we report that short sellers are somewhat more aggressive in NASDAQ stocks than in the NYSE stocks. Perhaps, this is because of fewer short selling restrictions for the former stocks. We return to this issue shortly. Overall, the results validate our earlier suggestion that short sellers are unlikely to perform a liquidity providing function during the prerebound stages of large price reversals. The data also corroborate our earlier observation that short selling during the prerebound stages is of lesser magnitude than long selling.
An important question that arises from our findings is: How do short sellers turn a profit? Although our data do not allow us to infer when short positions are being covered, we conjecture that some of the positions might be covered for profit. If a short seller opens a position during the price decline at price P0 and closes the position before the price rebounds to the P0 level, his profit is the difference between: 1) the opening price [P.sub.0], 2) the covering price P,, and 3) the transaction cost. In unreported analysis, we estimate that the maximum possible return on an intraday short position held during a reversal of [5; [infinity]) magnitude is 2.16%. There is, of course, a possibility of a negative return to such positions if the positions are opened too late during the prerebound stage and/or are closed too late during the postrebound stage. We estimate that the minimum possible return on an intraday short position opened during the prerebound stage and closed during the postrebound stage is -2.68%. Overall, although profiting from intraday short positions is possible, profits are by no means guaranteed.
C. Short Sale Restrictions
During our sample period, the uptick rule for the NYSE securities and the bid test for NASDAQ securities should restrict short selling in non-Pilot stocks during price declines. (17) The NYSE prohibits short sales on downticks when the most recent price change preceding the trade is negative. Consequently, a market order to sell short might not immediately execute and might be assigned a limit order status (Diether, Lee, and Werner, 2009a). In the meantime, the bid test on NASDAQ prohibits short sales at the bid or below bid prices on down bid quotes (i.e., when the bid quote is lower than the previous bid quote). Although the bid test should limit opening of new short positions during significant price declines, it is less restrictive than the tick test. The results in Panel C of Table III and in Panel B of Table IV are consistent with this notion. In what follows, we seek to shed more light on the effectiveness of the restrictions.
In addition to differences in restrictions, we consider several other criteria that might affect the intensity of prerebound short selling. First, the majority of price reversals may occur in Pilot stocks, for which short selling restrictions are not enforced during our sample period. Moreover, the majority of prerebound short sales may be from exempt traders (e.g., market makers, arbitrageurs, etc.). In addition, short sellers may route their trades to markets that are not enforcing the restrictions. We address these possibilities in Tables V and VI.
In Table V, we ask whether the absence of short selling restrictions in Pilot stocks allows for more active prerebound short selling. In Panel A, we report prerebound ASHRAT statistics separately for Pilot and non-Pilot stocks. To remove the effect of short positions opened by exempt market participants, we exclude short sales flagged E (for exempt) from this analysis. As expected, the data indicate that short sellers are more active in Pilot stocks, with prerebound ASHRAT1 ranging from 8.70% for the smallest to 60.84% for the largest reversals. Meanwhile, prerebound ASHRAT 1 statistics for the non-Pilot stocks are of smaller magnitude and range from 6.44% to 41.25%.
In Panels B and C, we split the sample into the NYSE and NASDAQ stocks to gauge the effect of differences in restrictions between the two listing markets. Earlier, we suggested that the uptick rule should be more effective than the bid test in deterring short sales during prerebound stages. The data confirm this suggestion. For Pilot securities, short selling activity in the NYSE and NASDAQ stocks, as represented by ASHRAT1, is virtually the same across reversals of all magnitudes. Specifically, the differences in ASHRAT1 between the NYSE and NASDAQ are statistically insignificant for all but the smallest reversals. However, for the non-Pilot stocks, abnormal short selling is higher for NASDAQ securities than it is for NYSE securities for reversals of all magnitudes. Specifically, ASHRAT1 ranges from a statistical zero to 31.28% for the NYSE non-Pilot stocks and ranges from 9.05% to 52.79% for NASDAQ non-Pilot stocks. Based on these findings, we conclude that the tick rule is a more successful deterrent of liquidity demanding short selling than the bid test.
In Table VI, we seek evidence that during the prerebound stages, short orders might be routed to markets that do not enforce short selling restrictions. At the time of our study, the sample stocks trade via nine different market centers: 1) the American Stock Exchange (AMEX), 2) ArcaEx (reporting through the Pacific Stock Exchange), 3) the Boston Stock Exchange, 4) the Chicago Stock Exchange, 5) the NASD Alternative Display Facility (ADF), 6) NASDAQ, 7) the NYSE, 8) INET (reporting though the National Stock Exchange), and 9) the Philadelphia Stock Exchange. (18) Boston, Chicago, INET, and Philadelphia volumes in the NYSE stocks as well as AMEX, Chicago, and ADF volumes in NASDAQ stocks comprise, in total, less than 1% of sample volume in these stocks. Therefore, we focus on short sales executed on the NYSE, NASDAQ, and Arca when it comes to NYSE stocks and on NASDAQ, INET, and Arca when it comes to NASDAQ stocks.
We are particularly interested in the short sales in NASDAQ stocks that are routed to Arca and INET. In 2003, Arca acquired an exchange status and no longer had to comply with NASD regulations, including the bid test. As reported in Diether et al. (2009a), the orders to short NASDAQ stocks on Arca were virtually unrestricted. Meanwhile, at the beginning of our sample period, INET held that the bid test was not applicable to orders sent to it because the National Stock Exchange (through which INET reported its trades at the time) did not have a short sale rule for NASDAQ stocks. On January 23, 2006, INET switched trade reporting to NASDAQ and began enforcing the bid test. We suggest that prerebound short sales could be extensively routed to Arca and INET (for the latter perhaps only before January 23, 2006) in search of timely executions.
Table VI contains market share statistics for short and long trades computed across four reversal magnitudes. In Panel A, we present the results for the NYSE stocks, whereas Panels B and C contain the results for NASDAQ stocks, respectively, before the switch of INET trade reporting to NASDAQ and after the switch. (19) For the NYSE stocks, the uptick rule extends to trades executed on all markets. Thus, we do not expect significant differences in execution locations between prerebound short and long volumes. However, we expect to observe such differences for NASDAQ stocks. The results confirm our expectations. Although there are no significant differences for the NYSE stocks (Panel A), short sales in NASDAQ stocks actively execute on Arca and INET (on the latter, during the before switch period) with market shares of the two venues growing in reversal magnitude. Specifically, in Panel B of Table VI, Arca's share of short sale executions increases from 17.4% during the smallest reversals to 28.7% during the largest reversals. INET's share is between 18.8% and 36.9% during the period when INET reports through the National Stock Exchange (Panel B), and declines significantly after the switch of reporting to NASDAQ in 2006 (Panel C). The stricter enforcement of the bid test in the second subperiod seems to result in Arca's capturing INET's former share.
For comparison, Arca's and INET's shares of long trades do not exhibit patterns that we find for short sales. Specifically, the shares of long trade executions do not increase in reversal magnitude on either of the two markets.
