Is Information Risk Priced for NASDAQ-listed Stocks?

Transcription

1 Is Information Risk Priced for NASDAQ-listed Stocks? Kathleen P. Fuller School of Business Administration University of Mississippi Bonnie F. Van Ness School of Business Administration University of Mississippi and Robert A. Van Ness School of Business Administration University of Mississippi Current version: February 9 th, 2007 Contact author: Robert Van Ness University of Mississippi School of Business 329 Holman Hall University, MS Electronic copy of this paper is available at:

2 Is Information Risk Priced for NASDAQ-listed Stocks? Abstract Easley, Hvidkjaer, and O Hara (2002), building upon the asset pricing model of Fama and French (1992), show that the probability of informed trading (PIN) is a determinant of asset returns for NYSE-listed securities. We extend this work by examining whether the PIN is a predictive factor for NASDAQ stocks, as many studies document significant differences between NYSE and NASDAQ listed securities. In the process we examine whether the use of PIN is appropriate for NASDAQ-listed securities. We find that PIN and certain stock characteristics correlate differently for our sample of NASDAQ stocks than that of Easley, Hvidkjaer, and O Hara s sample of NYSE stocks. We also determine that the risk of informed trading is only weakly priced for NASDAQ stocks. Contrary to Easley, Hvidkjaer, and O Hara (2002) we do not find evidence that excess returns increases as PIN increases. 2 Electronic copy of this paper is available at:

3 Is Information Risk Priced for NASDAQ-listed Stocks Introduction The probability of informed (PIN) measure is used in a number of studies for NYSE-listed securities (for example, Easley, Hvidkjaer, and O Hara, 2002, Chung and Zhoa, 2005, and Henry, 2005). PIN is also used in studies that examine NASDAQ-listed securities (Heidle and Huang, 2002). The primary purpose of this study is to investigate whether PIN is priced for NASDAQ-listed securities, and in doing so, determine if PIN is appropriate for analyse using NASDAQ-listed securities. In a widely cited study in the asset pricing literature, Fama and French (1992) examine the determinants of stock returns and find that beta, firm size, and book-to-market are priced factors. Researchers theorize that private information can influence equilibrium stock prices (Grossman and Stiglitz, 1980; and Wang, 1993). Expanding upon this theory, Easley, Hvidkjaer, and O Hara (2002), while controlling for the Fama and French (2002) factors, find that private information is a significant determinant in explaining stock returns for NYSE stocks. In this paper, we examine whether private information, proxied by the Easley, Kiefer, O Hara, and Paperman (1996) probability of informed trading (PIN) model, is also priced for NASDAQ stocks. Research shows significant differences between NYSE- and NASDAQ-listed securities. Previous research finds that the costs of trading securities are generally higher on dealer markets (NASDAQ) than on auction markets (NYSE). For example, Huang and Stoll (1996) find that execution costs (as measured by the quoted, effective, and realized spread) on NASDAQ are twice those on the NYSE. Lee (1993) and Petersen and Fialkowski (1994) find that execution costs are higher on competing exchanges compared to the NYSE. In a similar vein, Christie and Huang (1994) and Barclay (1997) find that trading costs decrease after stocks move from the NASDAQ to the NYSE. Others with similar findings include Goldstein (1993), Christie and Schultz (1994), Bessembinder (1999, 2003), and Chung, Van Ness, and Van Ness (2001). 3

