Short interest and frictions in the flow of information.This paper examines the correlation between short interest and price delay that parsimoniously measures the delay with which stock prices incorporate information. I find that price delay relates inversely to short interest indicating that short sellers reduce friction in the flow of information into stock prices. While price delay is shown to predict positive returns, this is mostly true in stocks with the least amount of short interest. Multivariate tests determine that the positive relationship between delay and future returns is decreasing in short interest. Results suggest that short sellers reduce delay and arbitrage the return premium commanded by delay.Prior research argues that some market-relevant information takes a considerable amount of time to impact stock prices. For instance, previous studies indicate that while some investors react to the news in earnings announcements immediately, the price response to earnings reports is sluggish (Latane and Jones, 1979; Rendleman, Jones, and Latane, 1982; Foster, Olsen, and Shevlin, 1984; Bernard and Thomas, 1989). Several theories exist to explain the delay in which information impacts prices. Some of these include liquidity constraints (Amihud and Mendelson, 1986; Brennan and Subrahmanyam, 1996; Pastor and Stambaugh, 2003), information asymmetry (Jones and Slezak, 1999; Coval and Moskowitz, 2001; Easley, Hvidkjaer, and O'Hara, 2002), and short sale constraints (Miller, 1977; Diamond and Verrecchia, 1987; Jones and Lamont, 2002). Interestingly, the delayed price response to market-wide information has been shown to command a healthy return premium. Hou and Moskowitz (2005) use a parsimonious measure of this type of friction (Delay hereafter) and find that the return premium is as large as 12% per year after accounting for other known factors that influence the predictability of returns. Furthermore, Hou and Moskowitz (2005) find that Delay helps to explain the size and value premium, as well as the effect of idiosyncratic risk and illiquidity on the predictability of returns. Additional results reported in their study suggest that the role Delay plays in predicting returns is unexplained by liquidity constraints and asymmetric information. However, the interaction between Delay and short selling is, to my knowledge, unresolved. Thus, the main objective of this study is to examine the effects of short interest on Delay and its return premium. I analyze NASDAQ-listed stocks from 1996 to 2007 to determine how short interest affects Delay and the return premium it commands. Additionally, my tests explicitly control for the NASDAQ bubble in an attempt to determine how bubbles also influence Delay. My first set of tests examines the correlation between Delay and short interest. Interestingly, I observe that the contemporaneous association between short interest and Delay is negative suggesting that short interest reduces frictions in the information flow (Miller, 1977; Jones and Lamont, 2002; Diether, Lee, and Werner, 2009; Boehmer and Wu, 2010). As a measure of robustness, I also examine the relationship between last quarter's short interest and current Delay. The purpose in doing so is to account for the possibility of reverse casuality (e.g., high Delay causing low short interest). Again, I find a significant negative correlation between lagged short interest and subsequent Delay indicating that high short interest in the previous quarter reduces Delay in the current quarter. Other robustness tests tend to support this conclusion. The negative association between short interest and Delay holds in multivariate tests after controlling for firm size, trading activity, and volatility among other things. In other tests, I find that Delay is higher during the bubble period than during the nonbubble period suggesting that the euphoria of investors during the NASDAQ bubble lead to greater market inefficiencies (Greenwood and Nagel, 2009). The observed inverse relationship between short selling and Delay is robust when I explicitly control for the bubble. My second set of tests focuses on Delay's return premium and the interaction between short interest and Delay. Consistent with the theory that predicts that short selling reduces frictions in the information flow (Miller, 1977; Diamond and Verrecchia, 1987), my double sorted portfolios, first by Delay, then by short interest, demonstrate that Delay's return premium is driven by stocks that are shorted the least. In multivariate tests, I find that short interest reduces Delay's return premium as the interaction between Delay and short interest relates inversely with future returns. This negative relationship also provides an important contribution to the short-selling literature. Research documents that short interest predicts negative future returns (Senchack and Starks, 1993; Figlewski and Webb, 1993; Dechow et al., 2001; Desai et al., 2002). (1) However, little has been written about what drives this return predictability. (2) When examining the negative correlation between future returns and the interaction between short interest and Delay, my results indicate that the return predictability of short sellers is increasing in Delay. Stated differently, short sellers that target stocks with higher Delay are better able to predict negative returns. These results begin to provide an understanding about what drives the common negative association between short interest and future returns. While these findings indicate that short sellers begin to arbitrage away the return premium commanded by Delay, a natural extension to my tests is to determine what restricts short sellers from completely arbitraging away the return premium. Interestingly, I find that the negative correlation between future returns and the interaction between short interest and Delay is weakened during the NASDAQ bubble period. The theory in Abreu and Brunnermeier (2002) argues that arbitrageurs face synchronization risk when expectations about the timing of price reversals are unsynchronized among peer arbitrageurs. In light of this theory, my results indicate that the inability of short sellers to completely arbitrage away Delay's return premium is driven by constraints, perhaps due to synchronization risk, that existed during the bubble. In addition, I test for and find evidence supporting the hypothesis that other types of short sale constraints may also reduce the ability of short sellers to lessen Delay's return premium. After sorting stocks into portfolios based on institutional ownership, an inverse proxy for short sale constraints (D'Avolio, 2002; Asquith, Pathak, and Ritter, 2005; Nagel, 2005; Xu, 2007), I determine that the negative interaction estimate for short interest and Delay is driven by stocks with low institutional ownership. (3) In other words, short sellers' ability to reduce Delay's return premium is driven by stocks that are most likely to face equity borrowing constraints. D'Avolio (2002) argues that while short sale constraints are not binding per se, approximately 16% of all stocks are nearly impossible to borrow. Many of these stocks facing equity borrowing constraints are likely to have the lowest institutional ownership. It is in these low institutional ownership stocks that short sellers are most successful at arbitraging away Delay's return premium. Absent these equity borrowing constraints, short sellers may be able to completely arbitrage away the return premium. These results support the idea that borrowing constraints may also prohibit short sellers from completely arbitraging Delay's return premium. These results further imply that imposing any additional constraints on short sellers may adversely affect the informational efficiency of stock prices. Combined, the implications of this study suggest first, that short selling reduces Delay making stocks prices more informationally efficient (Miller, 1977; Jones and Lamont, 2002). Additionally, the anomalous finding of a return premium for stocks with high Delay (Hou and Moskowitz, 2005) is more prevalent for those stocks that are shorted the least indicating that short sellers decrease the positive return premium commanded by Delay. Moreover, periods of investor euphoria, such as the NASDAQ bubble, both increase Delay and reduce the ability of short sellers to arbitrage Delay's return premium away. Furthermore, short sellers' ability to arbitrage away Delay's return premium is driven by stocks that are most likely to face equity borrowing constraints. Absent these constraints, short sellers may be able to completely arbitrage away the entire return premium. The remainder of this paper is organized as follows. Section I describes the data used in the analysis. Section II discusses the tests and formulates my expectations. Additionally, Section II presents the results of my empirical analysis. Section III provides my conclusions. I. Data The data used in this analysis come from a variety of sources. I obtain short interest data from January 1996 to December 2007 directly from NASDAQ. From the Center for Research on Security Prices (CRSP), I obtain prices, shares outstanding, market capitalization (size), returns, and volume. I use Compustat data to calculate book-to-market ratios (B/M) and First Call to acquire the number of analysts following each stock during each quarter for my sample (AnCov). From the 13f filing in the Spectrum database, I obtain the number of shares held by institutions at the quarterly level and scale institutional holdings by the number of shares outstanding (InstOwn). From CRSP, I adjust daily returns by subtracting the daily market return from individual stock returns. Using these daily market-adjusted returns, I calculate the standard deviation of daily returns (r_volt) during each quarter for each stock. (4) Using monthly CRSP files, I calculate turnover (turn) by summing the monthly volume to the quarterly level and then scaling this quarterly volume measure by the average number of shares outstanding during that quarter. Therefore, turnover represents the total number of shares traded during a particular quarter as a fraction of shares outstanding. I also sum CRSP monthly returns to the quarterly level so that ret is the cumulative quarterly return. I calculate the relative short interest (RSI) by scaling the number of uncovered shares in short positions at the settlement date measured nearest to the 15th of each month by the number of shares outstanding. Thus, RSI is the fraction of shares outstanding held in open short positions at the settlement date. I closely follow Hou and Moskowitz (2005) and calculate Delay by first estimating the following equation using weekly, Wednesday-to-Wednesday returns: (5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1) The dependent variable is the weekly return for stock i during week t. The independent variables are the contemporaneous market return and the lagged market return during week t - n, where n = { 1, 2, 3, or 4}. In a separate regression, I estimate Equation (1) using only contemporaneous market returns, thus restricting 3i.t-n = 0. According to the measure defined in Hou and Moskowitz (2005), Delay is calculated using the following equation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2) Equation (2) is one minus the ratio of the restricted [R.sup.2] to the unrestricted [R.sup.2]. As the value of the estimate for Equation (2) increases, a greater portion