D. Temporal Relations Among Price Declines, Short Selling, and Long Selling
The results thus far suggest that prerebound price declines are accompanied by liquidity demanding short and long sales. To shed some light on the temporal correlation between these two sale processes and intraday returns, we test for Granger causality between the following variables computed on a five-minute basis during the prerebound stage: 1) [SHIMB.sub.i,j]--short volume imbalance, 2) [LIMB.sub.i,j]--long volume imbalance, and 3) [RET.sub.i,j]--five-minute returns. To establish whether variable Y Granger-causes variable X, we estimate the following two equations:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)
where the subscript j indicates a five-minute value of one of the three variables of interest, i is the number of lagged observations of Y and X, and p = 3. The sums of squared residuals from the two models, [RSS.sub.u] = [[SIGMA].sup.J.sub.j=1] [[??].sup.2.sub.j] and [RSS.sub.r] = [[SIGMA].sup.J.sub.j=1] [[??].sup.2.sub.j], are then included in a test statistic [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. If the statistic is greater than the specified critical value, we reject the null-hypothesis that Y does not Granger-cause X, [H.sub.0]: [[beta].sub.1] = [[beta].sub.2] = xxx = [[beta].sub.p] = 0. We estimate Equations (5) and (6) separately for the four groups of reversals, [2; 3), [3; 4), [4; 5), and [5; [infinity]), and report p-values corresponding to the estimated test statistic S in Table VII. A p-value lower than 0.1 implies that we can reject the corresponding null hypothesis.
The results of Granger causality testing compiled in Table VII can be summarized by the following three statements: 1) abnormal short imbalances Granger-cause abnormal long imbalances and price declines, 2) abnormal long imbalances Granger-cause abnormal short imbalances and price declines, and 3) price declines during the larger reversals (i.e., reversals of [4; 5) and [5; [infinity]) magnitudes) Granger-cause long imbalances, but not short imbalances.
E. Determinants of the Prerebound Price Changes
The Granger causality tests imply that both short and long selling precede price declines. Given that our earlier tests suggest that the degree of long selling surpasses that of short selling, we are interested in learning which of the two processes has a more significant ceteris paribus effect on prices. Therefore, we test for a relation between both types of selling and intraday returns in a panel regression that controls for order imbalances and liquidity:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)
where [RET.sub.i,j] is the prerebound (Specifications -) or postrebound (Specification ) five-minute percentage return for stock i; [SHRAT1.sub.i,j] is the short ratio from Equation (1); [LRAT1.sub.i,j] is the abnormal long volume scaled by the number of shares outstanding; [SHIMB.sub.i,j] and [LIMB.sub.i,j] are short and long order imbalances in stock i, respectively; [QSP.sub.i,j] is the quoted spread; and [RET.sub.i,j-1] is the lagged return. All independent variables, aside from the lagged return, are standardized at the stock level allowing for stock fixed effects.
The model includes one lag for each of the variables to verify the causality of relations. Fitting the model on two or three lags of short and long ratios and order imbalances produces qualitatively similar results. In Table VIII, we present the coefficients from the models estimated for return reversals of [5; [infinity]) magnitudes. Results for the reversals of other magnitudes follow in Table IX. To conserve space, we report the coefficients of the control variables (estimated from Specification ) in the header of Table VIII. The coefficients estimated for the other specifications are not materially different.
Our earlier suggestion of a causal relationship between prerebound short selling and returns is confirmed in the multivariate setting by the negative coefficients of [SHRAT1.sub.j-1] in Specification  of Table VIII. We note that the causal effect is not likely to be attributable to short volume causing more short or long volume and, subsequently, more price pressure as contemporaneous short and long volumes are controlled for via the [SHRAT1.sub.j] and [LRAT1.sub.j] variables. The coefficient of [SHRAT1.sub.j] in Specification  indicates that increases in short volume not only precede, but also accompany negative returns. However, we refrain from claiming a causal link between negative returns and contemporaneous short selling, as the direction of the relation is not obvious.
Long selling, represented by the LRAT variables, has a marginally significant lagged effect on prices. Meanwhile, its contemporaneous effect is negative and notably significant. In fact, the impact of contemporaneous long selling on returns is about four times larger than that of contemporaneous short selling. This result corroborates our earlier assertion that prerebound long selling is more active and more liquidity demanding than short selling.
In Specification , we introduce order imbalances to control for the liquidity demanding nature of short and long volume. The coefficients of [SHRAT1.sub.j-1] and [SHRAT1.sub.j] remain significant. The order imbalance coefficients are positive, as expected, indicating that negative imbalances lead to or accompany negative returns. The effect of long sale imbalances is notably larger than that of short imbalances. The economic significance of this effect is compounded by the fact that nonshort order imbalances during prerebound stages are larger than short order imbalances (see Table IV).
In Specifications  and , we separate abnormal short volume by the venue of execution. As previously discussed, we expect that impatient short sellers in NASDAQ stocks will prefer routing their orders to Arca and INET (until the end of January 2006 for the latter), leading to larger price impacts of these orders. However, we do not expect to observe this effect for the NYSE-listed stocks. The results confirm our expectations. In Specification , the effect of short volume in the NYSE stocks is only slightly more negative when routed to Arca and NASDAQ as compared to short volume routed to the NYSE. Yet, the results for NASDAQ stocks during the July 2005-December 2005 period (Specification ) are strongly dependent upon the venue of execution, with trades routed to Area and INET having notably larger effects on the ensuing returns than trades routed to NASDAQ. (20)
In Specifications  and , we confirm our earlier conjecture that the relatively low priced and illiquid stocks are more susceptible to prerebound pressures than the higher priced and relatively liquid stocks. In summary, our examination of the prerebound price changes in the multivariate setting confirms that short sales have a negative effect on prices. Nevertheless, we note that the main negative effect comes from long sales and the imbalances that they create.
In Table IX, we present the results of running Specification  of Model (7) for reversals of all four magnitudes. We copy the results for the [5; [infinity]) reversals from Table VIII to facilitate comparison. We anticipate that short selling has a greater effect on prices during the reversals of larger magnitudes. The results support this expectation, as the coefficients of both lagged and contemporaneous SHRAT1 variables are significantly negative only for the reversals of [4; 5) and [5; [infinity]) magnitudes and are larger for the latter. We observe a similar pattern for the lagged short imbalances. Moreover, the contemporaneous effect of short imbalances is significant for reversals of all magnitudes, with the effect increasing in reversal magnitude. More importantly, for all reversal magnitudes, long volume and long order imbalances have a greater influence on returns than short order imbalances. In conclusion, although the evidence supports the notion of short sellers' having some effect on prereversal price changes, this effect is surpassed by that of long sales.
F. Event Window Returns
Our results indicate that the reversal episodes, for the most part, are caused by a temporary surplus of shares created by long and short sellers. Because there are no corporate announcements adjacent to these episodes, we do not expect any visible return patterns on days preceding and following the reversals. To ensure that our identification procedure is truly limited to no information events and to gauge whether reversals carry any value relevant information, we compute equal-weighted abnormal returns, ARs, on Days -1 and +1 as well as cumulative abnormal returns, CARs, during the following event windows: [-5; -1], [+1 ; +5], [-10, -1], and [+ 1; + 10], where Day 0 is the day of a reversal. The results are presented in Table X and contain no consistent return patterns. In the majority of event windows, abnormal returns that precede or follow intraday reversals are statistically indistinguishable from zero. We conclude that the reversal episodes are largely mechanical occurrences related to share supply and do not contain information that is relevant to short-term returns.