4 Along a similar, but somewhat contradictory, line, Affleck-Graves, Hegde, and Miller (1994) compare adverse selection components of the bid-ask spread between NYSE- and NASDAQ-listed securities. They find that the adverse selection component of the bid-ask spread is significantly larger on the NYSE than on NASDAQ. This finding implies that the cost of trading with informed traders is higher on the NYSE than on NASDAQ. In contrast, Heidle and Huang (2002) look at PIN for stocks that move from NASDAQ to the NYSE. They find that the probability of informed trading declines after stocks move from NASDAQ to the NYSE. Thus, implying the cost of trading with informed investors is higher on NASDAQ. These conflicting results, lead us to question whether the findings of Easley, Hvidkjaer, and O Hara (2002), that the probability of informed trading is priced for NYSE securities, also holds for NASDAQ securities. We feel that these conflicting results, adverse selection is higher (Affleck-Graves, Hegde, and Miller, 1994) and the probability of informed trading is lower (Heidle and Huang, 2002) on the NYSE than on NASDAQ, makes it worthwhile to examine whether the probability of informed trading is priced for NASDAQ stocks. Using a sample of NASDAQ-listed securities between 1992 and 2002, we find mixed evidence for the use of PIN for NASDAQ-listed securities. While Easley, Hvidkjaer, and O Hara (2002) find that PIN is a significant determinate for NYSE-listed stock returns, we only find weak support for the pricing of PIN for NASDAQ-listed stocks. We further show that the impact of PIN on required return for NASDAQ stocks is likely proxying for variability, volume, or the joint effect of spreads, variability, and volume. Finally, we do not find evidence that excess returns increase as PIN increases. It may be that the PIN estimation procedure does not work as well for NASDAQ securities (due to market structure), or it may be a result of differences in stock characteristics between NYSE and NASDAQ securities. Data and Methodology As our motivation for this study is to determine if PIN is priced for NASDAQ stocks, we should mention a slight difference between our study and that of Easley, Hviddkajaer, and O Hara (2002). 4

5 Easley, Hviddkajaer, and O Hara estimate the PIN annually for NYSE stocks for the years of 1983 to In contrast, we estimate the PIN of the NASDAQ securities on a quarterly basis, beginning in 1993 and ending with the last quarter of We conduct our analysis quarterly, rather than annually, so that we will have as many observations as possible during our study time period. We begin our sample in 1993 as the TAQ (Trade and Quote database from the NYSE) starts in We use the TAQ, CRSP, and Compustat databases for the years 1993 through We use the TAQ data to calculate the probability of informed trading (Easley, Kiefer, O Hara, and Paperman, 1996) on a quarterly basis for the years 1993 through We calculate the firms betas using the standard market model with CRSP data. Firm size and book-to-market are calculated using a combination of CRSP and COMPUSTAT data. We begin our sample with all NASDAQ firms that trade during the 1993 to 2002 period. We precondition the data prior to calculating our variables. To be included in the sample, a firm must have daily return, volume, and price information on CRSP for at least three months prior to the first quarterly PIN calculation. Firms must have a minimum of two years (up to five years) of past monthly return data from CRSP. Quarterly book value information must be available from COMPUSTAT and be positive and the price must be at least $5 each month to be included in the sample. As these data constraints are not always met for each stock, our quarterly samples contain between 1202 and 2500 stocks. The variable central to our study is the probability of informed trading (PIN). Easley, Kiefer, O Hara, and Paperman (1996) develop a trade flow model using order imbalances of buys and sales to generate the probability that a market maker will face an informed trader. The inputs for the model are the total buys and sales per day for the estimation period. We compute buys (B) and sales (S) for all trading days for the years 1993 through 2003 using the Lee and Ready (1991) algorithm. The model parameters θ = (α, µ, ε, δ) are estimated by maximizing the following likelihood function: 1 Initially, we questioned if one quarter was too short for proper estimation of PIN. One quarter is inline with several other PIN studies. For example, although Easley, Hvidkajaer, and O Hara (2002), use one year, Chung and Zhao (2005) use 59 days (and 64 days), Vega (2004) uses 40 days, while Henry (2005) uses monthly estimates. We find that only about 3% of our sample does not converge. Hence, we believe that our quarterly estimates are non-problematic. 5

