Sanders Chang, Lenisa Chang, F. Albert Wang University of Dayton and University of Cincinnati

1. A Dynamic Intraday Measure of the Probability of Informed Trading and Firm-Specific Return Variation Sanders Chang, Lenisa Chang, F. Albert Wang University of Dayton and University of Cincinnati

2. Motivation • The role of information in asset prices • Two types of traders: informed vs. uninformed (Kyle 1985, Black 1986, Campbell et al. 1993) • Existing Probability of informed trading (PIN) measures based on a sequential trade model (Easley et al. 1997, 2002) • But, PIN measures static info trading over a very long macro horizon (1 month to 1 year)

3. PIN Measure (Easley et al. 1997, 2002) • The likelihood function for a single trading day • Maximum likelihood estimation over T days

4. PIN Measure • The probability of informed trading • One must aggregate very fine intraday data (5-min intervals) within the trading day across multiple days • T • The variation and info content of intraday trades is diluted, or even lost in such a macro horizon

5. Twofold Aim of the Study • Develop a dynamic intraday version of PIN (i.e., DPIN) for informed trading at high frequencies: 15-minute intervals throughout the trading day • Examine the relationship between private information (measured by DPIN) and firm-specific return variation to validate Roll’s (1988) conjecture

6. Data (1993-2008) • Intraday transaction data come from the Trades and Quotes (TAQ) database • Share code, shares outstanding, etc. are from the Center for Research in Security Prices (CRSP) • NYSE stocks with at least 250 trades per month, excluding foreign firms, ETF, CEF, and REIT • Each trading day divided into 26 (15-min) intervals. • A total of 14,405,663 firm-interval observations

7. Herding vs. Contrarian Trades • The unexpected return of 15-min interval from residual • Calculate # of buy (NB), sell (NS), total trades (NT) for each interval based on Lee and Ready (1991) • Contrarian (herding) trades are to buy (sell) in presence of negative unexpected returns or to sell (buy) in presence of unexpected positive returns

8. Rationales behind DPIN • Uninformed trading is associated with negative serial correlation in stock returns, while informed trading has no correlation (Campbell et al 1993) • Unexpected returns exhibit significant negative serial correlation for herding trades while no serial correlation for contrarian trades (Aramov et al 2006)

9. Baseline DPIN Measure • Contrarian trades are closely akin to informed trades and herding trades are a good representation of uninformed trades (Aramov et al 2006) • The dynamic probability of informed trading (DPIN) during any given 15-minute interval is obtained by calculating the proportion of contrarian trades taking place during that interval

10. Table 1: Summary statistics for DPIN measures and firm characteristics (a) Yearly cross-sectional DPIN across all years (b) DPIN and firm characteristics Distribution of DPIN_BASE The DPIN_BASE measure yields adequate cross-sectional variation across stocks

11. DPIN with Disposition Effect • The disposition effect suggests that uninformed investors will be less willing to sell shares following price declines because of loss aversion • is an indicator variable that takes on the value of unity if the cumulative return over the last ten intervals is negative and zero otherwise

12. Table 1: Summary statistics for DPIN measures and firm characteristics (a) Yearly cross-sectional DPIN across all years (b) DPIN and firm characteristics Distribution of DPIN_DISP DPIN_DISP distribution mimics that of DPIN_BASE, but with slightly less than half the mean and median

13. DPIN with Size Effect • Informed traders are more likely to submit larger orders (Easley and O'Hara 1987) • is a "large trades" indicator variable that equals 1 if the trade size for stock i over interval j is larger than the stock's median interval trade size over the same trading day, and zero otherwise

14. Table 1: Summary statistics for DPIN measures and firm characteristics (a) Yearly cross-sectional DPIN across all years (b) DPIN and firm characteristics Distribution of DPIN_SIZE DPIN_SIZE distribution mimics that of PIN (Easley et al. 2002) with similar mean, median, left skew, and long right tail