IV. Conclusions and Discussion
In this study, we seek to provide evidence regarding short sellers' involvement in the episodes of significant intraday price pressures. Our analysis indicates that during the prerebound stages of large price reversals, short selling often intensifies and short sellers switch from their usual role as liquidity providers to demanding liquidity. Given its liquidity demanding nature and the price reversals that it accompanies, short selling in our sample possesses some features of the widely criticized predatory trading.
Nonetheless, it is important to emphasize that short sellers are not the only drivers of price declines in our sample. In fact, during large price reversals, the magnitude of abnormal short selling is markedly smaller than that of abnormal long selling. Long selling has a notably more significant downward effect on prices and is the main force behind the prerebound price declines.
We caution that our results should not be misinterpreted as a call to further restrict short selling. First, our sample selection procedure is backward looking in that it is based on the theoretical argument that predatory events lead to large price reversals. Thus, by construction, our identification procedure limits the sample to instances of reversals that actually materialize. Meanwhile, these episodes could constitute only a subset in a larger set of active short selling events, not all of which result in significant price fluctuations. Thus, our evidence is insufficient to conclude that active short selling always exacerbates price declines. Ideally, we would want to focus our identification procedure on reversals in short selling instead of price reversals. Such a procedure however proves prohibitively cumbersome, as the intraday time series of the SHRAT variables often do not contain an easily identifiable inflection point. Meanwhile, the estimation of the ASHRAT variables is impossible without conditioning on the magnitude of the price decline.
In addition, we emphasize the episodic nature of our findings. Most recent research agrees that the effect of short selling on markets is generally positive. Studies by Jones and Lamont (2002), Akbas et al. (2008), Boehmer et al. (2009), Diether et al. (2009b), Boehmer and Wu (2010), and Chakrabarty et al. (2011) report that short selling improves price efficiency, enhances price discovery, and benefits liquidity. Furthermore, studies that find evidence of price pressures or manipulation by short sellers are limited to relatively rare occurrences such as some cases of arbitrage (Bechmann, 2004; Mitchell et al., 2004) and certain corporate announcements (Henry and Koski, 2010). Our study belongs to the latter category. Given these results, it seems that the episodic welfare costs of unrestricted short selling are not sufficient to negate the overall benefits that originate from short selling as an investment practice. Regulators should, perhaps, use this notion to counter pressure to restrict short selling that often arises subsequent to significant market downturns.
The study greatly benefited from comments of two anonymous referees, Brad Barber, Hank Bessembinder, Ben Blau, Marcus Brunnermeier, Bill Christie (Editor), Ken Cyree, Kathleen Fuller, Lisa Kramer, Mark Lipson, Fabricio Perez, Robert Schwartz, Bill Shughart, Richard Warr, Adam Yore, and seminar/session participants at the 2009 Napa Conference on Financial Markets Research, 2008 American Finance Association Annual Meeting, 2007 RS-DeGroote Conference on Market Structure and Market Integrity, 2007 Northern Finance Association Annual Meeting, 2007 Financial Management Association Annual Meeting, 2006 FMA Doctoral Student Consortium, The Bank of Canada, Florida International University, Louisiana State University, the University of Memphis, the University of Mississippi, Mississippi State University, and Wilfrid Laurier University. Shkilko would like to acknowledge financial support from The NASDAQ Educational Foundation and the Social Sciences and Humanities Research Council of Canada (SSHRC). All remaining errors are our responsibility.
Akbas, E, E. Boehmer, B. Erturk, and S. Sorescu, 2008, "Why Do Short Interest Levels Predict Stock Returns?" Texas A&M University, University of Oregon, and Oklahoma State University, Working paper.
Alexander, G. and M. Peterson, 2008, "The Effect of Price Tests on Trader Behavior and Market Quality: An Analysis of Reg. SHO," Journal of Financial Markets 11, 84-111.
Amihud, Y., 2002, "Illiquidity and Stock Returns: Cross-Section and Time-Series Effects," Journal of Financial Markets 5, 31-56.
Attari, M., A. Mello, and M. Ruckes, 2005, "Arbitraging Arbitrageurs," Journal of Finance 60, 2471-2511.
Beber, A. and M. Pagano, 2011, "Short-Selling Bans Around the World: Evidence from the 2007-2009 Crisis," Journal of Finance, forthcoming.
Bechmann, K., 2004, "Short Sales, Price Pressure, and the Stock Price Response to Convertible Bond Calls," Journal of Financial Markets 7, 427-451.
Bessembinder, H., 2003, "Quote-Based Competition and Trade Execution Costs in NYSE-Listed Stocks," Journal of Financial Economics 70, 385-422.
Bessembinder, H. and K. Venkataraman, 2004, "Does an Electronic Stock Exchange Need an Upstairs Market?" Journal of Financial Economics 73, 3-36.
Blau, B., B. Van Ness, and R. Van Ness, 2009, "Short Selling and the Weekend Effect for NYSE Securities," Financial Management 38, 603-630.
Boehmer, E., C. Jones, and X. Zhang, 2008, "Which Shorts are Informed?" Journal of Finance 63, 491-527.
Boehmer, E., C. Jones, and X. Zhang, 2009, "Shackling Short Sellers: The 2008 Shorting Ban," University of Oregon, Columbia University, and Purdue University, Working paper.
Boehmer, E. and J. Wu, 2010, "Short Selling and the Price Discovery Process," University of Oregon and University of Georgia, Working paper.
Boulton, T. and M. Braga-Alves, 2010, "The Skinny on the 2008 Naked Short-Sale Restrictions," Journal of Financial Markets 13,397-421.
Brady, N., J. Cotting, R. Kirby, J. Opel, and H. Stein, 1988, "'Report of the Presidential Task Force on Market Mechanisms," US Government Printing Office, Washington D.C.
Brunnermeier, M. and L.H. Pedersen, 2005, "Predatory Trading," Journal of Finance 60, 1825-1863.
Carlin, B., M. Lobo, and S. Viswanathan, 2007, "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance 62, 2235-2274.
Chakrabarty, B., B. Li, V. Nguyen, and R. Van Ness, 2007, "Trade Classification Algorithms for Electronic Communications Network Trades," Journal of Banking and Finance 31, 3806-3821.
Chakrabarty, B., P. Moulton, and A. Shkilko, 201 l, "Short Sales, Long Sales, and the Lee-Ready Trade Classification Algorithm Revisited," Journal of Financial Markets, forthcoming.
Chen, J., S. Hanson, H. Hong, and J. Stein, 2008, "Do Hedge Funds Profit from Mutual-Fund Distress?" NBER, Working paper.
Chen, H. and V. Singal, 2003, "Role of Speculative Short Sales in Price Formation: The Case of the Weekend Effect," Journal of Finance 58, 685-705.
Chiyachantana, C., E Jain, C. Jiang, and R. Wood, 2004, "International Evidence on Institutional Trading Behavior and Price Impact," Journal of Finance 59, 869-898.
Chordia, T. and A. Subrahmanyam, 2004, "Order Imbalance and Individual Stock Returns: Theory and Evidence," Journal of Financial Economics 72, 485-518.