6 where each day s likelihood is given by: L ( θ M ) = I L( θ B i, S i ) i= 1 B ε ε L( θ B, S ) = (1 α) e e B! B ( µ + ε ) ( µ + ε ) + α(1 δ ) e e B! ε ε S ε + αδe S! S ε S! ε B ε e B! ( µ + ε ) ( µ + ε ) S! S and α is the probability of an information event, δ is the probability that a given signal is low, µ is the arrival rate of informed traders given a signal, and ε is the arrival rate of uninformed traders. The probability of informed trading (PIN) is calculated as: PIN αµ =. αµ + 2ε Fama and French (1992) find that the firm s beta, size, and book-to-market are significant factors in determining the stock s returns. After controlling for the Fama and French factors, Easley, Hvidkjaer, and O Hara (2002) find that private information (as proxied by PIN) is a significant factor in explaining stock returns. We follow the method of Easley, Hvidkjaer, and O Hara and estimate the following crosssectional regression model using NASDAQ stock returns as the dependent variable: R i,t=β 0+β 1[PIN i t 1] +β 2 Beta p +β 3 firm size it 1 +β 4 BM i t 1 +ε where firm size is the log of the firm s lagged size, on a quarterly basis, and PIN is the lag of the firm s quarterly PIN. BM is the log of the firm s lagged quarterly book value of equity divided by its lagged 6

7 quarterly market value of equity. 2 We exclude firms with negative book values and set BM values outside of the and fractiles equal to these factiles, respectively. Next, we sort our firms into 40 portfolios every January based on the estimated betas. We follow the methodology of Easley, Hvidkjaer, and O Hara (2002) to calculate the firm s beta and then the portfolio betas. Firm betas are calculated by regressing the firm s returns on the contemporaneous and lagged values of the CRSP NASDAQ index returns for each year. The estimated beta is the sum of the two coefficients. The firms are then sorted each year into 40 beta portfolios. We do this for each year in our sample. Then for each of the 40 portfolios, the portfolio returns are regressed on the contemporaneous and lagged values of the CRSP NASDAQ index returns. The estimated beta is the sum of the two coefficients. Since post-ranking portfolio betas are estimated from the full sample period, so there is one beta estimate for each of the 40 portfolios. Sample Statistics, PIN Estimates and Correlations Table I contains the summary statistics of our PIN estimates, the variables used to derive the PIN measure, as well as the variables used in the asset pricing tests. We find that PIN averages 24.77%. Easley, Hvidkjaer, and O Hara (2002) find, for NYSE stocks, an annual PIN of approximately 19.1%, while Heidle and Huang (2002) show that stocks that move from NASDAQ to the NYSE observe a decline in PIN from 33.28% to 21.81%. 3 Table II shows our variables sorted independently by PIN and size. Unlike Easley, Hvidkjaer, and O Hara (2002), we do not find that excess return increases from low to high PIN categories in any of the size categories. This finding is a first indication that PIN may not be priced into NASDAQ security returns, or it could be that this finding is a result of different stock characteristics between NYSE and NASDAQ listed securities. 2 Book value of equity is item 60 from the quarterly COMPUSTAT files and market value of equity is calculated as the shares outstanding times the closing price reported in CRSP. 3 Our results are not directly comparable to those of Easley, Hvidkjaer, and O Hara (2002) and Heidle and Huang (2002) as we do not have a matched sample. These numbers are shown only for reference. 7