of variation is explained by lagged market returns. Consequently, stocks with higher values obtained from Equation (2) represent stocks that have greater difficulty incorporating market-wide information into their prices. Following Hou and Moskowitz (2005), I estimate Equation (2) for each stock in my sample. Hou and Moskowitz (2005) note the results of this estimation as "first-stage" price delay. Since Delay is noisy, I follow Hou and Moskowitz (2005) and use a portfolio approach to reduce the errors-in-variable problem. I sort firms into portfolios based on market cap and the first stage delay and estimate the Delay for each portfolio assigning each stock within the portfolio this new portfolio-delay measure. Hou and Moskowitz (2005) refer to this portfolio-delay measure as "second-stage" delay. I conduct my entire analysis using both first and second stage delay measures and find that the results are qualitatively similar. The results using second stage delay are reported in this paper. Table I reports statistics that describe my sample. Since the NASDAQ bubble provides a unique opportunity to evaluate a period of inefficiency within a market, I partition the sample into three subtime periods. The prebubble period extends from the first quarter of 1996 to the first quarter of 1998. The bubble period is measured from the second quarter of 1998 to the first quarter of 2000. The postbubble period extends from the second quarter of 2000 to the fourth quarter of 2007. These subperiods are similar to those defined in Ofek and Richardson (2003) and Battalio and Schultz (2006). In Panel A, I find that the average (median) stock during the prebubble period has a price of $17.95 ($14.29) and a market cap of $573 million ($104 million). The average (median) stock also has a book-to-market ratio of 0.6102 (0.4643), a return volatility of 0.0381 (0.0345), turnover of 0.3862 (0.2341), and approximately 2.13 (1) analysts following. Further, the average (median) stock has nearly 27.5% (21.5%) of its outstanding shares held by institutions and 3.4% (2.6%) in uncovered short positions. The average (median) Delay measure obtained from Equation (2) is 0.316 (0.252). Similarly, Panels B and C report statistics that describe the sample during the bubble period and postbubble period, respectively. I see that prices and return volatility are highest during the bubble period. I also observe that market cap, book-to-market ratios, turnover, analyst coverage, institutional ownership, and RSI are increasing across the subperiods, while Delay is decreasing. The median Delay that I report is much higher than that reported in Hou and Moskowitz (2005), who find that the average delay measure in the fifth decile is 0.053 and 0.074 in the sixth decile. However, my sample only includes NASDAQ-listed stocks, while Hou and Moskowitz's (2005) are comprised of mostly NYSE-listed and AMEX stocks. Theissen (2000) reports that call and auction markets are much more informationally efficient than dealer markets supporting the idea that observed Delay should be higher on the NASDAQ than on the NYSE. For a broad cross section of NYSE stocks, I estimate Delay and find that the median delay measure is between 0.04 and 0.06, depending upon the time period, which is consistent with the findings in Hou and Moskowitz (2005). II. Results In this section, I analyze the correlation between short interest and Delay. Miller (1977) and Jones and Lamont (2002) argue that short selling enhances market efficiency. Therefore, I expect a negative relationship between short interest and Delay indicating that short interest reduces friction in the flow of information. I then examine the return premium commanded by Delay. Hou and Moskowitz (2005) demonstrate that stocks with higher Delay outperform stocks with lower Delay after controlling for a variety of factors that influence expected returns. I investigate to determine how the Delay return premium is affected by high levels of short selling. A. Determinants of Price Delay--Univariate Tests I begin by sorting stocks into portfolios based on Delay and analyzing different stock and trading characteristics within each portfolio. I re-sort these portfolios each quarter and report my results for each subperiod. (6) Table II, Panel A provides the results for the prebubble period. First, I find that market cap (size) is decreasing, while book-to-market ratios (B/M) are increasing across increasing Delay portfolios. I also find that return volatility (r_volt) is higher for stocks with higher Delay, while turnover (turn) and the number of analysts covering each stock (AnCov) is lower for stocks with higher Delay. These findings are similar to those in Hou and Moskowitz (2005) with the exception of turnover, which Hou and Moskowitz (2005) determine is positively related to Delay. (7) Next, I turn to the correlation between Delay and institutional ownership (InstOwn), which is an inverse proxy for short sale constraints (Asquith et al., 2005; Nagel, 2005; Xu, 2007). The idea behind this proxy is that stocks that have a higher proportion of shares held by institutions have a greater equity loan supply and, as such, lower borrowing costs. Stocks that are most likely to face binding short sale constraints are generally stocks with low InstOwn. D'Avolio (2002) confirms this conjecture by demonstrating that the equity loan supply is positively related to InstOwn. Interestingly, I find that stocks with the highest levels of Delay generally have the lowest institutional ownership. While this finding is consistent with the notion that stocks that face binding short sale constraints are less efficient (Miller, 1977), other interpretations also exist. For instance, a broad stream of research (Lo and MacKinlay, 1990; Meulbroek, 1992; Cornell and Sirri, 1992; Chakravarty and McConnell, 1997; Koski and Scruggs, 1998; Nofsinger and Sias, 1999; Chakravarty, 2001; Boehmer and Kelley, 2009) argues that institutional investors are more informed than other types of investors. Therefore, observing a negative correlation between InstOwn and Delay is consistent with the idea that institutional investors make stocks more informationally efficient. Finally, I examine RSI across Delay portfolios. Consistent with the idea that short selling reduces friction in the flow of information, I observe a significant negative correlation between Delay and RSI. Panels B and C confirm that the negative relationship between RSI and Delay is increasing in magnitude across subperiods. B. Determinants of Price Delay--Multivariate Tests Next, I examine the association between Delay and short interest after controlling for other factors that influence Delay. I do so by estimating the following equation using pooled data: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3) The dependent variable is Delay for each stock-quarter observation. The independent variables, which have been defined previously, include the contemporaneous size, B/M, r_volt, turn, AnCov, InstOwn, and RSI. I also include lagged returns ([ret.sub.i,t-4, t-1]) as Hou and Moskowitz (2005) find that Delay is stronger for firms that perform poorly during the past year. In addition, I include a dummy variable (BUB) that captures the bubble period (second quarter of 1998 to the first quarter of 2000). Table III reports the results from estimating Equation (3). A Hausman test rejects the presence of random effects although F-tests find differences across stocks and quarters. As such, I report two-way fixed-effects estimates. Pooled ordinary least squares (OLS) estimates, with and without controls for conditional heteroskedasticity using White's (1980) robust standard errors and two-dimensional clustering using Thompson (2006) standard errors, produce qualitatively similar results to those in Table III and in subsequent tables. (8) In Column 1 of Table III, I find that each of the estimates is similar in sign to the univariate relations reported in Table II. Interestingly, after controlling for other factors that influence the level of Delay including size, trading activity, and volatility, I find a negative correlation between RSI and Delay (estimate = -0.1036, p-value = 0.000) that is both statistically and economically significant. In economic terms, for every standard deviation increase in RS1, Delay decreases by approximately 0.01, ceteris paribus. (9) In Column 2, I confirm that the negative contemporaneous relationship between RSI and Delay holds when controlling explicitly for the bubble period. Note that when including the dummy variable BUB in the regression, I purposely do not include quarter fixed effects in order to avoid violating the full rank condition required for consistent fixed-effects estimates. When including BUB, I also find a significant negative estimate for size, which supports the univariate tests in Table II. My interpretation of the negative contemporaneous correlation between RSI and Delay is that short interest reduces Delay. However, it is possible that this negative association may be better explained the other way around. Specifically, high Delay stocks may be difficult to short, manifesting in a negative contemporaneous relationship. To account for this possibility, I estimate the following equation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4) Equation (4) is similar to Equation (3) except that I lag RSI by one quarter ([RSI.SUB.i,t-1]). Again, I control for fixed effects. Table III, Columns 3 and 4 report the results from estimating Equation (4). The variable of interest ([RSI.sub.i.t-1]) produces a significant negative estimate in Column 3 (-0.0638, p-value = 0.000) and in Column 4 (estimate = -0.0330,p-value = 0.000). These results suggest that high short interest during the last quarter leads to lower Delay during this quarter, which supports the idea that short selling improves the flow of information into prices. (10, 11) As a side note, when controlling explicitly for the bubble, I find that in Columns 2 and 4, the dummy variable BUB produces positive and significant estimates (estimates = 0.0447, 0.0458; p-values = 0.000, 0.000). This finding supports the idea that during bubbles, there is greater friction in information flow (Flood and Hodrick, 1986; Smith, Suchanek, and Williams, 1988). C. Short Interest and Price Delay--The Case of Short Sale Constraints Next, I examine the relationship between short interest and Delay while conditioning on the strength of short sale constraints. I do so by first partitioning stocks into quartiles based on InstOwn. As before, I re-sort stocks each quarter. I then estimate the following equation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5) I add an additional dummy variable LOW to Equation (4) that is equal to one when stock i is in the lowest InstOwn quartile. The interaction between LOW and RSI ([LOW.sub.i,t] x [RSI.sub.i,t]) captures the type of stocks that drive the negative relationship between RSI and Delay. A negative interaction estimate indicates that stocks that are most likely to face binding constraints drive the negative correlation between RSI and Delay. As before, I estimate the equation with and without explicit controls for the bubble. Table IV reports the fixed-effects estimates. When including BUB, I again exclude quarter fixed effects to avoid violating the full rank condition required for consistency. Column 1 reports the results after including the dummy variable LOW. I find that the estimate for LOW is positive