Internet Appendix Table A1: Determinants of VOIB Each month, we regress VOIB on firm size and proxies for N, v δ, and v z. OIB_SHR is the monthly order imbalance defined as (B S)/(B+S), where B (S) is the number of shares traded initiated by buyers (sellers). VOIB_SHR is the standard deviation of daily order imbalance in a month. The order imbalance volatility calculated using number of trades is termed VOIB_NUM. The number of informed agents, N, is measured as the number of informed institutional investors. Following Abarbanell, Bushee and Raedy (2003), we break down institutional investors into informed and uninformed types, where the informed institutions are defined as investment companies and independent investment advisors because such institutions are more likely to be active investors. Other institutions, such as bank trusts, insurance companies, corporate/private pension funds, public pension funds, university and foundation endowments, have longer investment horizons and trade less actively. Following Chordia, Huh and Subrahmanyam (2009), we employ earnings volatility as a proxy for v δ, where earnings volatility is the standard deviation of earnings per share (EPS) from the most recent eight quarters. Finally, we employ the average of daily dollar volume (in million dollars) as a proxy for v z. All independent variables are standardized in the cross section. The time-series averages of coefficient estimates from monthly crosssectional regressions are presented along with the associated Newey-West (1987) t-statistics. The coefficients are multiplied by 1000. VOIB_SHR VOIB_NUM Intercept 126.408*** 121.566*** (71.76) (92.67) N 0.459** 0.526*** (2.46) (3.28) v δ 0.178*** 0.216*** (6.17) (8.05) v z 0.795*** 1.133*** (6.05) (16.55) SIZE -7.123*** -7.203*** (-36.58) (-68.78) 1
Table A2: Summary Statistics before and after January 2001 Panel A (Panel B) presents the time-series averages of the cross-sectional statistics for common stocks listed on NYSE, AMEX and NASDAQ before (after) January 2001. The stock-month observation must have valid information to calculate the return, market capitalization, book-to-market ratio, and order imbalance, and must have the month-end price above one dollar. OIB_SHR is the monthly order imbalance defined as (B S)/(B+S), where B (S) is the number of shares traded initiated by buyers (sellers). VOIB_SHR is the standard deviation of daily order imbalance in a month. SVOIB_SHR is the difference between VOIB_SHR in the current month and the six-month moving average of VOIB_SHR in the previous month. The variables calculated using the number of trades are termed as OIB_NUM, VOIB_NUM, and SVOIB_NUM. The Amihud illiquidity (ILLIQ) is calculated as the monthly average of the daily ratio of the absolute return to the dollar volume. TURN is the logarithm of the monthly average of the daily turnover ratio calculated as the number of shares traded divided by shares outstanding. SPRD is the spread measure using the cheap alternative solution by Holden and Jacobsen (2014). The shocks to the Amihud illiquidity (SILLIQ), turnover (STURN), spread (SSPRD), and return standard deviation (SRet_Std) are computed similarly to SVOIB. Panel A: Descriptive statistics pre-2001 Statistics N Mean St. dev. Median Minimum Maximum OIB_SHR 2,444-0.079 0.442-0.119-0.864 0.760 VOIB_SHR 2,444 0.414 0.180 0.419 