8 Correlations between our sample variables and PIN are presented in table III. Some of the correlations are in the expected direction, while several are not. As expected and seen by Easley, Hvidkjaer and O Hara (2002), risk and PIN are positively related. We find support for this expectation as beta and standard deviation of daily returns for our sample of NASDAQ stocks are positively related. Unexpectedly, and contrary to the findings of Easley, Hvidkjaer, and O Hara we see that PIN is positively related to size and negatively related to spread. Our expectation is that as firm size increases PIN decreases, as larger firms are more difficult for informed traders to have superior information with which to trade. However, we do not find a negative relation. In addition, we expect that spreads and PIN are positively related, since market makers are expected to increase spreads when trading with informed traders. We find mixed evidence on the use of PIN for NASDAQ stocks evidence supporting, a positive relation with beta and standard deviation of returns, and evidence against, a positive relation with size and a negative relation with spread. While the positive relation with size and the negative relation with spread are contrary to the findings of Easley, Hvidkjaer, and O Hara s (2002), it may be due to the different market structure or due to the differing firms trading on NASDAQ. In general, NASDAQ trades smaller firms, and more technology-based firms than the NYSE. This could possibly explain why size is related differently to NASDAQ firms than Easley, Hvidkjaer, and O Hara s find for NYSE firms. The differences in our findings for the correlation of PIN and spread for our sample of NASDAQ stocks and those for NYSE stocks by Easley, Hvidkjaer, and O Hara may be due to the inherent differences in spreads for NYSE and NASDAQ firms. Huang and Stoll (1996) and Bessembinder (2003) show that spreads are significantly different for NYSE and NASDAQ stocks. Even though our evidence is mixed for the use of PIN for NASDAQ stocks, we believe that there is not enough convincing evidence to conclude that it does not work, so we will proceed to see if PIN is priced for NASDAQ stocks. We would like to point to our mixed findings for future researchers using PIN for studies of NASDAQ-listed securities Asset Pricing Tests 8

9 As in Easley, Hvidkjaer, and O Hara (2002), we use both the standard Fama and MacBeth (1973) methodology and a weighted least-squares regression as suggested by Litzenberger and Ramaswamy (1979) to account for time-varying volatility. Table IV contains the regression results. When controlling for size, book-to-market ratio, and beta, PIN appears to be a significant determinant of our NASDAQ asset returns in the Fama-MacBeth regression, but not for the weighted-least squares. 4 Consistent with Easley, Hvidkjaer, and O Hara, we do not find any statistical significance associated with book-to-market or beta. So, we find weak evidence that PIN affects asset returns for NASDAQ securities. 5 As mentioned by Easley, Hvidkjaer, and O Hara (2002), PIN may appear significant in the above regressions as a proxy for an omitted variable, namely a liquidity proxy such as spread, variability, or volume/turnover. This proxy effect appears reasonable in our case given the relatively high absolute correlations of PIN and spread and PIN and turnover in our sample. Table V shows the results of alternate regression specifications. The first set of regressions replaces PIN in the previous regression with spread and subsequently includes both PIN and spreads. Recall from Table III that the correlation between spread and PIN is Spreads are significant in both the Fama-MacBeth and weighted least-squares regressions when spread replaces PIN as an independent variable. This finding contrasts directly with Easley, Hvidkjaer, and O Hara (2002) who find that, while NYSE traders care about spreads, they are more concerned with the risk of holding the stock, which is directly affected by the level of private information. The positive impact of spreads, although normally expected, is also in contrast to expectations given the negative correlation between spreads and PIN in our NASDAQ sample. When both spreads and PIN are included in the regression, the coefficients of both spreads and PIN are significantly positive. Further, it appears that the effect of PIN on returns is 4 We replicate our results using quarterly estimates of PIN for NYSE stocks over the same time period as our NASDAQ sample. Our results for quarterly estimates of PIN are qualitatively similar to those of Easley, Hvidkjaer, and O Hara (2002), that PIN is priced for NYSE stocks. 5 It is likely that NASDAQ listed securities have different characteristics than NYSE listed securities, as NASDAQ companies are typically younger and smaller. Fama and French (2001) show that rate of new listings on NASDAQ increases substantially after Additionally, Fama and French (2004) show a decline in survival rates for firms due to delisting as a result of poor performance. To see if our results are a function of these types of firms, all tables are reproduced with only the NASDAQ stocks that survive over our time period (these results are available from the authors upon request). An analysis of only the surviving firms produces results that are quantitatively similar to the results for the entire sample of NASDAQ stocks reported in this paper. 9