Christophe, S., M. Ferri, and J. Angel, 2009, Short Selling and the Weekend Effect in NASDAQ Stock Returns," Financial Review 44, 31-57.
Christophe, S., M. Ferri, and J. Hsieh, 2010, "Informed Trading Before Analyst Downgrades: Evidence from Short Sellers," Journal of Financial Economics 95, 85-106.
Coval, J. and E. Stafford, 2007, "Asset Fire Sales (and Purchases) in Equity Markets," Journal of Financial Economics 86, 479-512.
Cramer, J., 2002, Confessions of a Street Addict, New York, NY, Simon and Schuster.
Dechow, E, A. Hutton, L. Meulbroek, and R. Sloan, 2001, "Short-Sellers, Fundamental Analysis, and Stock Returns," Journal of Financial Economics 61, 77-106.
Diamond, D. and R. Verrecchia, 1987, "Constraints on Short-Selling and Asset Price Adjustment to Private Information," Journal of Financial Economics 18, 277-311.
Diether, K., K.H. Lee, and I. Werner, 2009a, "It's SHO Time! Short-Sale Price Tests and Market Quality,"Journal of Finance 64, 37-73.
Diether, K., K.H. Lee, and I. Werner, 2009b, "Short-Sale Strategies and Return Predictability," Review of Financial Studies 22, 575-607.
Ellis, K., R. Michaely, and M. O'Hara, 2000, "The Accuracy of Trade Classification Rules: Evidence from NASDAQ," Journal of Financial and Quantitative Analysis 35, 529-552.
Flynn, J., 1934, Security Speculation: Its Economic Effects, New York, NY, Harcourt, Brace.
Grossman, S., 1992, "The Informational Role of Upstairs and Downstairs Markets," Journal of Business 65, 509-529.
Harrison, J. and D. Kreps, 1978, "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," Quarterly Journal of Economics 92, 323-336.
Henry, T. and J. Koski, 2010, "Short Selling Around Seasoned Equity Offerings," Review of Financial Studies 23, 4389-4418.
Huebner, S., 1934, The Stock Market, 2nd Ed., New York, NY, Appleton-Century.
Jones, C. and O. Lamont, 2002, "Short-Sale Constraints and Stock Returns," Journal of Financial Economics 66, 207-239.
Kot, H.W., 2007, "What Determines the Level of Short-Selling Activity?" Financial Management 36, 123-141.
Lee, C. and M. Ready, 1991, "Inferring Trade Direction from Intraday Data," Journal of Finance 46, 733-746.
Lipson, M. and A. Puckett, 2006, "Institutional Trading During Extreme Market Movements," University of Virginia and University of Tennessee, Working paper.
Lowenstein, R., 2000, When Genius Failed: The Rise and Fall of Long-Term Capital Management, New York, NY, Random House.
Madhavan, A. and M. Cheng, 1997, "In Search of Liquidity: Block Trades in the Upstairs and Downstairs Markets," Review of Financial Studies 10, 175-203.
Miller, E., 1977, "Risk, Uncertainty, and Divergence of Opinion," Journal of Finance 32, 1151-1168.
Mitchell, M., T. Pulvino, and E. Stafford, 2004, "Price Pressure Around Mergers," Journal of Finance 59, 31-63.
Scheinkman, J. and W. Xiong, 2003, "Overconfidence and Speculative Bubbles," Journal of Political Economy 111, 1183-1219.
(1) "There's a Better Way to Prevent 'Bear Raids'" by R. Pozen and Y. Bar-Yam, The Wall Street Journal, November 18, 2008; "Anatomy of the Morgan Stanley Panic" by S. Pulliam et al., The Wall Street Journal, November 24, 2008; "Restore the Uptick Rule, Restore Confidence" by C. Schwab, The Wall Street Journal, December 9, 2008, among others.
(2) Emergency Orders Pursuant to Section 12(k)(2) of the Securities and Exchange Act of 1934: Release No. 58166, July 15, 2008, Release No. 34-58592, September 18, 2008, and Release No. 58591, September 21, 2008.
(3) SEC release #34-61595 can be found at http://www.sec.gov/rules/final/2010/34-61595.pdf.
(4) Boehmer et al. (2009), Diether et al. (2009b), and Chakrabarty et al. (2011) suggest that short sellers usually provide liquidity.
(5) Bechmann (2004) and Mitchell, Pulvino, and Stafford (2004) demonstrate that these two types of arbitrage often result in increased price pressures from investors who open short positions.
(6) Chen and Singal (2003) hypothesize that some short sellers pursue speculative strategies. Blau, Van Ness, and Van Ness (2009) and Christophe, Ferri and Angel (2009) find no evidence of such speculative activity by short sellers.
(7) These theoretical models are supplemented by abundant anecdotal evidence of skillful manipulators trading against other market participants. Examples include Flynn (1934), Huebner (1934), Brady et al. (1988), Lowenstein (2000), and Cramer (2002).
(8) "Hedge Fund Realities," The Wall Street Journal, February 26, 2007.
(9) We use a longer sample to estimate abnormal short selling statistics (discussed shortly). The longer sample includes additional six months--January 2005 through June 2005.
(10) Regulation SHO was adopted by the SEC in June, 2004. According to rule 202T of the Regulation, the SEC established a Pilot Program to study the effects of elimination of short sale restrictions. The Pilot Program required that self-regulatory organizations make trade-by-trade short selling data publicly available.
(11) We check for sample robustness by restricting the sample to stock-days with (a) 50 and (b) 70 identifiable intervals j. Qualitatively, the main findings do not change when these checks are performed.
(12) Specifically, we allow m to vary among the following intervals: [2; 3), [3; 4), [4; 5), and [5; [infinity]).
(13) For instance, if the [[ret.sub.max,pre]; [ret.sub.min]] stage consists of 20 five-minute intervals, and the ([ret.sub.min]; [ret.sub.max,post]] stage consists of 50 five-minute intervals, then the prerebound stage is divided into ten 10-minute periods, whereas the postrebound stage is divided into ten 25-minute periods. If the number of five-minute intervals in either stage is not evenly divisible by 10, we retain the quantity of pre- and postrebound periods, but adjust their length to accommodate the extra intervals. For instance, if the ([ret.sub.min]; [ret.sub.max,post]] stage in the example above consisted of 55 five-minute intervals, the odd post-rebound periods (lst, 3rd, 5th, etc.) would last 25 minutes and the even periods would last 30 minutes.
(14) To divide stocks into low and high price-liquidity categories, we first define liquidity as the inverse of the Amihud's (2002) illiquidity measure. Next, we assign two ranks to each sample stock: one based on its average price relative to the other sample stocks and the other rank based on the stock's relative liquidity. Next, we add the two ranks together, sort the stocks by the resulting composite rank, and divide them into terciles based on the composite rank. Stocks in the upper tercile have relatively high prices and liquidity, whereas stocks in the lower tercile have relatively low prices and liquidity. We report the results for the upper and lower terciles in Table II and in the subsequent tables.