15. DIPN_SIZE vs. PIN (Easley et al. 1997, 2002) • Informed traders are more likely to submit large orders given information event (Easley et al. 1987) • By construction, DIPN_SIZE implicitly assumes information event occurs only with large orders • DIPN_SIZE is closest to the PIN of Easley et al. (1997, 2002) partly because Size may serve as a proxy for the occurrence of the information event

16. Table 1: Summary statistics for DPIN measures and firm characteristics (a) Yearly cross-sectional DPIN across all years (b) DPIN and firm characteristics Yearly DPIN: Summary Statistics The means and medians of the refined DPINs are quite close to the PIN measure of Easley et al. (2002): 0.191 and 0.185

17. Yearly Cross-Sectional Average DPIN over Time Yearly C-S average DPINs mimic that of PIN (Easley et al. 2002) with little year-to-year variation or with much stability over time

18. Table 1: Summary statistics for DPIN measures and firm characteristics (a) Yearly cross-sectional DPIN across all years (b) DPIN and firm characteristics Intraday DPIN and Firm Characteristics Stocks with higher DPIN are more opaque as they are associated with much smaller firm size, lower volume, and higher illiquidity

19. Intraday DPIN: Summary Statistics The STDs are much higher and the medians for the two refined DPINs are zero, hence no information events for many intervals

20. The U-shaped Intraday DPIN for large size The U-shaped intraday pattern is consistent with the clustering of uninformed trading and the corresponding strategic informed trading (Kyle 1985, Admati and Pfleiderer 1988)

21. Table 1: Summary statistics for DPIN measures and firm characteristics (a) Yearly cross-sectional DPIN across all years (b) DPIN and firm characteristics The Inverse U-shaped DPIN for Small Size Stealth trading: informed traders break up large orders into a series of small trades to hide their information (Barclay and Warner 1993, Chakravarty 2001, Alexander and Peterson 2007)

22. Is DPIN a Good Proxy for Informed Trading? • The yearly DPIN is consistent with the prior literature of informed trading as it closely mimics the PIN measure of Easley et al. (2002) • The intraday DPIN is closely associated with firm characteristics in terms of the degree of opaqueness • The intraday DPIN captures strategic informed trading: a U-shaped pattern for large trades (Wood et al. 1985, Jain and Joh 1988) and an inverse U-shaped pattern for small trades (Blau et al. 2009)

23. Firm-Specific Return Variation (FSRV) • A daily market model regression (e.g., Roll 1988, Durnev et al. 2004, 2005, and Chen et al. 2007) • The R-squared statistic from the regression: • FSRV measures the unexplained daily variation in a firm’s return after market returns

24. Empirical Tests • Fama-MacBeth (1973) Regression with a total of N = 4,191 stocks and T = 3,994 days in regressions • Regression on first-differenced data to remove firm fixed effects and lower persistence in the data

25. Table 1: Summary statistics for DPIN measures and firm characteristics (a) Yearly cross-sectional DPIN across all years (b) DPIN and firm characteristics Can DPIN Explain FSRV? • DPIN and its lag are jointly significant at the 1% level • Informed trading causes firm-specific return variation – Roll √

26. Table 1: Summary statistics for DPIN measures and firm characteristics (a) Yearly cross-sectional DPIN across all years (b) DPIN and firm characteristics Can DPIN Explain FSRV (Cont’d)? • ∆DPIN and its lag are jointly significant at the 1% level • Informed trading causes firm-specific return variation – Roll √

27. Robustness Check • Equally weighted and valued weighted market model to measure FSRV • Fama-MacBeth regressions on time-demeaned data (Skoulakis 2008) to eliminate firm fixed effects • Reverse causality by regressing DPIN on FSRV • All robustness checks render support to our main finding: Informed trading causes firm-specific return variation, and not vice versa

28. Conclusion • Construct a dynamic PINmeasurethat is easy to implement, compared to the existing static PIN measure (Easley et al. 1997, 2002) • The intraday DPIN captures strategic informed trading: a U-shaped pattern for large trades and an inverse U-shaped pattern for small trades • Use DPIN to examine the empirical link between private info and firm-specific return variation (FSRV) • Confirm Roll’s (1988) conjecture that FSRV is driven by private info, and not vice versa