and significant (estimate = 0.0374, p-value = 0.000) supporting the notion that stocks with low institutional ownership have higher Delay. Column 2 indicates that the positive association between the dummy variable LOW and Delay holds after controlling for the bubble. In Column 3, I find that the interaction between RSI and LOW is negative and statistically significant (estimate = -0.2051, p-value = 0.000). It is important to note the economic significance of this interaction term. The cumulative effect of low institutional ownership on the relation between RSI and Delay is the sum of the coefficients [[beta].sub.8] and [[beta].sub.10]. For stocks without low institutional ownership, the effect of RSI on Delay is only the coefficient [[beta].sub.8]. When comparing the sum of estimates [[beta].sub.8] and [[beta].sub.10] to [[beta].sub.8] only, I find that the negative correlation between RSI and Delay for low institutional ownership stocks is three times greater than the negative relationship for other stocks. This result suggests that stocks that are more likely to face binding short sale constraints drive the negative association between RSI and Delay. These results hold when controlling explicitly for the bubble period in Column 4. (12) An important implication arising from the findings in Table IV is that additional constraints to short sellers may adversely affect market efficiency. (13,14) D. Price Delay's Return Premium--Univariate Tests After accounting for other known factors that influence expected returns, Hou and Moskowitz (2005) find that Delay commands a return premium of, at times, 12% per year. I continue my analysis by examining the effect short selling has on Delay's return premium. I begin by examining future returns across the Delay-sorted portfolios described earlier in the paper. I focus on the four-factor risk-adjusted returns in my analysis. Similar results are found using FamaFrench three-factor risk-adjusted returns and market-adjusted returns using either the CRSP equally weighted or the value-weighted index as the appropriate market benchmark. Further, the results reported in this paper draw the same conclusions when using CRSP raw returns. (15) My second set of tests attempts to determine the effect of short selling on the return premium commanded by Delay. First, I examine risk-adjusted returns from quarter t + 1 to t+4 across both single- and double-sorted portfolios, first by Delay and then by RSI. I once again report the results separately for the different subperiods. Table V, Panel A presents future risk-adjusted returns across Delay portfolios before the RSI sort. I find that the difference between the extreme Delay portfolios is 13.10%, which is slightly larger than the difference reported in Hou and Moskowitz (2005). Using methods similar to those used in this paper, Hou and Moskowitz (2005) report differences in extreme portfolios for NASDAQ-listed stocks that are nearly three times greater than differences in the extreme portfolios for NYSE/AMEX stocks. Hou and Moskowitz (2005) argue that the larger return premium for NASDAQ stocks is likely explained by the smaller NASDAQ stocks relative to NYSE/AMEX stocks. Therefore, I attribute the marginally higher Delay return premium in this study to the fact that I only include NASDAQ-listed stocks in my analysis. Panel A also reports the results after the second sort by RSI. (16) The results indicate that differences between the extreme RSI portfolios at the bottom of Columns 1 to 4 are significantly negative in Columns 2 to 4 (the difference in Column 4 is significant at the 0.10 level--p-value = 0.061) suggesting that short interest relates negatively to future returns, consistent with the previous research (Senchack and Starks, 1993; and Desai et al., 2002). Additionally, I determine that the positive return premium commanded by Delay is only evident in the low RSI portfolios. That is, the difference between Quartiles IV and I in Column 5 is positive and significant in the first three rows of the panel. The difference in Column 5 is insignificant for stocks in RSI Quartile IV. In Panel B, the single sort results (by Delay only) demonstrate that the difference in extreme Delay portfolios is 24.47%. This return premium is twice as large as the return premium reported by Hou and Moskowitz (2005). However, Hou and Moskowitz (2005) did not control explicitly for the bubble period. Perhaps the large Delay return premium during the bubble period also helps to explain the larger return premium for NASDAQ-Iisted stocks in Hou and Moskowitz (2005). After the second sort (by RSI), I find that the return premium is positive in each of the RSI quartiles. However, the difference between extreme Delay quartiles is highest in the lowest RSI quartile. Interestingly, I note that future returns are increasing in each column indicating that the ability of short interest to predict negative returns is not apparent during the bubble period. (17) Panel C reports that the difference between extreme Delay portfolios is 18.33% during the postbubble period. After the second sort, I find that short interest is again able to predict negative returns as the difference between extreme RSI quartiles is negative and significant across each Delay portfolio (the difference is only marginally significant in Column 1--p-value = 0.105). While the difference between extreme Delay portfolios is positive across each RSI quartile, the difference monotonically decreases across RSI quartiles suggesting that Delay's return premium is decreasing in the level of short interest. (18) Moreover, I find that the difference between extreme RSI quartiles is decreasing across Delay quartiles in Panel C suggesting that short interest's ability to predict negative returns is increasing in Delay. (19) E. Price Delay's Return Premium--Multivariate Tests I recognize the need to control for other factors that influence future returns. As such, I estimate the following equations: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7) The dependent variable is the four-factor risk-adjusted return for stock i during quarters t+1 to t+j, where j = {1, 2, or 4}. I include size and B/M to control for the size and value effects (Banz, 1981; Fama and French, 1992, 1996; Gulen, Xing, and Zhang, 2011), past returns ([ret.sub.i,t] and [ret.sub.i,t-4,t-1]) to control for the momentum effect (Jegadeesh and Titman, 1993; Carhart, 1997), r_volt to account for the idiosyncratic risk factor (Malkiel and Xu, 2003), and turn to control for liquidity effects (Brennan and Subrahmanyam, 1996; Pastor and Stambaugh, 2003). The variables of interest are RSI, Delay, and the interaction of these two variables. In Equation (7), I control explicitly for the bubble period. If short sellers are able to predict future negative returns (Diamond and Verrecchia, 1987; Senchack and Starks, 1993; Aitken et al., 1998; Dechow et al., 2001; Desai et al., 2002; Christophe et al., 2004; Boehmer et al., 2008; Blau et al., 2009; Diether et al., 2009), then the estimate for RSI is expected to be negative. A positive estimate for Delay is consistent with the findings in Hou and Moskowitz (2005). If stocks with high short interest have less of a Delay-induced return premium, then the interaction estimate is expected to be negative. Tables VI and VII present the results from estimating Equations (6) and (7). Based on a Hausman test, I report the two-way fixed effects estimates although the results are robust to controls for conditional heteroskedasticity and clustering in the errors across both stocks and quarters. Columns 1 to 3 provide my results when using risk-adjusted returns during quarter t+1, while Columns 4 to 6 (Columns 7 to 9) report the results when using returns from quarters t+l to t+2 (t+4). In Table VI, my first observation is that the estimates for size, B/M, r_volt, and turn are consistent with my predictions based on findings in the prior literature. The results in Table VI do not demonstrate evidence of a momentum effect as the estimates for past returns ([ret.sub.i,t] and [ret.sub,i,t-4,t-1]) are negative in each column. This is more consistent with the idea that contrarian investors can obtain profits when focusing on individual stock returns instead of portfolio returns (Lo and MacKinlay, 1990; Jegadeesh and Titman, 1993). After controlling for these factors, I find that RSI relates negatively to future returns in Columns 1, 4, and 7. Note that this relationship is increasing in strength across longer durations of j. These results are both statistically and economically significant. For instance, in Column 7, a one standard deviation increase in RSI decreases next year's risk-adjusted return by more than 5%. Additionally, I find consistency with Hou and Moskowitz (2005) as the estimate for Delay relates positively to future returns in Columns 2, 5, and 8 with the relationship again strengthening across columns. In economic terms, a one standard deviation increase in Delay in Column 8 results in nearly a 13% increase in next year's risk-adjusted return, ceteris paribus. The magnitude of this estimate is similar to the magnitude of Delay's return premium reported in Hou and Moskowitz (2005). Interestingly, the interaction between RSI and Delay produces negative estimates in Columns 3, 6, and 9. The negative interaction estimate is subject to two interpretations, both of which contribute to the literature. First, the negative interaction estimate suggests that when RSI increases, the return premium commanded by Delay decreases. For example, a one standard deviation increase in RSI reduces Delay's return premium by approximately 5%, holding all else constant. Combined with the earlier results in this study, this assertion indicates that short selling not only reduces Delay, but it can also reduce the return premium found in high Delay stocks. The second interpretation of the negative interaction estimate is that short sellers that target stocks with high Delay are better at predicting negative returns than short sellers that target stocks with low Delay. My results indicate that short sellers, who are generally thought of as informed investors (Diamond and Verrecchia, 1987; Boehmer et al., 2008), apparently take advantage of friction that causes delayed responses in stock prices to market-wide information. Table VII reports the results after controlling explicitly for the bubble period. The results are qualitatively similar to those in Table VI. (20) F. Price Delay's Return Premium--The Case of the Bubble My next set of tests examines the effect of the bubble period on the return predictability of RSI, Delay, and the interaction between the two. Results in the previous subsection suggest that short sellers can arbitrage away some of Delay's return premium. Naturally, the question arises, "Why isn't the return premium completely arbitraged away by short sellers?" I seek to address this query next. The univariate results in Table V indicate that the bubble period dramatically affected the return predictability of short interest. As such, I estimate the following equation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] Equation (8) is similar to Equation (7) except that I interact BUB with RSI, Delay, and the interaction of RSI and Delay to determine how the return predictability of these variables changes during the bubble period. Table VIII reports the results from estimating Equation (8) while controlling for stock fixed effects. (21) Columns 