(15) We acknowledge that although short sellers are unlikely to provide liquidity while selling during prerebound price declines, they might provide liquidity while covering their fleeting positions, especially if such covering occurs during prerebound price declines. We thank an anonymous reviewer for bringing this issue to our attention.
(16) A buyer-initiated short sale may sound as an oxymoron. Nevertheless, Diether et al. (2009b) and Chakrabarty et al. (2011) suggest that most short sales are, in fact, buyer-initiated in that short orders are submitted as liquidity providing orders. However we anticipate that during the unusual events that we study, short sellers will switch from providing liquidity to demanding it.
(17) As we mentioned earlier, Reg. SHO Pilot stocks were exempt from these restrictions. In addition, certain trades by registered specialists and bona fide market makers, certain trades by arbitrageurs, certain trades by underwriters, as well as certain odd lot and equalization trades were exempt from short selling restrictions in all stocks.
(18 ) More specifically, the NYSE stocks trade on the NYSE, NASDAQ, Arca, INET, and Boston, Chicago, and Philadelphia stock exchanges, whereas NASDAQ stocks trade on NASDAQ, Arca, INET, ADE AMEX, and the Chicago Stock Exchange.
(19) We identify the July 2005 to December 2005 period as before switch and the February 2006 to June 2006 period as after switch. We omit January 2006 to allow for a transition period.
(20) In unreported results, we run Specification  for the February 2006 to June 2006 period, during which/NET was enforcing the bid test. In this specification, the estimated coefficient of the INET_SHRAT variable is -0.002, marginally significant at the 0.10 level. This result corroborates our suggestion that the lack of restrictions on INET in the first half of our sample period allowed for more impactful short sales.
Andriy Shkilko, Bonnie Van Ness, and Robert Van Ness *
* Andriy Shkilko is an Assistant Professor in the School of Business and Economics at Wilfrid Laurier University, Waterloo, Ontario. Canada. Bonnie Van Ness is a Professor in the School of Business Administration at the University of Mississippi, University, MS. Robert Van Ness is a Professor in the School of Business Administration at the University of Mississippi, University, MS.
Table I. Summary Statistics This table reports summary statistics for the sample of stocks that undergo intraday price reversals from July 2005 to June 2006. In Panel A, we report 1) market capitalization (in $ millions), 2) daily trading volume (in share thousands), 3) the standard deviation, [sigma], of five-minute cumulative returns, 4) price-to-earnings ratio, and 5) market-to-book ratio. Statistics available on a daily basis are computed as averages during the 20 days preceding each reversal. Other statistics are computed based on the most recent information preceding the reversal. For comparison, we report similarly computed statistics for the universe of the NYSE and NASDAQ stocks with prices greater than or equal to $5. In addition, we present the number of reversal episodes per stock, percent of Pilot stocks that are subject to reversals, percent of Pilot stock reversals in all reversals, and the number of stocks that are subject to reversals. In Panel B, we provide the summary statistics for short ratios, SHRATI and SHRAT2, computed by scaling five-minute short volume by the number of shares outstanding and the total volume, respectively. The former ratio is multiplied by a factor of 1,000 for display purposes. All averages are first computed on a stock basis and then averaged across stocks. Mean Standard 25% Median 75% Deviation Panel A. Company and Sample Characteristics Market capitalization, $ million Sample 4,378 15,300 389 943 2,645 Universe 2,816 12,778 133 386 1,344 Volume, thousand shares Sample 998 3,435 149 318 772 Universe 670 2,833 26 138 464 [sigma] Sample 0.006 0.012 0.004 0.006 0.008 Universe 0.009 0.015 0.004 0.006 0.010 p/e Sample 17.88 86.19 8.18 17.16 26.05 Universe 17.58 86.67 3.50 15.99 24.85 m/b Sample 2.31 4.04 1.24 1.68 2.52 Universe 2.37 5.68 1.14 1.56 2.38 Number of reversals 2.82 1.72 1 2 4 per stock Pilot stocks with 79.01 -- -- -- -- reversals Pilot stock reversals 20.40 -- -- -- -- in all reversals NYSE stocks among 51.84 -- -- -- -- reversal stocks # stocks with reversals 3,588 -- -- -- -- Panel B. Short Ratios SHRAT 1 Sample 0.046 0.110 0.017 0.029 0.051 Universe 0.039 0.152 0.007 0.019 0.040 SHRAT2 Sample 0.331 0.077 0.287 0.333 0.381 Universe 0.315 0.103 0.259 0.318 0.376 Table II. Reversal Returns This table contains cumulative intraday percent returns for a sample of large price reversals. A day is identified as an event day for stock i if the stock's price declines by two or more standard deviations of the stock's historical intraday returns and subsequently rebounds by 90% to 110% of the initial decline by the end of the day. Each event day is divided into two stages: [[ret.sub.max,pre]; [ret.sub.min]] and ([ret.sub.min]; [ret.sub.max,post]], where [ret.sub.max,pre] is the maximum [ret.sub.j] during the prerebound stage, [ret.sub.max,post] is the maximum [ret.sub.j] during the postrebound stage, and [ret.sub.min]; is the minimum [ret.sub.j]. Each stage is further divided into 10 periods for a total of 20 time periods per event day. Event days are divided into four groups according to the magnitude of the prerebound price decline. In particular, we distinguish between the days during which prices fall by 1) 2 to 3, 2) 3 to 4, 3) 4 to 5, and 4) 5 and more [[sigma].sub.i] s. Panel A contains pre-and postrebound cumulative returns by stage. Panel B reports period-by-period cumulative returns and the number of reversals in each magnitude category. Panel C presents prerebound cumulative returns