0.064 0.831 SVOIB_SHR 2,444 0.001 0.125 0.001-0.483 0.552 OIB_NUM 2,444-0.071 0.384-0.095-0.790 0.695 VOIB_NUM 2,444 0.312 0.151 0.298 0.048 0.743 SVOIB_NUM 2,444 0.001 0.099-0.003-0.389 0.513 ILLIQ 2,444 0.070 0.335 0.003 0.000 7.823 SILLIQ 2,444-0.006 0.375 0.000-8.391 5.999 TURN 2,436 0.786 0.673 0.581 0.164 5.333 STURN 2,411-0.025 0.481-0.046-2.297 2.466 SPRD 2,180 1.979 1.878 1.360 0.224 15.210 SSPRD 2,160-0.001 0.007 0.000-0.102 0.034 Panel B: Descriptive statistics post-2001 Statistics N Mean St. dev. Median Minimum Maximum OIB_SHR 3,687-0.011 0.153 0.007-0.662 0.469 VOIB_SHR 3,687 0.284 0.193 0.217 0.057 0.875 SVOIB_SHR 3,687-0.004 0.069-0.004-0.434 0.327 OIB_NUM 3,687 0.003 0.125 0.014-0.515 0.399 VOIB_NUM 3,687 0.251 0.182 0.187 0.045 0.847 SVOIB_NUM 3,687-0.003 0.065-0.003-0.417 0.335 ILLIQ 3,687 0.072 0.445 0.001 0.000 9.135 SILLIQ 3,687-0.004 0.453 0.000-5.668 8.283 TURN 3,675 1.171 1.348 0.764 0.022 9.458 STURN 3,645 0.006 0.512-0.026-2.224 3.499 SPRD 3,667 1.178 1.765 0.446 0.038 12.483 SSPRD 3,666 0.000 0.000 0.000-0.011 0.001 2
Table A3: Fama-MacBeth Regression Estimates Using an ARMA(1,1) Model for VOIB to Extract Shocks This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates between July 1983 and December 2012. The order imbalance is calculated using the number of shares traded in Column 1 and using the number of trades in Column 2. We use an ARMA(1,1) model for VOIB to extract shocks. The dependent variable is the risk-adjusted return calculated using the Fama-French (1993) factors as well as the momentum factor and the liquidity factor of Pastor and Stambaugh (2003) with loadings conditional on the size and book-to market ratio. All independent variables (except R1 and R212) are lagged one month. OIB is the monthly order imbalance defined as (B- S)/(B+S), where B (S) is the trades initiated by buyers (sellers). VOIB is the standard deviation of daily order imbalance in a month. POIB is the logistic transform of the ratio of number of days with positive order imbalance and total number of trading days in the month. SVOIB is the difference between VOIB in the current month and the six-month moving average of VOIB in the previous month. SIZE represents the logarithm of market capitalization. BM is the logarithm of the bookto-market ratio. R1 is the lagged one month return. R212 is the cumulative returns over the second through the twelfth months prior to the current month. TURN is the logarithm of the monthly average turnover ratio calculated as the trading volume divided by shares outstanding. StdTURN is the standard deviation of TURN in the past 36 months. ILLIQ represents the Amihud measure of illiquidity. SPRD is the spread measure using the cheap alternative solution by Holden and Jacobsen (2014). ACC represents accruals, measured as in Sloan (1996). AG is the asset growth computed in Cooper, Gulen and Shill (2008). ISSUE represents new issues as in Pontiff and Woodgate (2008). IVOL is the idiosyncratic volatility computed as in Ang, Hodrick, Xing, and Zhang (2006). PROFIT is the profitability variable as in Fama and French (2006). SUE is the standardized unexpected earnings, computed as the most recent quarterly earnings less the earnings four quarters ago, standardized by its standard deviation estimated over the prior eight quarters. MAX is the maximum daily return in the last