1 to 3 report the results for j = 1, while Columns 4 to 6 (Columns 7 to 9) present the results for j = 2 (j = 4). The results in Table VIII are similar for different values of j. As such, I only discuss Columns 7 to 9 for brevity. In Column 7, I find that the interaction between BUB and RSI is positive and significant (estimate = 1.1923, p-value = 0.000) indicating that short interest becomes less able to predict future negative returns during the bubble. In fact, when comparing the interaction estimate for BUB and RSI to the estimate for RSI alone, I determine that short interest is completely unable to predict negative returns as the sum of the estimates [[beta].sub.7] and [[beta].sub.11] is positive. (22) This result may help resolve conflicting arguments in the literature. Ofek and Richardson (2003) argue that short sellers did not short technology stocks due to binding short sale constraints, while Battalio and Schultz (2006) contend that short sale constraints were not binding during the bubble as pessimistic investors could synthetically short stocks in the options market rather inexpensively. Here, I observe that short selling during the bubble was not profitable as the common negative correlation between RSI and future returns became positive during the bubble. This result indicates that short sellers may have refrained from shorting not because constraints were binding, but instead because of the possibility of lower profits. In Column 8, I find that the interaction between BUB and Delay is negative and significant (estimate = -0.0561, p-value = 0.015) indicating that the return premium commanded by Delay is weaker during the bubble. However, note that the interaction between BUB and Delay is mixed in Columns 2 and 5. Interestingly, I determine that the three-way interaction between BUB, RSI, and Delay produces an estimate that is highly positive and significant (estimate = 4.7203, p-value = 0.000). When compared to the interaction between RSI and Delay in Column 9 of the same table (estimate = -1.1124), the large three-way interaction estimate suggests that the negative relationship between the interaction of RSI and Delay and future returns was highly positive during the bubble period. (23) Here, I find that short sellers' were unable to arbitrage away Delay's return premium during the bubble. If synchronization risk provides a legitimate limit to arbitrage, as Abreu and Brunnermeier (2002) argue, and if synchronization risk was abundantly apparent during the bubble period, then this type of constraint may restrict short sellers from completely arbitraging away Delay's return premium. G. Price Delay's Return Premium--The Case of Short Sale Constraints Earlier, I found that the negative relationship between short interest and Delay is driven by stocks that are most likely constrained. Next, I examine the interaction between short sale constraints and my variables of interest that predict future returns. Similar to the tests in Table IV, I sort stocks into portfolios based on InstOwn, which is commonly used as an inverse proxy for short sale constraints (Asquith et al., 2005; Nagel, 2005; Xu, 2007), and estimate the following equation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] Equation (9) is similar to Equation (7) except I include the dummy variable LOW and multiple interaction variables. [LOW.sub.i,t] x [PREDICT.sub.j,i,t] is first defined as the interaction between the dummy variable LOW and RSI. Here, a negative interaction estimate indicates that the return predictability of short interest is driven by stocks that are most likely constrained, consistent with the prediction in the theoretical model of Diamond and Verrecchia (1987). Next, I define [LOW.sub.i,t] x [PREDICT.sub.j,i,t] as the interaction between LOW and Delay. A positive interaction between LOW and Delay indicates that the return premium commanded by Delay is driven by stocks with the highest likelihood of binding short sale constraints. Finally, I define [LOW.sub.i,t] x [PREDICT.sub.j,i,t] as the three-way interaction between LOW, RSI, and Delay. A negative three-way interaction estimate suggests that the ability of short interest to reduce Delay's return premium is driven by stocks that are most likely constrained. For brevity, in Table IX, I report the results of my estimation when j = 4, although alternative specifications produce qualitatively similar results. Columns 1 to 3 of Table IX report the two-way fixed effects estimates, while Columns 4 to 6 present the stock fixed-effects estimates and controls for the bubble period. Columns 1 and 4 report a negative and significant interaction estimate for [LOW.sub.i,t] x [RSI.sub.i,t] suggesting that the return predictability of short interest is driven by stocks that are most likely constrained, consistent with theory in Diamond and Verrecchia (1987). In particular, Column 1 indicates that the negative interaction estimate is -0.6125, while the estimate for RSI is -0.5488. These results suggest that the total return predictability contained in short interest (the sum of RSI and LOW x RSI) is 2.12 times greater for stocks with low institutional ownership than for other stocks. Column 2 reports that the estimate for [LOW.sub.i,t] x [Delay.sub.i,t] is negative and significant (estimate = -0.1053, p-value = 0.000) although the interaction estimate becomes insignificant when controlling for the bubble period in Column 5 (estimate -0.1083, p-value = 0.433). Finally, the estimate for [LOW.sub.i,t] x [RSI.sub.i,t] x [Delay.sub.i,t] is negative and significant in both Columns 3 and 6. In Column 3, I find that the negative relationship between the interaction of RSI and Delay and future returns is driven primarily by stocks with low institutional ownership. Column 6 shows that when controlling explicitly for the bubble period, the cumulative effect of low institutional ownership on the predictive ability of the interaction between RSI and Delay is (the sum of RSI x Delay and LOW x RSI x Delay) -1.0670. (24) This result suggests that the return predictability of the interaction between RSI and Delay is 1.86 times greater for stocks with low institutional ownership than for other stocks. The negative three-way interaction estimate indicates that the negative association between the interaction of RSI and Delay and future returns is driven by stocks that are most likely to face binding short sale constraints. Here, short interest's ability to reduce the return premium commanded by Delay is driven by constrained stocks. This conclusion provides another potential explanation why short sellers' may not completely arbitrage away Delay's return premium. D'Avolio (2002) argues that most stocks are borrowable and that equity borrowing constraints are not generally binding. However, D'Avolio (2002) reports that 16% of all stocks are nearly impossible to borrow. Undoubtedly, some of the stocks facing equity borrowing constraints have the lowest institutional ownership. It is in these stocks, with the lowest institutional ownership, that short sellers are most successful at arbitraging away Delay's return premium. If all of the stocks in the lowest institutional ownership quartile were borrowable, perhaps short sellers could indeed arbitrage Delay's return premium away completely. III. Conclusion This study examines the interaction between short interest and the Hou and Moskowitz (2005) measure of Delay, which parsimoniously characterizes frictions in the flow of market-wide information into prices or the delay with which stock prices respond to information. Results in this paper reveal a significant negative correlation between short interest and Delay indicating that short selling reduces Delay and assists in making markets more informationally efficient. Additional robustness tests tend to support this conclusion. When conditioning on the tightness of short sale constraints, I find that the negative relationship between short interest and Delay becomes stronger suggesting that the reduction in Delay caused by short interest is strongest in stocks that are most likely to face binding short sale constraints. While Hou and Moskowitz (2005) find that Delay commands a healthy return premium, my findings suggest that short interest reduces that return premium. In fact, my univariate tests reveal a significant return premium exists only for those stocks that are shorted the least. Results from my multivariate tests indicate that a standard deviation increase in short interest reduces the annual Delay return premium by approximately 5%. In other tests, I find that short interest's ability to reduce Delay's return premium is weakened during the NASDAQ bubble, but is stronger when conditioning on stocks that are most likely to face equity borrowing constraints. 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Meulbroek, L., 1992, "An Empirical Analysis of Illegal Insider Trading," Journal of Finance 47, 1661-1699. Miller, E.M., 1977, "Risk, Uncertainty, and Divergence of Opinion," Journal of Finanee 32, 1151-1168. Nagel, S., 2005, "Short Sales, Institutional Investors and the Cross-Section of Stock Returns," Journal of Financial Economics 78, 277-309. Nofsinger, J. and R.W Sias, 1999, "Herding and Feedback Trading by Institutional and Individual Investors," Journal of Finance 54, 2263-2295. Ofek, E. and M. Richardson, 2003, "DotCom Mania: The Rise and Fall of Internet Stock Prices," Journal of Finance 58, 1113-1137. Pastor, L. and R. Stambaugh, 2003, "Liquidity Risk and Expected Stock Returns," Journal of Political Economy 111,642-685. Rendleman, R.J., C.P. Jones, and H.A. Latane, 1982, "Empirical Anomalies Based on Unexpected Earnings and the Importance of Risk Adjustment," Journal of Financial Economics 10, 269-287. Senchack, A.J. and L.T. Starks, 1993, "Short Sale Restrictions and Market Reaction to Short-Interest Announcements," Journal of Financial and Quantitative Analysis 28, 177-194. Smith, V.L., G.L. Suchanek, and A.W. Williams, 1988, "Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Asset Markets," Econometrica 56, 1119-1151. Theissen, E., 2000, "Market Structure, Information Efficiency and Liquidity: An Experimental Comparison of Auction and Dealer Markets," Journal of Financial Markets 3, 333-363. Thompson, S.B., 2006, "Simple Formulas for Standard Errors that Cluster by Both Firm and Time," Harvard University Working Paper. White, H., 1980, "A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroscedasticity," Eeonometriea 48, 817-838. Xu, J., 2007, "Price Convexity and Skewness," Journal of Finance 62, 2521-2552. (1) See also Diamond and Verrecchia (1987), Aitken et al. (1998), Christophe, Ferri, and Angel (2004), Boehmer, Jones, and Zhang (2008), Blau, Van Ness, and Van Ness (2009), and Diether et al. (2009). (2) Boehmer, Jones, and Zhang (2010) find some evidence that a large portion of short sellers' return predictability is driven by short selling prior to firm-specific announcements, such as earnings announcements and analyst recommendations. To the contrary, Engelberg, Reed, and Ringgenberg (20 ! 