separately for the NYSE and NASDAQ stocks and the percent of events in the NYSE stocks, whereas Panel D contains prerebound cumulative returns for stocks in low and high price liquidity terciles. We define liquidity as the inverse of the Amihud (2002) illiquidity measure and assign two ranks to each sample stock: 1) one based on its average price relative to the other sample stocks and 2) the other based on the stock's relative liquidity. Next, we add the two ranks together, sort the stocks by the resulting composite rank, and divide them into terciles. In Panel D, we report return statistics for the upper and the lower terciles. [2; 3) [3; 4) [4; 5) [5; [infinity]) Panel A. % Pre- and Postrebound Cumulative Return by Stage Pre -1.42 *** -1.51 *** -1.81 *** -2.02 *** Post -0.07 -0.12 -0.15 -0.16 Panel B. % Pre- and Postrebound Cumulative Return by Period -10 0.10 0.11 0.12 0.09 -9 -0.24 ** -0.25 * -0.30 ** -0.37 ** -8 -0.38 ** -0.40 *** -0.45 *** -0.54 *** -7 -0.50 *** -0.52 *** -0.60 *** -0.72 *** -6 -0.61 *** -0.63 *** -0.74 *** -0.87 *** -5 -0.71 *** -0.75 *** -0.87 *** -1.05 *** -4 -0.82 *** -0.89 *** -1.01 *** -1.18 *** -3 -0.95 *** -1.02 *** -1.20 *** -1.36 *** -2 -1.12 *** -1.20 *** -1.43 *** -1.57 *** -1 -1.42 *** -1.51 *** -1.81 *** -2.02 *** I -1.29 *** -1.35 *** -1.61 *** -1.74 *** 2 -1.09 *** -1.11 *** -1.28 *** -1.28 *** 3 -0.97 *** -0.94 *** -1.05 *** -0.95 *** 4 -0.87 *** -0.82 *** -0.87 *** -0.68 *** 5 -0.77 *** -0.72 *** -0.72 *** -0.42 *** 6 -0.69 *** -0.60 *** -0.54 *** -0.25 * 7 -0.61 *** -0.46 *** -0.36 ** -0.13 8 -0.51 *** -0.31 * -0.13 -0.03 9 -0.36 * -0.12 0.07 0.08 10 -0.07 0.12 0.15 0.16 # of Events 2,242 1,688 1,284 1,067 Panel C. % Prerebound Cumulative Return by Listing Exchange NYSE -1.09 *** -1.30 *** -1.40 *** -1.59 *** NASDAQ -1.74 *** -1.81 *** -2.26 *** -2.45 *** of events, 54.56 55.50 54.87 55.75 NYSE Panel D. % Prerebound Cumulative Return by Price-Liquidity Ranking Tercile Low -1.65 *** -1.75 *** -2.15 *** -2.52 *** High -1.13 *** -1.25 *** -1.53 *** -1.64 *** *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table III. Short Selling During Price Reversals This table contains abnormal short ratios, ASHRATI and ASHRAT2, computed via Equations (3) and (4), respectively. Each event day d is divided into two stages: [[ret.sub.max,pre]; [ret.sub.min]] and ([ret.sub.min]; [ret.sub.max,post]], where [ret.sub.max,pre] is the maximum [ret.sub.j] during the prerebound stage, [ret.sub.max,post]] is the maximum [ret.sub.j] during the postrebound stage, and [ret.sub.min] is the minimum [ret.sub.j] on day d. Each stage is divided into 10 periods. Event days are divided into groups by the prerebound price decline magnitude, namely, [2; 3); [3; 4); [4; 5); and [5; [infinity]). Panel A presents adjusted short ratios computed during the pre- and postrebound stages. Panel B contains period-by-period statistics. Panel C provides prerebound statistics computed separately for the NYSE and NASDAQ stocks, whereas Panel D contains prerebound statistics computed for stocks in low and high price-liquidity terciles. ASHRAT1 [2; 3) [3; 4) [4; 5) [5; [infinity]) Panel A. Pre- and Postrebound Aggregate Statistics Pre 4.35 * 10.90 *** 26.60 *** 51.22 *** Post 0.91 -1.39 3.43 5.48 * Panel B. Pre- and Postrebound Statistics by Period -10 4.29 * 5.45 13.55 ** 34.18 *** -9 6.01 * 6.30 * 16.57 *** 43.28 *** -8 2.42 7.51 * 23.86 *** 57.32 *** -7 5.79 * 12.48 ** 27.40 *** 58.93 *** -6 2.85 14.19 *** 31.77 *** 65.17 *** -5 5.88 * 18.61 *** 42.14 *** 80.53 *** -4 7.89 ** 15.62 *** 38.57 *** 68.22 *** -3 4.91 * 14.44 *** 27.61 *** 41.03 *** -2 0.91 13.10 *** 25.94 *** 33.94 *** -1 2.55 1.34 18.62 *** 12.62 ** 1 2.14 -12.80 *** 2.72 8.73 ** 2 3.47 * -5.52 ** 9.84 ** -9.68 ** 3 -1.34 -6.74 ** 2.04 -19.83 *** 4 -5.42 ** 3.33 -1.79 12.26 * 5 -1.49 -15.08 ** 4.21 * 6.74 * 6 11.78 ** 10.93 ** 1.16 9.31 * 7 -3.09 * 1.83 5.72 ** 1.15 8 1.55 2.17 2.66 13.82 ** 9 4.21 * 4.64 4.08 * 19.28 ** 10 -2.69 3.35 3.61 13.02 * Panel C. Prerebound Statistics by Listing Exchange NYSE 4.22 6.00 13.24 *** 26.63 *** NASDAQ 6.09 14.14 *** 41.63 *** 69.66 *** Panel D. Prerebound Statistics by Price-Liquidity Ranking Tercile Low 11.19 ** 20.88 *** 37.04 *** 88.54 *** High -3.21 -3.68 13.59 *** 16.02 *** ASHRAT2 [2; 3) [3; 4) [4; 5) [5; [infinity]) Panel A. Pre- and Postrebound Aggregate Statistics Pre -3.88 ** -4.94 ** -1.45 -1.68 Post -2.16 -3.18 * -3.00 * -5.81 ** Panel B. Pre- and Postrebound Statistics by Period -10 0.96 1.66 0.21 -1.82 -9 -2.63 -4.73 * -0.71 -5.43 ** -8 -4.59 * -5.12 ** -5.58 ** -6.04 -7 -4.76 * -7.80 *** -2.57 -5.81 -6 -3.00 -4.00 * -1.43 4.88 ** -5 -5.94 * -2.64 4.07 * 5.52 *** -4 -5.76 * -4.18 1.10 1.48 -3 -6.00 ** -6.32 ** -1.83 -1.36 -2 -4.07 * -7.24 ** -0.41 -2.03 -1 -3.02 -9.01 *** -7.33 *** -6.32 *** 1 -5.56 ** -8.98 *** -8.41 *** -8.09 2 -3.40 -8.12 *** -8.04 *** -12.37 *** 3 -4.35 * -5.92 ** -4.30 ** -11.17 *** 4 -4.63 ** -3.98 -2.91 -10.51 *** 5 -3.04 * -3.35 -3.21 -6.22 *** 6 -1.46 -1.78 -2.16 -4.45 ** 7 -0.34 -2.50 -2.46 -3.04 * 8 2.09 -0.63 -1.06 -1.06 9 -2.53 2.18 1.18 -2.53 10 1.61 1.23 1.31 1.38 Panel C. Prerebound Statistics by Listing Exchange NYSE -4.90 ** -6.29 *** -2.52 * -2.72 ** NASDAQ -2.97 ** -3.95 ** -0.39 -1.01 Panel D. Prerebound Statistics by Price-Liquidity Ranking Tercile Low -3.59 * -3.36 * -0.58 -1.08 High -4.09 ** -6.14 *** -2.08 -2.43 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table IV. Order Imbalances This table reports short and long order imbalances, SHIMB and LIMB, respectively, during large intraday price reversals. In Panel A, the reversals are separated into four subgroups by magnitude [namely, [2; 3); [3; 4); [4; 5); and [5; oo)] and into pre- and post-rebound stages. Order imbalances are computed as the difference between the buyer and the seller initiated short (long) volume divided by the total short (long) volume. Order direction is identified via the Chakrabarty et al. (2007) algorithm. All statistics are significantly different from zero at the 0.01 level. In Panel B, we present the results separately for the NYSE and NASDAQ stocks. In both panels, we test for the statistical significance of cross-sectional differences between SHIMB and LIMB for each of the four reversal magnitudes (Panel A) and for each exchange (Panel B). SHIMB LIMB Panel A. By Reversal Magnitude [2; 3) Pre -0.17*** -0.27 Post 0.18*** 0.12 [3; 4) Pre -0.18*** -0.29 Post 0.17* 0.14 [4; 5) Pre -0.20*** -0.32 Post 0.18** 0.13 [5; [infinity]) Pre -0.24*** -0.35 Post 0.19** 0.14 Panel B. By the Listing Exchange NYSE Pre -0.17*** -0.31 Post 0.15** 0.12 NASDAQ Pre -0.22*** -0.28 Post 0.21*** 0.15 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0. 