10 strengthened by inclusion of both variables. This finding leads us to believe that the influence of PIN on returns is not proxying for the effect of spreads. However, the contradiction between the positive influence of both variables and the negative correlations between these variables add to the controversy between information and spreads for NASDAQ listed securities. Next, we look at the impact of variability, as measured by the standard deviation of daily returns. Standard deviation is positively related to returns and further, overwhelms PIN when both are included in the same regression equation. While the data suggests that the previously documented effect of PIN on spreads is perhaps a proxy for the effect of variability, this suggestion is weakened by the low correlation between PIN and standard deviation of daily returns. As in the Easley, Hvidkjaer, and O Hara (2002) analysis, inclusion of standard deviation changes the significance of Beta in the return equation. We replicate our analysis substituting our volume measures for PIN. Our volume measures are turnover, which is daily volume divided by shares outstanding, and the quarterly coefficient of variation of average daily turnover. Our correlation analysis reveals a positive correlation between PIN and turnover (0.2175) and a negative correlation between PIN and the coefficient of variation of turnover ( ). The signs of the substituted variables are as expected, however, only the coefficient of variation of turnover appears significant. When both PIN and the volume measures are included, only the coefficient of variation appears to significantly impact returns. Finally, we include spread, standard deviation of daily returns, turnover, and coefficient of variation of turnover in the analysis. The same three factors that are significant when included separately are significant when included together. Those factors are spreads, standard deviation (positive), and coefficient of variation of turnover (negative). Further, inclusion of these factors reduce the impact of Beta to an insignificant level. When PIN is added to the equation with the all the alternative variables, it shows only significance in the Fama-MacBeth estimation. Thus, we can not conclude that PIN is not proxying for the joint effect of these alternative variables on spread. 10

11 We also adjust for risk using the three-factor model developed by Fama and French (1993) to estimate abnormal returns for monthly portfolios. 6 This model controls for the non-independence of returns over market sensitivity, size, and book-to-market effects. We estimate a Fama-French three-factor model as follows: r it r Ft = α + b RMRF + s SMB + h HML + ε it it i it i it i it where r it r Ft is the return on a value-weighted portfolio of our stocks in month t minus the three-month Treasury bill return in month t, RMRF is the excess return on a value-weighted aggregate market proxy, SMB is the difference in the returns of a value-weighted portfolio of small stocks and large stocks, and HML is the difference in the returns of a value-weighted portfolio of high book-to-market stocks and low book-to-market stocks, and ε it is the error. We first verify that our sample is consistent with prior research for the Fama-French (1993) threefactor model. As reported in Table VI, contrary to prior research, we find that the intercept is positive and significant for our sample of stocks. However, we find the other factors are significant and the adjusted R 2 is 93.02%. We also estimate a modified Fama-French three-factor model as follows: r r = α + b RMRF + s SMB + h HML + d PIN + ε it Ft it it t it t it t it t it where all variables remain as previously defined and PIN is the probability of informed trading in period t. As reported in Table VI we find that PIN is positive and highly significant. Thus, we find for the Fama-French asset pricing model that PIN is a significant determinant of returns. We also estimate the model using the lagged PIN and find it also to be positive and highly significant. Including PIN and lagged PIN also increase the fit of the model as the adjusted R 2 increase. 7 6 We thank Ken French for providing the data. 7 One issue raised in the using the Fama-French three-factor model is whether the PIN factor can be traded. Given that the state of the market is fixed during any one month, investors may not be able to trade on this information. Therefore, we are not analyzing a trading strategy. However, as Cooper, Gutierrez, and Marcum (2005) note, while the Fama-French three factor model works reasonably well in sample, it does not perform as well out-of-sample, and therefore may not be appropriate for use in trading strategies. 11