0) find that the common negative correlation between short-selling activity and future returns is stronger on days with corporate announcements, such as earnings announcements and analyst recommendations. These latter findings suggest that the information contained in short selling is driven by the short sellers' ability to process information that is already public. (3) Institutions are generally lenders of shares to short sellers. Therefore, when institutional ownership is low, the equity loan supply is low and borrowing costs are subsequently high. (4) Market-adjusted returns are adjusted using the value-weighted CRSP index following Canina et al. (1998) and Chen, Hong, and Stein (2001). (5) Hou and Moskowitz (2005) use Wednesday-to-Wednesday returns to control for autocorrelations that are apparent in Friday-to-Friday returns and Monday-to-Monday returns (Chordia and Swaminatham, 2000). (6) In Panel A of Table II, there are 2,472 stock-quarter observations in each Delay portfolio. In Panel B, there are 3,146 stock-quarter observations in each portfolio. In Panel C, there are 14,743 stock-quarter observations in each portfolio. (7) Further, Hou and Moskowitz (2005) observe a slight negative relationship between volume and price Delay. It is possible that using NASDAQ stocks, which generally have less shares outstanding than NYSE stocks, explains this inconsistency. (8) In unreported results, I perform simple regressions of Delay regressed separately on each independent variable. These results confirm my univariate findings in Table II. Note that the estimate for size is not statistically different from zero (p-value = 0.459). (9) For instance, the average stock during the postbubble period has a Delay of 0.21. Holding all else equal, a one standard deviation increase in RS! would decrease the average stock's Delay to 0.20 representing a 4.75% decline in Delay. (10) I recognize that determining causation is a difficult task. In other unreported tests, I conduct modified Granger-like causation tests. Specifically, I regress current Delay on both lagged (last quarter's) Delay and lagged (last quarter's) RSI. The results of this regression reports a positive estimate for lagged Delay (estimate = 0.0772, p-value = 0.000) and a negative estimate for lagged RSI (estimate = -0.0945, p-value = 0.000). I then regress current RSI on both lagged Delay and lagged RSI. I find that lagged RSI produces a positive estimate (estimate = 0.7356, p-value = 0.000) and lagged Delay produces an insignificant estimate (estimate = 0.0005, p-value = 0.726). These results tend to support my interpretation that causation runs from short interest to Delay instead of Delay to short interest. I thank an anonymous referee for this insightful suggestion. (11) Jensen (2005) and Gao (2010) find that corporate governance measures, such as agency costs and managerial horizon, may also affect misvaluation of stock prices. While outside the scope of this study, an examination of the relationship between short interest, corporate governance, and delay might be a fruitful area for future research. (12) Performing the same comparison to determine the economic significance reveals that the negative correlation between RSI and Delay is nearly four times greater for low institutional ownership stocks than for high institutional ownership stocks when explicitly controlling for the bubble period. (13) The results in Table V are robust to specifying LOW as a dummy variable capturing stocks that have institutional ownership below the median. I also specify the dummy variable LOW to capture stocks that are priced below $5. Given D'Avolio (2002), who indicates that short sale constraints are most likely to bind for low priced stocks, this proxy seems reasonable. Indeed, I find that the results are consistent with those reported in Table IV as the interaction between RSI and the dummy variable produces reliably negative estimates. (14) In unreported tests, I include lagged RSI ([RSI.sub.i,t-1]) as the variable of interest instead of contemporaneous RSI. I find that the interaction between LOW and lagged RSI produces significant negative estimates without explicit controls for the bubble (estimate -0.1109, p-value = 0.000) and with controls for the bubble (estimate = -0.1563, p-value = 0.000). (15) In unreported tests, I sort stocks into stock-quarter portfolios based on Delay and report future risk-adjusted returns across subsequent quarters (quarter t+l, quarters t+l to t+2, and quarters t+l to t+4). The results from these tests indicate that stocks with the highest level of Delay generally have future returns at the quarterly level greater than stocks with the lowest level of Delay, supporting the finding in Hou and Moskowitz (2005). (16) There are 2,472 stock-quarter observations in each Delay portfolio in Panel A of Table V. Further, there are 618 observations in each double sorted portfolio in Panel A. Similarly, there are 786 observations in the double sorted portfolios in Panel B and 3,685 observations in the double sorted portfolios in Panel C. (17) This peculiar result may be explained by the theory in Abreu and Brunnermeier (2002) that suggests that arbitrageurs face risk about when prices will move. In Abreu and Brunnermeier's (2002) framework, my findings indicate that short sellers had difficulty in determining when prices were going to decrease during the bubble period. Further, if short sales are generally executed by hedge funds as Boehmer et al. (2008) suggest, then these findings might also be explained by the results in Brunnermeier and Nagel (2004) that demonstrate that hedge funds did not actively attempt to arbitrage the apparent mispricing of the bubble. My findings confirm that short positions during the bubble were extremely unprofitable supporting the idea that short sellers that did attempt to arbitrage the bubble's mispricing were unable to do so, perhaps because of the risk discussed in Abreu and Brunnermeier (2002). (18) I recognize that the hedge returns for low short interest/high Delay stocks is quite large (25% risk-adjusted). However, Boehmer, Huszar, and Jordan (2010) find that the monthly four-factor alphas in the decile with the lowest short interest is 1.6% larger than the alphas in the decile with the highest short interest indicating that annual hedge returns are over 18% for stocks with low short interest relative to stocks with high short interest. When I combined these large hedge returns with the large hedge returns in Hou and Moskowitz (2005), the low short interest/high Delay hedge returns of 25% seem reasonable. (19) This finding is particularly interesting in light of theory in Abreu and Brunnermeier (2002) that argues that synchronization risk presents an important limit to arbitrage. The NASDAQ bubble is an example of the synchronization risk faced by short sellers. Blau and Pinegar (2011) find that after controlling for other factors that influence levels of short interest, short interest was significantly lower during the bubble period than during the nonbubble period. Additionally, in this study, I confirm that the common negative relationship between short interest and future returns is significantly weaker than normal during the bubble period. Combined, these findings indicate that synchronization risk may have sidelined short sellers during the NASDAQ bubble. Perhaps the ability of short interest to reduce the return premium commanded by Delay is subject to limits to arbitrage, such as the synchronization risk discussed in Abreu and Brunnermeier (2002). I explore this suggestion later. (20) I recognize the difficulty in interpreting regression results based on the interaction of two continuous variables. In unreported tests, I create two dummy variables. The first dummy variable captures stock quarter observations that are in the quartile with the highest Delay. The second dummy variable captures stock quarter observations that are in the quartile with the highest relative short interest (RSI). I then estimate Equation (7) substituting the continuous Delay variable for the High Delay dummy variable. The interaction between RSI and the High Delay dummy variable results in a reliably negative estimate (estimate = -0.2307,p-value = 0.000) and indicates that the common negative relation between current RSI and future returns is stronger in stocks with high Delay. I then estimate Equation (7) substituting the continuous RSI variable with the High RSI dummy variable and interact the dummy variable with Delay. The interaction between the continuous variable Delay and the High RS1 dummy variable produces a negative estimate as well (estimate = 4). 1120, p-value = 0.002). This result suggests that the positive correlation between current Delay and future returns is weaker in stocks with high relative short interest. (21) Quarterly Fixed Effects are excluded when including a dummy variable for the bubble period (BUB) to avoid violating the full-rank assumption required for consistent fixed-effects estimates. (22) According to an F-test, the sum of these coefficients (-0.5002 + 1.1923 = 0.6921) is statistically significant at the 0.01 level. (23) According to an F-test, the sum of these coefficients (-1.1124 + 4.7203 = 3.6079) is statistically significant at the 0.01 level. (24) As before, I specify the dummy variable LOW to capture stocks that are priced below $5. Consistent with the results reported in Table IX, I find that the three-way interaction estimate is negative and significant. Benjamin Blau * * Benjamin Blau is an Assistant Professor of Finance at Utah State University, Logan. UT.
Table I. Summary Statistics
The table reports the statistics that describe my sample. Price is
the average monthly ending CRSP price, while Size is the market
capitalization obtained from CRSP BIM is the book-to-market ratio using
the book value of equity from Compustat and the market cap from CRSP
R_volt is the return volatility calculated by taking the standard
deviation of the daily return in each quarter for each stock. Turn is
the turnover of quarter volume from CRSP scaled by the number of
shares outstanding. AnCov is the number of analysts covering each
stock during each quarter. InstOwn is the percentage of shares
outstanding held by institutions. RSI is the relative short interest
computed as the short interest scaled by shares outstanding. Delay is
the measure of price delay as defined in Hou and Moskowitz (2005).
Following prior research (Ofek and Richardson, 2003; Battalio and
Schultz, 2006), 1 partition this sample into three time periods. The
prebubble period (Panel A) is from January 1996 to March 1998, while
the bubble period (Panel B) is from March 1998 to March 2000. Finally,
the postbubble period (Panel C) is from March 2000 to December 2008.
Price Size BIM R -volt Turn AnCov InstOwn RSI Delay
Panel A. Prebubble Period
Mean 17.95 573,817,292 0.6102 0.0381 0.3862
Std. Dev. 16.32 4,781,470,887 1.5479 0.0186 0.4581
Median 14.29 103,692,938 0.4643 0.0345 0.2341
Panel B. Bubble Period
Mean 18.24 1,088,527,748 0.6512 0.0437 0.4281
Median 21.17 11,830,971,349 2.0197 0.0252 0.6240
Std. Dev. 12.98 110,540,708 0.4906 0.0385 0.2357
Panel C. Postbubble Period
Mean 17.14 1,303,496,388 0.6855 0.0365 0.4862
Median 20.64 10,385,195,571 1.8351 0.0233 0.8342
Std. Dev. 12.46 175,669,916 0.5058 0.0305 0.2488
Panel A. Prebubble Period
Mean 2.1288 0.2753 0.0338 0.3155
Std. Dev. 3.7417 0.2239 0.0726 0.2865
Median 1.0000 0.2146 0.0264 0.2523
Panel B. Bubble Period
Mean 2.3051 0.3022 0.0420 0.3162
Median 3.9524 0.3110 0.0869 0.2959
Std. Dev. 1.0000 0.2373 0.0085 0.2250
Panel C. Postbubble Period
Mean 2.9659 0.4036 0.0847 0.2122
Median 4.967 0.4274 0.1382 0.2176
Std. Dev. 1 0.3412 0.0275 0.1417
Table II. Delay-Sorted Portfolios
The table reports the different variables across delay-sorted
portfolios. For exposition, I report Size in $billions of dollars.