10 level. Table V. The Effect of Restrictions on Prerebound Short Selling This table contains abnormal short ratio statistics, ASHRAT 1 and ASHRAT2, computed during the prere-bound stages of sample reversals. Short sales that are exempt from restrictions (e.g., trades by registered specialists and bona fide market makers, trades by arbitrageurs, trades by underwriters, odd-lot, and equalization trades) are excluded. Panel A contains prerebound statistics separately for Pilot and non-Pilot stocks. Panels B and C further subdivide the sample into the NYSE-listed and NASDAQ stocks, respectively. At the bottom of Panel C, we report the statistical significance of differences in short ratios between the NYSE and NASDAQ (Pilot and non-Pilot) stocks. ASHRA T1 [2; 3) [3; 4) [4; 5) Panel A. NYSE and NASDAQ Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot 8.70 * 17.71 *** 33.51 *** Non-Pilot 6.44 * 4.46 19.56 *** Panel B. NYSE Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot 7.05 * 15.81 ** 34.10 *** Non-Pilot 4.17 1.28 11.49 ** Panel C. NASDAQ Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot 9.88 * 16.71 *** 32.04 *** Non-Pilot 9.05 ** 5.23 26.60 *** Difference: Pilot * -- -- Difference: non-Pilot *** *** ASHRA T1 ASHRA T2 [5; [infinity]) [2; 3) [3; 4) [4; 5) Panel A. NYSE and NASDAQ Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot 60.84 *** -1.77 -1.01 0.19 Non-Pilot 41.25 *** -6.03 * -8.94 ** -3.18 Panel B. NYSE Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot 58.08 *** -1.14 -1.47 -0.59 Non-Pilot 31.28 *** -8.15 * -10.60** -4.11 Panel C. NASDAQ Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot 61.93 *** -2.07 -0.85 1.01 Non-Pilot 52.79 *** -2.98 -4.99 -0.99 Difference: Pilot -- -- -- -- Difference: non-Pilot *** * ** * ASHRA T2 [5; [infinity]) Panel A. NYSE and NASDAQ Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot -0.14 Non-Pilot -3.26 Panel B. NYSE Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot 0.82 Non-Pilot -3.84 Panel C. NASDAQ Prerebound Aggregate Statistics, Nonexempt Short Sales Pilot -0.44 Non-Pilot -2.55 Difference: Pilot -- Difference: non-Pilot -- *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table VI. Cross-Market Distribution of Short Volume This table contains statistics on the percentage of short and long volumes executed during the prerebound stages of reversals on the more active market centers (i.e., Area, NASDAQ, and the NYSE for the NYSE stocks and Area, INET, and NASDAQ for NASDAQ stocks). The reversals are separated into four subgroups by magnitude [namely, [2; 3); [3; 4); [4; 5); and [5; [infinity])]. Panel A reports the results for the NYSE stocks, Panel B presents the results for NASDAQ stocks from July 2005 to December 2005, and Panel C provides the results for NASDAQ stocks from February 2006 to June 2006. The market share statistics are computed on a stock basis and are then averaged across stocks. Panel A. NYSE Stocks, July 2005 to June 2006 Short Volume Long Volume NYSE Arca NASDAQ NYSE Arca NASDAQ [2; 3) 79.6 5.9 11.7 78.0 3.1 17.8 [3; 4) 80.4 4.4 13.2 81.6 1.6 16.2 [4; 5) 79.3 3.2 15.3 83.4 2.7 13.6 [5; [infinity]) 82.7 4.2 11.8 84.8 1.7 13.2 Panel B. NASDAQ Stocks, July 2005 to December 2005 Short Volume Long Volume INET Arca NASDAQ INET Arca NASDAQ [2; 3) 18.8 17.4 63.8 22.3 13.8 63.8 [3; 4) 29.6 28.0 41.7 18.7 17.1 64.1 [4; 5) 32.4 29.5 37.3 16.5 15.5 67.9 [5; [infinity]) 36.9 28.7 33.2 25.5 15.8 58.5 Panel C. NASDAQ Stocks, February 2006 to June 2006 Short Volume Long Volume INET Arca NASDAQ INET Arca NASDAQ [2; 3) 5.4 32.7 60.7 34.5 19.2 46.1 [3; 4) 7.5 37.7 54.5 26.5 14.8 58.3 [4; 5) 4.1 43.6 52.1 29.3 17.3 53.0 [5; [infinity]) 6.4 49.5 43.4 31.4 15.2 53.1 Table VII. Granger Causality This table contains p-values from testing for Granger causality between the following variables computed on the five-minute basis during the prerebound stages of return reversals: SHIMB;, short volume imbalance; LIMB, long volume imbalance; and RET,, returns. The Granger causality tests from variable Y to X with p lags first estimate the unrestricted model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] and then estimate the restricted model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. Next, the sums of squared residuals from these two models, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], are included in a test statistic [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. If the statistic is greater than the specified critical value (i.e., the corresponding p-value is lower than 0.1), the null hypothesis [H.sub.0]: [[beta].sub.1] = [[beta].sub.2] = 0 is rejected. Each hypothesis is estimated separately for four reversal subgroups by magnitude [namely, [2; 3); [3; 4); [4; 5); and [5; [infinity])]. For each hypothesis, we report p-values for three lags. p-value lag1 lag2 lag3 [H.sub.O]: SHIMB [2; 3) 0.00 0.00 0.00 [not equal to] >LIMB [3; 4) 0.00 0.00 0.00 [4; 5) 0.00 0.00 0.00 [5; [infinity]) 0.00 0.00 0.00 HO: LIMB [not equal [2; 