12 In summary, the positive relationship between PIN and asset returns is not robust to the inclusion of alternate explanatory variables using the Fama-MacBeth methodology but is using a Fama-French three-factor model. Thus, we can not convincingly conclude that the risk of informed trading is an important determinant of required returns for NASDAQ stocks. Conclusions Easley, Hvidkjaer, and O Hara (2002) present evidence that the probability of informed trading is a factor in explaining returns for NYSE stocks. We examine whether this finding also holds for NASDAQ stocks since Affleck-Graves, Hegde, and Miller (1994) find that adverse selection is significantly larger on the NYSE than on NASDAQ, which implies that the cost of trading with informed traders is higher on the NYSE than on NASDAQ, while Heidle and Huang (2002) find that the probability of informed trading declines after stocks move from NASDAQ to the NYSE, which implies that the cost of trading with informed investors is higher on NASDAQ. 8 We feel that these conflicting results merit an examination of whether the probability of informed trading is also priced for NASDAQ stocks. While Easley, Hvidkjaer, and O Hara (2002) find that the probability of informed trading is a robust, significant factor in explaining returns on the NYSE, we find that PIN is only weakly priced for NASDAQ stocks. As shown in our results, we believe that the impact of PIN on required return for NASDAQ stocks is likely proxying for variability, volume, or the joint effect of spreads, variability, and volume. Further, we do not find evidence that excess returns increases as PIN increases. It may be that the PIN estimation procedure does not work as well for NASDAQ securities, as our correlations of NASDAQ stock characteristics and PIN do not consistently conform to expectations. It may be that differences in firm characteristics or market structure leads to different relations between size and spreads for NYSE and NASDAQ stocks. Our results may also imply that the relevance of PIN for NYSE stocks 8 Chung, Li, and McInish (2004) provide additional evidence that PIN is related to trading, as they show that PIN is positively related to the price impact of trades. 12

13 may disappear as the NYSE (with the merger with Archipelago) moves more towards a NASDAQ type market. This would be an interesting area for future research. 13

14 References: Affleck-Graves, J., S. Hegde, and R. Miller, 1994, Trading mechanisms and the components of the bidask spread. Journal of Finance 49, Barclay, M., 1997, Bid-ask spreads and the avoidance of odd-eighth quotes on NASDAQ: an examination of exchange listings. Journal of Financial Economics 45, Bessembinder, H., 1999, Trade execution costs on NASDAQ and the NYSE: a post-reform comparison. Journal of Financial and Quantitative Analysis 34, Bessembinder, H., 2003, Trade execution costs and market quality after decimalization. Journal of Financial and Quantitative Analysis 38, Christie, W., and R. Huang, 1994, Market structures and liquidity: a transactions data study of exchange listings. Journal of Financial Intermediation. 3, Christie, W., and P. Schultz., 1994, Why do NASDAQ market makers avoid odd-eighth quotes? Journal of Finance 49, Chung, K., B. Van Ness, and R. Van Ness., 2001, Can the treatment of limit orders reconcile the differences in trading costs between NYSE and NASDAQ issues? Journal of Financial and Quantitative Analysis 36, Chung, K., M. Li, 2003, Adverse-selection Costs and the Probability of Information-based trading. The Financial Review 38, Chung, K., M. Li, and T. McInish, 2004, Information-based trading, price impacts of trades, and trade autocorrelation. The Journal of Banking and Finance 29, Chung, K., and X. Zhoa, 2005, Decimal Pricing and Information-Based Trading: Tick Size and Informational Efficiency of Asset Price, forthcoming, The Journal of Business Finance and Accounting. Cooper, Michael, Roberto C. Gutierrez, Jr., and William Marcum, 2005, On the Predictability of Stock Returns in Real Time, Journal of Business 78, Easley, Hvidkjaer, and O Hara, 2002, Is information risk a determinant of asset returns? Journal of Finance, 57, Fama, E., and K. French, 1992, The cross section of expected returns, Journal of Finance, 47, Fama, Eugene F., and Kenneth R. French, 1993, Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics 33, Fama, E., and K. French, 2001, Disappearing dividends: Changing firm characteristics or lower propensity to pay, Journal of Financial Economics 60,