Panel A provides the results for the prebubble period, while
Panel B presents the findings for the bubble period. The results for
the postbubble period can be found in Panel C. I report the difference
between Quartile IV and Quartile I along with ap-value (in parentheses)
that tests the null hypothesis that the values in these quartiles are
equal.
Delay Size B/M R -volt
(1) (2) (3) (4)
Panel A. Prebubble Period
QI (Low) 0.0282 1.1540 0.4022 0.0324
QII 0.1125 0.5135 0.6779 0.0401
QIII 0.4244 0.5311 0.5576 0.0354
QIV (High) 0.7155 0.0664 0.8109 0.0449
QIV QI 0.6873 -1.0876 0.4087 0.0125
(0.000) (0.000) (0.000) (0.000)
Panel B. Bubble Period
QI (Low) 0.0274 3.5258 0.4001 0.0371
QII 0.1441 0.5351 0.4526 0.0395
QIII 0.3377 0.0663 0.7952 0.0463
QIV (High) 0.7483 0.0494 0.9628 0.0520
QIVQI 0.7209 -3.4764 0.5627 0.0149
(0.000) (0.000) (0.000) (0.000)
Panel C. Postbubble Period
Q1 (Low) 0.0196 2.9690 0.4166 0.0289
QII 0.0870 1.5294 0.5212 0.0323
QIII 0.2164 0.6759 0.7823 0.0401
QIV (High) 0.5215 0.0774 1.0140 0.0448
QIV QI 0.5019 -2.8916 0.5974 0.0159
(0.000) (0.000) (0.000) (0.000)
Turn AnCov InstOwn RSI
(5) (6) (7) (8)
Panel A. Prebubble Period
QI (Low) 0.4964 3.2691 0.3553 0.0499
QII 0.4050 1.9737 0.2617 0.0324
QIII 0.3716 2.3136 0.2956 0.0341
QIV (High) 0.2658 0.9117 0.1855 0.0182
QIV QI -0.2306 -2.3574 -0.1668 -0.0317
(0.000) (0.000) (0.000) (0.000)
Panel B. Bubble Period
QI (Low) 0.6318 4.7568 0.4086 0.0718
QII 0.4934 2.6778 0.3732 0.0576
QIII 0.2889 0.9724 0.2243 0.0219
QIV (High) 0.2843 0.6599 0.1971 0.0151
QIVQI -0.3475 -4.0969 -0.2115 -0.0567
(0.000) (0.000) (0.000) (0.000)
Panel C. Postbubble Period
Q1 (Low) 0.7135 5.2816 0.5668 0.1364
QII 0.5399 3.6792 0.4797 0.1070
QIII 0.4071 2.1495 0.3397 0.0639
QIV (High) 0.2895 0.8101 0.2326 0.0328
QIV QI -0.4240 -4.4715 -0.3342 -0.1036
(0.000) (0.000) (0.000) (0.000)
Table III. Panel Regressions
The table reports the results from estimating the following equation
using pooled data:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
The dependent variable is Delay for stock i during quarter t. As
independent variables, I include the contemporaneous size
([size.sub.i,t]), book-to-market ratio (B/[M.sub.i,t]), return
volatility ([r_volti.sub.i,t]), share turnover ([turn.sub.i,t]),
analyst coverage ([AnCov.sub.i,t]), and the prior year return
([ret.sub.i,t]). In addition, I also incorporate institutional
ownership ([InstOwn.sub.i,t]) and relative short interest
([RSI.sub.i,t]). A Hausman test reveals observed differences
across stocks and quarters, so I report two-way fixed effects
estimates although results using pooled OLS while controlling for
conditional heteroskedasticity and two-dimensional clustering are
qualitatively similar; p-values are reported in parentheses.
(1) (2) (3) (4)
intercept 0.5953 0.4428 0.5922 0.4417
(0.000) (0.000) (0.000) (0.000)
[size.sub.t] 0.0001 -0.0004 0.0002 -0.0004
(0.207) (0.020) (0.133) (0.031)
[B/M.sub.t] 0.0056 0.0061 0.0055 0.0060
(0.000) (0.000) (0.000) (0.000)
[r_volt.sub.t] 1.0237 1.5955 1.0511 1.6625
(0.000) (0.000) (0.000) (0.000)
[turn.sub.t] -0.0206 -0.0278 -0.0234 -0.0315
(0.000) (0.000) (0.000) (0.000)
[AnCov.sub.t] -0.0022 -0.0032 -0.0023 -0.0035
(0.000) (0.000) (0.000) (0.000)
[ret.sub.t-4,t-1] -0.0290 -0.0312 -0.0292 -0.0309
(0.000) (0.000) (0.000) (0.000)
[instown.sub.t] -0.0213 -0.0304 -0.0249 -0.0371
(0.000) (0.000) (0.000) (0.000)
[RSI.sub.1] -0.1036 -0.1015
(0.000) (0.000)
[RSI.sub.t-1] -0.0638 -0.0330
(0.000) (0.000)
[BUB.sub.1] 0.0447 0.0458
(0.000) (0.000)
Adj. [R.sup.2] 0.7360 0.3586 0.7353 0.3575
Stock FE Yes Yes Yes Yes
Quarter FE Yes No Yes No
Table IV. Panel Regressions
The table reports the results from estimating the following equation
using pooled data:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
The dependent variable and the independent variables are defined
before. I include a dummy variable that captures stocks that are in
the lowest institutional ownership quartile and interact the dummy
variable with RSI. My purpose for doing so is to determine if the
relationship between short interest and Delay is driven by stocks
that are most likely constrained (low InstOwn stocks) or stocks that
are least likely constrained. A Hausman test reveals observed
differences across stocks and quarters. As such, I report two-way
fixed effects estimates although results, using pooled OLS while
controlling for conditional heteroskedasticity and two-dimensional
clustering, are qualitatively similar; p-values are reported in
parentheses.
(1) (2) (3) (4)
intercept 0.5727 0.4157 0.5697 0.4123
(0.000) (0.000) (0.000) (0.000)
[size.sub.t 0.0001 -0.0004 0.0001 -0.0004
(0.272) (0.018) (0.272) (0.018)
B/[M.sub.t] 0.0056 0.0061 0.0056 0.0060
(0.000) (0.000) (0.000) (0.000)
[r_volt.sub.t] 0.9779 1.5154 0.9730 1.5039
(0.000) (0.000) (0.000) (0.000)
[turn.sub.t] -0.0202 -0.0272 -0.0190 -0.0257
(0.000) (0.000) (0.000) (0.000)
[AnCov.sub.t] -0.0020 -0.0030 -0.0021 -0.0031
(0.000) (0.000) (0.000) (0.000)
[ret.sub., 4.t,1] -0.0286 -0.0308 -0.0285 -0.0308
(0.000) (0.000) (0.000) (0.000)
[instown.sub.t] -0.0137 -0.0206 -0.0146 -0.0216
(0.000) (0.000) (0.000) (0.000)
[RSI.sub.t] -0.1007 -0.0957 -0.0960 -0.0898
(0.000) (0.000) (0.000) (0.000)
[LOW.sub.t] 0.0374 0.4318 0.0425 0.0494
(0.000) (0.000) (0.000) (0.000)
[RSI.sub.t] x [LOW.sub.t] -0.2051 -0.2534
(0.000) (0.000)
[BUB.sub.t] 0.0437 0.0439
(0.000) (0.000)
Adj. [R.sup.2] 0.7377 0.3609 0.7380 0.3613
Stock FE Yes Yes Yes Yes
Quarter FE Yes No Yes No
Table V. Future Returns across Double-Sorted (Delay and RSI)
Portfolios
The table reports future four-factor risk-adjusted returns, measured
from quarter t+1 to t+4 across double sorted portfolios, first by
Delay and then by RSI. I calculate the difference between the extreme
RSI quartiles in each column and the difference between the extreme
Delay quartiles in each row; p-values testing the whether the
differences are significant are reported in parentheses. Panel A
contains the results during the prebubble period, while Panel B
presents the results for the bubble period. Panel C provides the
future returns for the postbubble period.