month. DISP is the analyst dispersion in earnings forecasts and DISPD is a dummy that equals to one if the stock is covered by at least two analysts and zero otherwise. SSTT is the small size trade imbalance as in Hvidkjaer (2008). HiloSprd is the high-low spread estimate of Corwin and Schultz (2012). INSTV is the average of the eight most recent quarterly absolute institutional ownership percentage changes. ILLIQV is the idiosyncratic volatility of liquidity in Akbas, Armstrong and Petkova (2011). PIN is the probability of informed trade measured by Easley, Kiefer, O Hara, and Paperman (1996). Ret_Std is the standard deviation of daily returns in a month. SSPRD, SOIB, SPOIB, STURN, SStdTURN, SIVOL, SILLIQ, SDISP, and SRet_Std are defined similarly as SVOIB. All variables are winsorized at the 0.5% and 99.5% levels. N is the average number of stocks per month. Newey-West t-statistics are reported in parentheses. *,**, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively. SHR NUM Model 1 2 Intercept 3.493*** 3.353*** (4.86) (4.73) VOIB 1.232** 1.391** (2.28) (2.48) SVOIB -1.946*** -2.036*** (-5.07) (-5.01) ILLIQ 1.246 1.194 (1.14) (1.12) SILLIQ -3.425** -3.433*** (-2.57) (-2.59) TURN 0.086 0.117 (1.00) (1.36) STURN 0.839*** 0.798*** (8.53) (8.14) SPRD 0.341*** 0.331*** (5.71) (5.43) SSPRD -27.745*** -27.792*** (-5.05) (-4.97) OIB -0.423-0.158 (-1.15) (-0.36) SOIB 0.573 0.737* (1.57) (1.68) 3
Table A3 (continued) POIB 0.030-0.113* (0.47) (-1.94) SPOIB -0.001 0.099* (-0.02) (1.70) SIZE -0.188*** -0.174*** (-4.54) (-4.23) BM -0.025-0.026 (-0.49) (-0.52) R212 0.000 0.011 (-0.00) (0.06) R1-0.050*** -0.050*** (-10.16) (-10.17) STDTURN -0.142*** -0.152*** (-3.05) (-3.23) SSTDTURN -0.064-0.057 (-0.47) (-0.42) IVOL 16.497 17.081 (0.77) (0.81) SIVOL -13.491-12.552 (-0.76) (-0.71) ACC -1.091*** -1.084*** (-3.25) (-3.22) AG -0.188*** -0.191*** (-2.91) (-2.99) ISSUE -1.024*** -1.029*** (-3.36) (-3.39) PROFIT 0.016 0.004 (0.21) (0.06) SUE 0.027** 0.027** (2.26) (2.22) Max 4.864*** 4.873*** (3.64) (3.75) DISP -0.303*** -0.315*** (-2.82) (-2.94) SDISP 0.073 0.074 (0.64) (0.66) DISPD -0.108-0.124 (-1.39) (-1.60) SSTT 13.257 5.437 (1.03) (0.37) HiLoSprd 6.957 7.687 (1.02) (1.09) INSTV 0.125 0.101 (1.07) (0.91) ILLIQV -0.134** -0.121** (-2.25) (-2.01) PIN -4.455*** -4.580*** (-3.85) (-3.97) Ret_Std -62.065*** -62.290*** (-3.38) (-3.45) SRet_Std 18.936 18.192 (1.22) (1.18) Adj. R-sq 0.060 0.060 N 1379 1379 4
Table A4: Fama-MacBeth Regression Estimates with Other Control Variables This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates between July 1983 and December 2012. In this table, we add two more control variables: SHiloSprd and O/S. SHiloSprd is HiloSprd shock, where HiloSprd is the high-low spread estimate of Corwin and Schultz (2012). O/S is the ratio of option trading volume and stock trading volume, measured as in Roll, Schwartz and Subrahmanyam (2010). The order imbalance is calculated using the number of shares traded in Columns 1 to 3 and using the number of trades in Columns 4 to 6. The dependent variable is the risk-adjusted return calculated using the Fama-French (1993) factors as well as the momentum factor and the liquidity factor of Pastor and Stambaugh (2003) with loadings conditional on the size and book-to market ratio. All independent variables (except R1 and R212) are lagged one month. OIB is the monthly