15 Fama, E., and K. French, 2005, New lists: Fundamentals and survival rates, forthcoming, Journal of Financial Economics. Goldstein, M., 1993, Specialist vs. dealer market: a comparison of displayed bid-ask spreads on NASDAQ and the NYSE. University of Pennsylvania working paper. Grossman, S. and J. Stiglitz, 1980, On the impossibility of informationally efficient markets, American Economic Review, 70, Heidle, G. and R. Huang, 2002, Information-Based Trading in Dealer and Auction Markets: An Analysis of Exchange Listings, Journal of Financial and Quantitative Analysis, 37, Henry, T., 2005, Constrained short selling and the probability of informed trade. Working paper, University of Washington. Huang, R. and H. Stoll, 1996, Dealer versus auction markets: A paired comparison of execution costs on NASDAQ and the NYSE. Journal of Financial Economics 41, Lee, Charles M. C., 1993, Market integration and price execution for NYSE-listed securities. Journal of Finance 48, Petersen, M. and D. Fialkowski, 1994, Posted versus effective spreads: Good prices or bad quotes? Journal of Financial Economics 35, Vega, C., 2004, Are investors overconfident? Working paper, University of Rochester. Wang, J., 1993, A model of intertemporal asset prices under asymmetric information, Review of Economic Studies, 60,

16 Table I Summary Statistics Panel A of this table contains the cross-sectional mean, median, high, low, and standard deviations for the following quarterly variables used in calculating the Probability of Informed Trading (PIN) for 1993 through 2002: α, the probability of an information event; δ, the probability of a low signal, µ, the rate of arrival of informed traders, and PIN, the probability of informed trading (using the PIN model of Easley, Kiefer, O Hara, and Paperman, 1996). Panel B contains the summary statistics of the variables used in our asset pricing tests. Return is the percentage monthly return in excess of the one-month T-bill rate, Betas are portfolio betas estimated from the full period using 40 portfolios, Size is the logarithm of yearend market value of equity, BM is the logarithm of book value of equity divided by market value of equity, Spread is the average daily percentage spread for firm in quarter t-1, STD is the standard deviation of daily returns, Turnover is the log of the average daily turnover for firm in quarter t-1 and Cvturn is the log of the coefficient of variation in the average daily turnover in quarter t-1. Panel A: Probability of Informed Trading Summary Statistics Variable Mean Median Min Max Std. Dev. α δ µ PIN Panel B: Asset Pricing Variables Summary Statistics Variable Mean Median Min Max Return Beta Size BM Spread STD Turnover Cvturn

17 Table II Portfolio Returns This table contains results for portfolios of stocks sorted by size and PIN (using the PIN model of Easley, Kiefer, O Hara, and Paperman (1996)). Size is the market value of equity at the end of year and PIN is the probability of informed trading. Each year stocks are sorted into three PIN groups and five size groups. In addition to the excess returns, the number of stocks in each portfolio are presented. Size/PIN Low Medium High Size/PIN Low Medium High Excess returns Number of Stocks Small Large Small Large Small Large ,429.9 Size , ,352.5 Small Large PIN

18 Table III Correlations Below are correlations between variables for all NASDAQ stocks (Panel A), and the stocks which were listed on NASDAQ throughout the time period (Panel B). Return is the return of each of the stock portfolios, PIN is the probability of informed trading (using the PIN model of Easley, Kiefer, O Hara, and Paperman (1996)), Betas are portfolio betas estimated from the full period using 40 portfolios, Size is the logarithm of year-end market value of equity, BM is the logarithm of book value of equity divided by market value of equity, Spread is the average daily percentage spread for firm in quarter t-1, STD is the standard deviation of daily returns, Turnover is the log of the average daily turnover for firm in quarter t-1 and Cvturn is the log of the coefficient of variation in the average daily turnover in quarter t-1. Return PIN Beta Size BM Spread STD Turnover PIN Beta Size BM Spread STD Turnover Cvturn