3) 0.02 0.00 0.00 to] > SHIMB [3; 4) 0.00 0.00 0.00 [4; 5) 0.00 0.00 0.00 [5; [infinity]) 0.00 0.00 0.00 HO: SHIMB [not equal [2; 3) 0.00 0.00 0.00 to] > RET [3; 4) 0.00 0.00 0.00 [4; 5) 0.00 0.00 0.00 [5; [infinity]) 0.00 0.00 0.00 HO: RET [not equal [2; 3) 0.34 0.22 0.24 to] > SHIMB [3; 4) 0.27 0.18 0.17 [4; 5) 0.24 0.24 0.21 [5; [infinity]) 0.32 0.17 0.12 HO: LIMB [not equal [2; 3) 0.00 0.02 0.00 to] > RET [3; 4) 0.00 0.00 0.00 [4; 5) 0.00 0.00 0.00 [5; [infinity]) 0.00 0.00 0.00 HO: RET [not equal [2; 3) 0.20 0.16 0.10 to] > LIMB [3; 4) 0.24 0.21 0.12 [4; 5) 0.14 0.08 0.02 [5; [infinity]) 0.07 0.02 0.00 Table VIII. Determinants of Intraday Returns: Largest Reversals [5; [infinity]) This table contains coefficients from a regression model in Equation (7) with 1) prerebound five-minute returns and 2) postrebound returns as dependent variables. The vector of independent variables includes [SHRAT1.sub.i,j], the short sale ratio from Equation (1); [LRAT1.sub.i,j]. the abnormal long volume scaled by the number of shares outstanding; [SHIMB.sub.i,j] and [LIMB.sub.i,j], short and long order imbalances in stock i, respectively; [QSP.sub.i,j], the quoted spread; and [RET.sub.i,j-1], the lagged return. All independent variables aside from lagged returns are standardized at the stock level. The model is estimated as a panel and includes one lag for all volume and order imbalance variables. We report the coefficients for the control variables (with p-values in parentheses) in this header. The reported coefficients are estimated for Specification [1 ]: [QSP.sub.j-1] = - 0.012 (0.09); [QSP.sub.j] = -0.046 (0.00); [RET.sub.j-1] = 0.113 (0.00); and INTERCEPT = -0.186 (0.00). Coefficients estimated for other specifications are qualitatively similar. The NASDAQ sample in Specification  is restricted to July 2005 to December 2005. Results from February 2006 to June 2006 are available upon request. p-values are in parentheses. Prerebound All stocks NYSE NASDAQ     [SHRATl.sub.j-1] -0.003 -0.004 -- -- (0.00) (0.00) [SHRAT1.sub.j] -0.005 -0.005 -0.002 -0.006 (0.00) (0.00) (0.05) (0.00) [LRAT.sub.j-1] -0.005 0.002 0.003 0.001 (0.08) (0.10) (0.04) (0.11) [LRAT.sub.j] -0.019 -0.014 -0.012 -0.015 (0.00) (0.00) (0.00) (0.00) [SHIMB.sub.j-1] -- 0.003 -- -- (0.02) [SHIMB.sub.j] -- 0.048 -- -- (0.00) [LIMB.sub.j-1] -- 0.017 -- -- -- (0.00) [LIMB.sub.j] -- 0.091 -- -- (0.00) -- ARCH_[SHRAT.sub.j-1] -- -- -0.004 -0.011 (0.05) (0.00) INET_[SHRAT.sub.j-1] -- -- -- -0.007 (0.00) NASD_[SHRAT.sub.j-1] -- -- -0.003 -0.003 (0.02) (0.08) NYSE_[SHRAT.sub.j-1] -- -- -0.002 (0.15) Adj. [R.sup.2] (%) 12.14 18.97 16.08 21.85 Prerebound Postrebound Low price High price All liquidity liquidity stocks  [6l  [SHRATl.sub.j-1] -0.008 -0.001 0.000 (0.00) (0.00) (0.72 [SHRAT1.sub.j] -0.010 -0.001 0.000 (0.00) (0.02) (0.14) [LRAT.sub.j-1] -0.003 0.000 0.003 (0.04) (0.19) (0.04) [LRAT.sub.j] -0.017 -0.010 0.004 (0.00) (0.00) (0.00) [SHIMB.sub.j-1] 0.005 0.001 0.006 (0.00) (0.21) (0.01 [SHIMB.sub.j] 0.061 0.035 0.042 (0.00) (0.00) (0.00) [LIMB.sub.j-1] 0.029 0.005 0.009 (0.00) (0.04) (0.00) [LIMB.sub.j] 0.126 0.056 0.050 (0.00) (0.00) (0.00 ARCH_[SHRAT.sub.j-1] - _ INET_[SHRAT.sub.j-1] NASD_[SHRAT.sub.j-1] NYSE_[SHRAT.sub.j-1] Adj. [R.sup.2] (%) 26.39 6.24 6.08 Table IX. Determinants of Intraday Returns: Reversals of All Magnitudes This table contains coefficients from a regression model in Equation (7) with prerebound five-minute returns as dependent variables. We run the model for the four subgroups of price reversals [namely, [2; 3); [3; 4); [4; 5); and [5; [infinity])]. The vector of independent variables includes [SHRAT1.sub.i,j], the short sale ratio from Equation (1); [LRAT1.sub.i,j], the abnormal long volume scaled by the number of shares outstanding; [SHIMB.sub.i,j] and [LIMB.sub.i,j], short and long order imbalances in stock i, respectively; [QSP.sub.i,j], the quoted spread; and [RET.sub.i,j-1], the lagged return. All independent variables aside from the lagged return are standardized at the stock level. The model includes one lag for all volume and order imbalance variables. p-values are in parentheses. [2; 3) [3; 4) [4; 5) [5; [infinity]) [SHRAT.sub.j-1] -0.005 0.001 -0.003 -0.004 (0.56) (0.64) (0.00) (0.00) [SHRATl.sub.j] 0.002 0.001 -0.004 -0.005 (0.01) (0.68) (0.01) (0.00) [LRAT.sub.j-1] 0.000 0.003 0.004 0.002 (0.95) (0.09) (0.08) (0.10) [LRAT.sub.j] -0.002 -0.012 -0.014 -0.014 (0.06) (0.00) (0.00) (0.00) [SHIMB.sub.j-1] 0.001 0.001 0.002 0.003 (0.14) (0.07) (0.00) (0.02) [SHIMB.sub.j] 0.007 0.040 0.039 0.048 (0.08) (0.00) (0.00) (0.00) [LIMB.sub.j-1] 0.001 0.001 0.011 0.017 (0.62) (0.16) (0.00) (0.00) [LIMB.sub.j] 0.021 0.076 0.085 0.091 (0.04) (0.02) (0.00) (0.00) [QSP.sub.j-1] 0.000 0.003 -0.009 -0.011 (0.98) (0.32) (0.13) (0.09) [QSP.sub.j] -0.003 -0.011 -0.029 -0.046 (0.06) (0.02) (0.00) (0.00) [RET.sub.j-1] 0.021 0.093 0.100 0.113 (0.02) (0.00) (0.00) (0.00) INTERCEPT -0.018 -0.013 -0.009 -0.004 (0.00) (0.00) (0.00) (0.10) Adj. [R.sup.2] (%) 9.48 10.65 20.92 18.97 Table X. Abnormal Returns Around Reversal Episodes The table presents abnormal (market-adjusted) return estimates, ARs, on Days -1 and +1, as well as cumulative abnormal return estimates, CARS, computed during the following event windows: [-5; -1], [+1; +5], [-10; -1], and [+1; +10], where Day 0 is the day of a reversal. We compute abnormal returns separately for the reversals of four different magnitudes. p-values are reported in parentheses. [2; 3) [3; 4) [4; 5) [5; [infinity]) -1 0.00 0.00 0.02 -0.05 (0.99) (0.99) (0.81) (0.52) +1 -0.02 -0.07 -0.04 -0.21 (0.77) (0.59) (0.63) (0.01) [-5; -1] 0.04 -0.01 -0.05 -0.03 (0.20) (0.79) (0.39) (0.55) [+1; +51 0.067 0.07 0.01 0.02 (0.06) (0.09) (0.55) (0.63) [-10; -1] -0.07 0.06 0.00 -0.01 (0.01) (0.07) (0.98) (0.78) [+1; +10] 0.04 0.00 0.00 0.03 (0.12) (0.99) (0.98) (0.50)