order imbalance defined as (B-S)/(B+S), where B (S) is the trades initiated by buyers (sellers). VOIB is the standard deviation of daily order imbalance in a month. POIB is the logistic transform of the ratio of number of days with positive order imbalance and total number of trading days in the month. SVOIB is the difference between VOIB in the current month and the six-month moving average of VOIB in the previous month. SIZE represents the logarithm of market capitalization. BM is the logarithm of the book-to-market ratio. R1 is the lagged one month return. R212 is the cumulative returns over the second through the twelfth months prior to the current month. TURN is the logarithm of the monthly average turnover ratio calculated as the trading volume divided by shares outstanding. StdTURN is the standard deviation of TURN in the past 36 months. ILLIQ represents the Amihud measure of illiquidity. SPRD is the spread measure using the cheap alternative solution by Holden and Jacobsen (2014). ACC represents accruals, measured as in Sloan (1996). AG is the asset growth computed in Cooper, Gulen and Shill (2008). ISSUE represents new issues as in Pontiff and Woodgate (2008). IVOL is the idiosyncratic volatility computed as in Ang, Hodrick, Xing, and Zhang (2006). PROFIT is the profitability variable as in Fama and French (2006). SUE is the standardized unexpected earnings, computed as the most recent quarterly earnings less the earnings four quarters ago, standardized by its standard deviation estimated over the prior eight quarters. MAX is the maximum daily return in the last month. DISP is the analyst dispersion in earnings forecasts and DISPD is a dummy that equals to one if the stock is covered by at least two analysts and zero otherwise. SSTT is the small size trade imbalance as in Hvidkjaer (2008). INSTV is the average of the eight most recent quarterly absolute institutional ownership percentage changes. ILLIQV is the idiosyncratic volatility of liquidity in Akbas, Armstrong and Petkova (2011). PIN is the probability of informed trade measured by Easley, Kiefer, O Hara, and Paperman (1996). Ret_Std is the standard deviation of daily returns in a month. SSPRD, SOIB, SPOIB, STURN, SStdTURN, SIVOL, SILLIQ, SDISP, SRet_Std and SHiloSprd are defined similarly as SVOIB. All variables are winsorized at the 0.5% and 99.5% levels. N is the average number of stocks per month. Newey-West t-statistics are reported in parentheses. *,**, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively. SHR NUM Model 1 2 3 4 5 6 Intercept 2.579*** 1.733 1.593 2.207*** 0.648 0.573 (3.63) (1.61) (1.48) (3.08) (0.55) (0.49) VOIB 3.101*** 9.094*** 9.440*** 3.703*** 11.213*** 11.489*** (3.53) (3.70) (3.84) (4.50) (4.00) (4.11) SVOIB -4.253*** -6.834*** -7.129*** -5.289*** -8.906*** -9.131*** (-5.51) (-3.12) (-3.26) (-7.21) (-3.63) (-3.72) ILLIQ 1.449 34.415 45.692 1.313 20.514 30.071 (1.35) (0.52) (0.66) (1.26) (0.30) (0.43) SILLIQ -3.601*** -30.060-35.201-3.532** -16.884-21.580 (-2.58) (-0.64) (-0.74) (-2.55) (-0.35) (-0.44) TURN 0.146* 0.099 0.116 0.201** 0.206 0.222 (1.75) (0.67) (0.79) (2.39) (1.30) (1.42) STURN 0.729*** 0.401** 0.388** 0.643*** 0.280* 0.269* (7.47) (2.57) (2.50) (6.79) (1.78) (1.72) SPRD 0.311*** 0.577 0.474 0.300*** 0.729 0.651 (5.48) (1.25) (1.01) (5.13) (1.56) (1.38) SSPRD -23.246*** -19.171-15.392-23.558*** -22.918-19.533 (-4.54) (-0.31) (-0.25) (-4.52) (-0.37) (-0.32) OIB -0.387-2.010* -2.101* -0.481-2.864-2.971* (-1.05) (-1.86) (-1.93) (-1.06) (-1.62) (-1.68) SOIB 0.515 2.231* 2.282* 1.008** 4.633*** 4.726*** (1.39) (1.86) (1.88) (2.25) (2.61) (2.65) POIB 0.009 0.004 0.019-0.066 0.093 0.110 (0.14) (0.03) (0.15) (-1.10) (0.85) (0.99) 5