19 Table IV Asset-pricing Tests This table presents the coefficients from the cross-sectional regression asset pricing tests averages though time, using standard Fama and Macbeth methodology. We also run weighted least squares as suggested by Lizenberger and Ramaswamy to account for time-varying volatility. Betas are portfolio betas estimated from the full period using 40 portfolios, PIN is the probability of informed trading (using the PIN model of Easley, Kiefer, O Hara, and Paperman (1996)), Size is the logarithm of year-end market value of equity, and BM is the logarithm of book value of equity divided by market value of equity. T-values are reported in parenthesis below coefficient estimates. Fama-Macbeth Beta PIN Size BM * * (1.851) (2.237) (-7.874) (-0.952) L-R WLS (1.677) * Significant at the 5% level (1.302) * (-8.975) (-0.980) 19

20 Table V Additional Asset Pricing Tests This table presents the coefficients from the cross-sectional regression asset pricing tests averages though time, using standard Fama and Macbeth methodology. We also run weighted least squares as suggested by Lizenberger and Ramaswamy to account for time-varying volatility. Beta is the portfolio beta of the firms, PIN is the probability of informed trading (using the PIN model of Easley, Kiefer, O Hara, and Paperman (1996)), Size is the market value of equity, and BM is the book to market. Spread is the quarterly average percentage spread. STD is the standard deviation of daily returns for firm in quarter t-1, Turnover is the log of the average daily turnover for firm in quarter t-1 and Cvturn is the log of the coefficient of variation in the average daily turnover in quarter t-1. Fama-MacBeth L-R WLS Beta PIN Size BM Spread STD Turnover Cvturn * * * (2.093) (-6.343) (-0.967) (4.273) * * * (1.976) (-6.785) (-1.073) (4.700) Fama-MacBeth L-R WLS * (2.054) (1.843) * (4.007) * (2.661) * (-6.151) * (-6.849) (-0.844) (-1.109) * (4.685) * (5.006) Fama-MacBeth L-R WLS (0.809) (0.548) * (-7.209) * (-8.608) (0.335) (-0.107) * (4.590) * (4.668) Fama-MacBeth L-R WLS (0.765) (0.537) (1.600) (0.865) * (-7.079) * (-8.306) (0.381) (0.196) * (4.528) * (4.598) Fama-MacBeth L-R WLS (1.433) (1.207) * (-9.341) * ( ) (-0.875) (-1.356) (1.204) (0.972) * (-8.244) * (-6.620) Fama-MacBeth L-R WLS (1.429) (1.194) (1.200) (0.594) * (-9.078) * (-9.755) (-0.833) (-1.043) (1.162) (0.963) * (-8.031) * (-6.490) Fama-MacBeth L-R WLS (0.456) (0.099) * (-7.519) * (-7.855) (0.726) (0.613) * (2.963) * (3.475) * (4.067) * (4.000) (0.665) (0.715) * (-8.670) * (-7.741) Fama-MacBeth L-R WLS (0.502) (0.154) * (2.208) (1.429) * indicates significance at the 5% level * (-7.314) * (-7.817) (0.758) (0.734) * (3.323) * (3.769) * (3.762) * (3.805) (0.710) (0.720) * (-8.627) * (-7.699) 20

21 Table VI Fama-French Asset-pricing Tests This table contains the coefficients of ordinary least squares across using the Fama-French three factor model. RMRF is the excess return on a value-weighted aggregate market proxy for month t, SMB is the difference in the returns of a value-weighted portfolio of small stocks and large stocks for month t, and HML is the difference in the returns of a value-weighted portfolio of high book-to-market stocks and low book-to-market stocks for month t, PIN is the probability of informed trading for month t estimated using the PIN model of Easley, Kiefer, O Hara, and Paperman (1996)) model, and Lag PIN is the probability of informed trading for month t-1. Intercept RMRF SMB HML PIN Lag PIN Adj. R ** ** ** ** 93.0% ** ** ** ** ** 94.4% ** ** ** ** ** 95.1% ** indicates significance at the 1% level 21