Delay QI Delay QII Delay QIII Delay QIV QIV- QI
Panel A. Prebubble Period
All stocks -0.0470 0.0365 0.0737 0.0840 0.1310
(0.000)
RSI QI -0.0631 0.0860 0.1430 0.1009 0.1640
(0.000)
RSI QII -0.1156 0.0192 0.0765 0.1228 0.2384
(0.000)
RSI QIII -0.0110 0.0452 0.0497 0.0645 0.0755
(0.023)
RSI QIV 0.0020 -0.0045 0.0258 0.0477 0.0457
(0.238)
QIV to QI 0.0651 -0.0950 -0.1172 -0.0533
(0.063) (0.004) (0.000) (0.061)
Panel B. Bubble Period
All stocks -0.0957 -0.0285 -0.0098 0.1490 0.2447
(0.000)
RSI QI -0.2991 -0.1988 -0.2237 -0.0113 0.2878
(0.000)
RSI QII -0.1714 -0.1579 -0.0625 0.0857 0.2571
(0.000)
RSI QIII 0.0235 0.0754 0.0874 0.2009 0.1774
(0.003)
RSI QIV 0.0645 0.1674 0.1594 0.3209 0.2564
(0.000)
QIV to QI 0.3636 0.3662 0.3831 0.3322
(0.000) (0.000) (0.000) (0.000)
Panel C. Postbubble Period
All stocks -0.0918 0.0116 0.0287 0.0915 0.1833
(0.000)
RSI QI -0.0531 0.0687 0.0957 0.1981 0.2512
(0.000)
RSI QII -0.1229 -0.0054 0.0544 0.1309 0.2538
(0.000)
RSI QIII -0.1224 -0.0019 0.0169 0.0792 0.2016
(0.000)
RSI QIV -0.0687 -0.0152 -0.0524 -0.0422 0.0265
(0.221)
QIV to QI -0.0156 -0.0839 -0.1481 -0.2047 0.0265
(0.105) (0.000) (0.000) (0.000) (0.221)
Table VI. Panel Regressions-Future Returns
This table reports the results from estimating the following
equation using pooled data:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
The dependent variable is the cumulative four-factor risk-adjusted
return from quarter t+1 to quarter t+j, where j = {1, 2, or 4}. The
independent variables include factors that have been shown to predict
future returns. I control for market capitalization ([size.sub.i,t]),
book-to-market ratios ([BlM.sub.i,t]), current and past market-
adjusted returns ([ret.sub.i,t] and [ret.sub.i,t-4,t-1] return
volatility ([r_volt.sub.i,t]), share turnover ([turn.sub.i,t]),
relative short interest ([RSl.sub.i,t]), and Hou and Moskowitz's
(2005) measure of delay ([Delay.sub.i,t]). I use a continuous
interaction variable ([RSI.sub.i.t] x [Delay.sub.i,t]) to determine
the effect of current delay on future returns when conditioning on
short interest. A Hausman test reveals observed differences across
stocks and quarters. As such, I provide two-way fixed effects
estimates although the results using pooled OLS, while controlling
for conditional heteroskedasticity and two-dimensional clustering, are
qualitatively similar; p-values are reported in parentheses.
[ret.sub.q+1] [ret.sub.q+1,q+2]
(1) (2) (3) (4) (5)
intercept 0.0844 0.0091 0.0331 0.1574 -0.0080
(0.173) (0.884) (0.594) (0.069) (0.927)
[size.sub.q] -0.0025 -0.0025 -0.0026 -0.0050 -0.0049
(0.000) (0.000) (0.000) (0.000) (0.000)
B/[M.sub.q] 0.0062 0.0055 0.0058 0.0105 0.0090
(0.000) (0.000) (0.000) (0.000) (0.000)
[ret.sub.q] -0.0268 -0.0155 -0.0223 -0.0766 -0.0542
(0.000) (0.003) (0.000) (0.000) (0.000)
[ret.sub.q-4,q-1] -0.0412 -0.0368 -0.0386 -0.0707 -0.0677
(0.000) (0.000) (0.000) (0.000) (0.000)
[r_volt.sub.q] 1.4504 1.4282 1.3492 2.8149 2.6847
(0.000) (0.000) (0.000) (0.000) (0.000)
[turn.sub.q] -0.0237 -0.0312 -0.0221 -0.0542 -0.0650
(0.000) (0.000) (0.000) (0.000) (0.000)
[RSI.sub.q] -0.2008 -0.1636 -0.3347
(0.000) (0.000) (0.000)
[Delay.sub.q] 0.0997 0.0906 0.2354
(0.000) (0.000) (0.000)
[RSI.sub.q] x -0.2208
[Delay.sub.q] (0.001)
Adj. [R.sup.2] 0.1262 0.1248 0.1276 0.1677 0.1680
Stock FE Yes Yes Yes Yes Yes
Quarter FE Yes Yes Yes Yes Yes
[ret.sub.q+1,q+2] [ret.sub.q+1,q+4]
(6) (7) (8) (9)
intercept 0.0308 0.2091 -0.1379 -0.0738
(0.722) (0.069) (0.231) (0.521)
[size.sub.q] -0.0050 -0.0086 -0.0085 -0.0086
(0.000) (0.000) (0.000) (0.000)
B/[M.sub.q] 0.0095 0.0169 0.0138 0.0145
(0.000) (0.000) (0.000) (0.000)
[ret.sub.q] -0.0650 -0.2115 -0.1675 -0.1849
(0.000) (0.000) (0.000) (0.000)
[ret.sub.q-4,q-1] -0.0704 -0.1602 -0.1407 -0.1450
(0.000) (0.000) (0.000) (0.000)
[r_volt.sub.q] 2.5518 4.8400 4.4665 4.2369
(0.000) (0.000) (0.000) (0.000)
[turn.sub.q] -0.0503 -0.0919 -0.1076 -0.0832
(0.000) (0.000) (0.000) (0.000)
[RSI.sub.q] -0.2789 -0.5708 -0.4882
(0.000) (0.000) (0.000)
[Delay.sub.q] 0.2186 0.5141 0.4825
(0.000) (0.000) (0.000)
[RSI.sub.q] x -0.2216 -0.1214
[Delay.sub.q] (0.015) (0.065)
Adj. [R.sup.2] 0.1714 0.2214 0.2262 0.2310
Stock FE Yes Yes Yes Yes
Quarter FE Yes Yes Yes Yes
Table VII. Panel Regressions-Future Returns
This table the results from estimating the following equation
using pooled data:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
The dependent variable is the cumulative four-factor risk-adjusted
return from quarter t+ l to quarter t+j, where j = {1, 2, or 4}. The
independent variables include factors that have been shown to predict
future returns. I control for market capitalization ([size.sub.i,t]),
book-to-market ratios (B-[M-sub.i,t]), current and past market-
adjusted returns ([ret.sub.i,t] and [ret.sub.i,t,t-1]), return
volatility ([r_volt.sub.i,t]), share turnover ([turn.sub.i,t]),
relative short interest ([RSI.sub.i,t]), and Hou and Moskowitz's
(2005) measure of delay ([Delay.sub.i,t]). I use a continuous
interaction variable ([RSI.sub.i,t] x [Delay.sub.i,t]) to determine
the effect of current delay on future returns when conditioning on
short interest. I explicitly control for the bubble period by
including a dummy variable BUB. A Hausman test reveals observed
differences across stocks. As such, I report stock fixed effects
estimates although the results using pooled OLS, while controlling
for conditional heteroskedasticity and two-dimensional clustering, are
qualitatively similar.; p-values are reported in parentheses.
[ret.sub.q+l] [ret.sub.q+l,q+2]
(1) (2) (3) (4) (5)
intercept 0.0802 0.0542 0.0548 0.0964 0.0429
(0.213) (0.399) (0.394) (0.284) (0.633)
[size.sub.q] -0.0027 -0.0027 -0.0027 -0.0052 -0.0051
(0.000) (0.000) (0.000) (0.000) (0.000)
B/[M.sub.q] 0.0066 0.0062 0.0066 0.0116 0.0108
(0.000) (0.000) (0.000) (0.000) (0.000)
[ret.sub.q] -0.0108 -0.0047 -0.0088 -0.0659 -0.0548
(0.010) (0.267) (0.037) (0.000) (0.000)
[ret.sub.q-4,q-1] -0.0583 -0.0555 -0.0571 -0.0998 -0.0946
(0.000) (0.000) (0.000) (0.000) (0.000)
[r_volt.sub.q] 0.5782 0.6664 0.5194 1.6652 1.7244
(0.000) (0.000) (0.000) (0.000) (0.000)
[turn.sub.q] -0.0205 -0.0272 -0.0193 -0.0554 -0.0640
(0.000) (0.000) (0.000) (0.000) (0.000)
[RSI.sub.q] -0.1487 -0.0795 -0.2192
(0.000) (0.000) (0.000)
[Delay.sub.q] 0.0464 0.0580 0.1044
(0.000) (0.000) (0.000)
[RSI.sub.q] x -0.5463
[Delay.sub.q] (0.000)
BUB 0.0043 0.0050 0.0016 -0.0132 -0.0142
(0.221) (0.152) (0.638) (0.007) (0.004)
Adj. [R.sup.2] 0.0465 0.0456 0.0481 0.0860 0.0863
Stock FE Yes Yes Yes Yes Yes
Quarter FE No No No No No
[ret.sub.q+l,q+4]
(6) (7) (8) (9)
intercept 0.0439 0.1926 0.0807 0.0938
(0.526) (0.103) (0.495) (0.426)
[size.sub.q] -0.0052 -0.0090 -0.0089 -0.0089
(0.000) (0.000) (0.000) (0.000)
B/[M.sub.q] 0.0113 0.0191 0.0175 0.0181
(0.000) (0.000) (0.000) (0.000)
[ret.sub.q] -0.0607 -0.2309 -0.2085 -0.2191
(0.000) (0.000) (0.000) (0.000)
[ret.sub.q-4,q-1] -0.0968 -0.1751 -0.1645 -0.1684
(0.000) (0.000) (0.000) (0.000)
[r_volt.sub.q] 1.5130 3.2699 3.3404 2.9136
(0.000) (0.000) (0.000) (0.000)
[turn.sub.q] -0.0527 -0.0921 -0.1079 -0.0867
(0.000) (0.000) (0.000) (0.000)
[RSI.sub.q] -0.1157 -0.4209 -0.3153
(0.000) (0.000) (0.000)
[Delay.sub.q] 0.1206 0.2225 0.2292
(0.000) (0.000) (0.000)
[RSI.sub.q] x -0.7705 -0.6399
[Delay.sub.q] (0.000) (0.000)
BUB -0.0189 -0.0499 -0.0531 -0.0617
(0.000) (0.000) (0.000) (0.000)
Adj. [R.sup.2] 0.0887 0.1673 0.1686 0.1721
Stock FE Yes Yes Yes Yes
Quarter FE No No No No
Table VIII. Panel Regressions-Future Returns
This table reports the results from estimating the following equation
using pooled data:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
The dependent variable is the cumulative four-factor risk-adjusted
return from quarter t+1 to quarter t+j where j = {1, 2, or 4}. The
independent variables include factors that have been shown to predict
future returns. I control for market capitalization ([size.sub.i,t]),
book-to-market ratios (B/[M.sub.i,t]), current and past market-adjusted
returns ([ret.sub.i,t] and [ret.sub.i,t-4,t-1]), return volatility
([r_volt.sub.i,t]), share turnover ([turn.sub.i,t]), relative short
interest ([RSI.sub.i,t]), and Hou and Moskowitz's (2005) measure of
delay ([Delay.sub.i,t]). I use a continuous interaction variable
([RSI.sub.i,t] x [Delay.sub.i,t]) to determine the effect of current
delay on future returns when conditioning on short interest. I also
control explicitly for the bubble period by including a dummy variable
BUB that is equal to one if the quarter is between March 1998 and
March 2000. Furthermore, I interact short interest (BUB x
[RSI.sub.i,t]), Delay (BUB x [Delay.sub.i,t]), and the continuous
interaction variable with the BUB dummy (BUB x [RSI.sub.i,t] x
[Delay.sub.i,t]) to determine if the relation changes during the
bubble period. A Hausman test reveals observed differences across
stocks and quarters. As such, I report two-way fixed effects estimates
although results using pooled OLS, while controlling for conditional
heteroskedasticity and two-dimensional clustering, are qualitatively
similar; p-values are reported in parentheses.
[ret.sub.q+l] [ret.sub.q+1,g+2]
(1) (2) (3) (4) (5)
intercept 0.0829 0.0630 0.0574 0.1017 0.0396
(0.197) (0.327) (0.372) (0.257) (0.660)
[size.sub.q] -0.0026 -0.0027 -0.0027 -0.0051 -0.0051
(0.000) (0.000) (0.000) (0.000) (0.000)
B/[M.sub.q] 0.0067 0.0063 0.0067 0.0117 0.0108
(0.000) (0.000) (0.000) (0.000) (0.000)
[ret.sub.q] -0.0118 -0.0020 -0.0081 -0.0678 -0.0559
(0.005) (0.638) (0.055) (0.000) (0.000)
[ret.sub.q-4.q-1] -0.0591 -0.0545 -0.0568 -0.1015 -0.0950
(0.000) (0.000) (0.000) (0.000) (0.000)
[r_volt.sub.q] 0.5421 0.6688 0.4851 1.5943 1.7235
(0.000) (0.000) (0.000) (0.000) (0.000)
[turn.sub.q] -0.0202 -0.0280 -0.0192 -0.0547 -0.0637
(0.000) (0.000) (0.000) (0.000) (0.000)
[RSI.sub.q] -0.1757 -0.0756 -0.2723
(0.000) (0.000) (0.000)
[Delay.sub.q] 0.0210 0.0577 0.1141
(0.003) (0.000) (0.000)
[RSI.sub.q] x -0.7422
[Delay.sub.q] (0.000)
BUB -0.0133 -0.0262 -0.0109 -0.0478 -0.0022
(0.001) (0.000) (0.003) (0.000) (0.752)
BUB x 0.4062 0.7992
[RSI.sub.q] (0.000) (0.000)
BUB x 0.1120 -0.0430
[Delay.subq] (0.000) (0.015)
BUB x 1.9567
[RSI.sub.q] x (0.000)
[Delay.sub.q]
Adj. [R.sup.2] 0.0482 0.0469 0.0499 0.0892 0.0863
Stock FE Yes Yes Yes Yes Yes
Quarter FE No No No No No
[ret.sub.q+1,g+2] [ret.sub.q+1,g+4]
(6) (7) (8) (9)
intercept 0.0476 0.2005 0.0763 0.1000
(0.593) (0.089) (0.519) (0.396)
[size.sub.q] -0.0052 -0.0088 -0.0089 -0.0089
(0.000) (0.000) (0.000) (0.000)
B/[M.sub.q] 0.0115 0.0192 0.0174 0.0184
(0.000) (0.000) (0.000) (0.000)
[ret.sub.q] -0.0597 -0.2338 -0.2099 -0.2174
(0.000) (0.000) (0.000) (0.000)
[ret.sub.q-4.q-1] -0.0965 -0.1776 -0.1650 -0.1679
(0.000) (0.000) (0.000) (0.000)
[r_volt.sub.q] 1.4638 3.1642 3.3391 2.8309
(0.000) (0.000) (0.000) (0.000)
[turn.sub.q] -0.0526 -0.0912 -0.1075 -0.0865
(0.000) (0.000) (0.000) (0.000)
[RSI.sub.q] -0.1099 -0.5002 0.2353 -0.3057
(0.000) (0.000) (0.000) (0.000)
[Delay.sub.q] 0.1203 -0.0375 0.2285
(0.000) (0.000) (0.000)
[RSI.sub.q] x -1.0522 -1.1124
[Delay.sub.q] (0.000) (0.000)
BUB -0.0371 -0.1016 -0.0375 -0.0922
(0.000) (0.000) (0.000) (0.000)
BUB x 1.1923
[RSI.sub.q] (0.000)
BUB x -0.0561
[Delay.subq] (0.015)
BUB x 2.8139 4.7203
[RSI.sub.q] x (0.000) (0.000)
[Delay.sub.q]
Adj. [R.sup.2] 0.0906 0.1709 0.1687 0.1748
Stock FE Yes Yes Yes Yes
Quarter FE No No No No
Table IX. Panel Regressions-Future Returns
This table reports the results from estimating the following equation
using pooled data:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
The dependent variable and the independent variables are defined as
before with the exception of the variable [PREDICT.sub.i,t]. Similar to
Table IV, I include a dummy variable (LOW) that captures stocks that
are in the lowest institutional ownership quartile and interact the
dummy variable with the variable PREDICT. PREDICT is defined as RSI in
Columns I and 4, as Delay in Columns 2 and 5, and as [RSI.sub.i,t] x
[Delay.sub.i,t] in Columns 3 and 6. The purpose for including the
three-way interaction ([LOW.sub.i,t] x [RSI.sub.i,t] x [Delay.sub.i,t])
is to determine whether the correlation between future returns and
the interaction between RSI and Delay is driven by stocks that are
most likely constrained (low InstOwn stocks) or stocks that are least
likely constrained. A Hausman test reveals observed differences across
stocks and quarters. As such, I report two-way fixed effects estimates
although results using pooled OLS, while controlling for conditional
heteroskedasticity and two-dimensional clustering, are qualitatively
similar; p-values are reported in parentheses.
(1) (2) (3) (4) (5)
intercept 0.1529 -0.1905 -0.1006 0.1249 0.0189
(0.186) (0.099) (0.338) (0.293) (0.873)
[size.sub.q] -0.0086 -0.0085 -0.0086 -0.0090 -0.0089
(0.000) (0.000) (0.000) (0.000) (0.000)
[B/[M.sub.q] 0.0168 0.0136 0.0144 0.0189 0.0174
(0.000) (0.000) (0.000) (0.000) (0.000)
[ret.sub.q] -0.2123 -0.1677 -0.1852 -0.2318 -0.2090
(0.000) (0.000) (0.000) (0.000) (0.000)
[ret.sub.q-4,q-1] -0.1594 -0.1403 -0.1448 -0.1744 -0.1648
(0.000) (0.000) (0.000) (0.000) (0.000)
[r_volt.sub.q] 4.7776 4.4167 4.1936 3.2017 3.2969
(0.000) (0.000) (0.000) (0.000) (0.000)
[turn.sub.q] -0.0885 -0.1068 -0.0817 -0.0886 -0.1073
(0.000) (0.000) (0.000) (0.000) (0.000)
[RSI.sub.q] -0.5488 -0.4929 -0.3970
(0.000) (0.000) (0.000)
[Delay.sub.q] 0.5559 0.4831 0.2269
(0.000) (0.000) (0.000)
[RSI.sub.q] x 0.0098
[Delay.sub.q] (0.945)
LOW 0.0636 0.0864 0.0419 0.0746 0.0706
(0.000) (0.000) (0.001) (0.000) (0.000)
LOW x [RSI.sub.q] -0.6125 -0.6254
(0.000) (0.000)
LOW x [Delay.sub.q] -0.1053 -0.1083
(0.000) (0.433)
LOW x [RSI.sub.q] x -1.0508
[Delay.sub.q] (0.002)
BUB -0.0482 -0.0522
(0.000) (0.000)
Adj. [R.sup.2] 0.2221 0.2267 0.2313 0.1680 0.1680
Stock FE Yes Yes Yes Yes Yes
Quarter FE Yes Yes Yes No No
(6)
intercept 0.0418
(0.724)
[size.sub.q] -0.0089
(0.000)
[B/[M.sub.q] 0.0180
(0.000)
[ret.sub.q] -0.2184
(0.000)
[ret.sub.q-4,q-1] -0.1685
(0.000)
[r_volt.sub.q] 2.8779
(0.000)
[turn.sub.q] -0.0859
(0.000)
[RSI.sub.q] -0.3138
(0.000)
[Delay.sub.q] 0.2279
(0.000)
[RSI.sub.q] x -0.5739
[Delay.sub.q] (0.000)
LOW 0.0556
(0.000)
LOW x [RSI.sub.q]
LOW x [Delay.sub.q]
LOW x [RSI.sub.q] x -0.4931
[Delay.sub.q] (0.046)
BUB -0.0607
(0.000)
Adj. [R.sup.2] 0.1724
Stock FE Yes
Quarter FE No
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