Table A4 (continued) SPOIB 0.012-0.060-0.072 0.052-0.150-0.167 (0.18) (-0.48) (-0.57) (0.88) (-1.30) (-1.45) SIZE -0.141*** -0.048-0.043-0.115*** 0.009 0.012 (-3.40) (-0.82) (-0.73) (-2.76) (0.14) (0.18) BM -0.032-0.122** -0.123** -0.032-0.130** -0.130** (-0.64) (-2.08) (-2.11) (-0.63) (-2.21) (-2.22) R212-0.039-0.525-0.518-0.039-0.544* -0.538* (-0.20) (-1.57) (-1.55) (-0.20) (-1.68) (-1.67) R1-0.050*** -0.039*** -0.040*** -0.050*** -0.042*** -0.043*** (-10.29) (-5.83) (-5.86) (-10.31) (-6.08) (-6.10) STDTURN -0.136*** 0.088 0.084-0.146*** 0.047 0.041 (-2.93) (0.89) (0.86) (-3.13) (0.46) (0.41) SSTDTURN -0.105 0.244 0.264-0.092 0.350 0.366 (-0.77) (0.90) (0.98) (-0.67) (1.30) (1.36) IVOL 12.403-13.302-11.364 15.159-8.227-5.954 (0.58) (-0.38) (-0.33) (0.71) (-0.24) (-0.17) SIVOL -9.752 7.968 7.036-10.015 2.906 1.437 (-0.55) (0.29) (0.26) (-0.57) (0.11) (0.05) ACC -1.090*** -0.610-0.575-1.076*** -0.538-0.514 (-3.25) (-1.25) (-1.17) (-3.19) (-1.11) (-1.05) AG -0.190*** -0.164*** -0.163** -0.193*** -0.159** -0.158** (-2.90) (-2.60) (-2.56) (-2.99) (-2.57) (-2.53) ISSUE -1.039*** -1.006** -1.025** -1.063*** -1.118*** -1.137*** (-3.39) (-2.52) (-2.54) (-3.47) (-2.82) (-2.84) PROFIT 0.022-0.051-0.056 0.004-0.052-0.056 (0.31) (-0.59) (-0.65) (0.05) (-0.62) (-0.67) SUE 0.026** -0.019-0.019 0.026** -0.025-0.024 (2.18) (-0.93) (-0.91) (2.12) (-1.20) (-1.17) Max 5.104*** 6.184*** 6.357*** 5.167*** 6.679*** 6.855*** (3.89) (3.73) (3.84) (4.03) (3.92) (4.01) DISP -0.298*** -0.158-0.152-0.315*** -0.162-0.156 (-2.80) (-0.95) (-0.92) (-2.98) (-0.99) (-0.96) SDISP 0.064 0.240 0.247 0.074 0.235 0.242 (0.55) (1.24) (1.28) (0.64) (1.24) (1.29) DISPD -0.126-0.167-0.164-0.152* -0.177-0.177 (-1.61) (-0.99) (-0.97) (-1.93) (-1.03) (-1.03) SSTT 14.060-11.238-10.167 5.737-25.143** -23.899** (1.09) (-1.24) (-1.13) (0.39) (-2.46) (-2.40) HiLoSprd 7.834 3.167 13.552 10.238 1.007 10.100 (0.92) (0.29) (0.89) (1.17) (0.09) (0.65) INSTV 0.118-0.170-0.175 0.085-0.181-0.185 (1.02) (-1.46) (-1.48) (0.79) (-1.45) (-1.46) ILLIQV -0.140** -0.012-0.012-0.129** 0.034 0.037 (-2.32) (-0.07) (-0.07) (-2.10) (0.20) (0.22) PIN -5.241*** -14.132*** -14.303*** -5.334*** -13.749*** -13.926*** (-3.89) (-4.54) (-4.60) (-4.16) (-4.69) (-4.77) Ret_Std -58.893*** -26.225-31.322-62.121*** -34.255-39.617 (-3.24) (-0.87) (-1.04) (-3.43) (-1.13) (-1.31) SRet_Std 15.457-2.988 0.493 16.954 2.389 6.352 (1.00) (-0.12) (0.02) (1.10) (0.10) (0.26) SHiLoSprd 1.827-14.836 0.371-13.845 (0.24) (-1.19) (0.05) (-1.12) O/S -0.015*** -0.014*** -0.015*** -0.014*** (-2.87) (-2.78) (-2.91) (-2.81) Adj. R-sq 0.061 0.065 0.066 0.061 0.066 0.067 N 1496 1157 1157 1496 1157 1157 6
Table A5: Fama-MacBeth Regressions for Robustness Checks Using VOIB_NUM This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates between July 1983 and December 2012. Model 1 (Model 2) uses raw return (mid quote return from open to close) as the dependent variable. In Models 3 (Model 4), all shock variables are calculated using the three-month (twelve-month) moving averages accordingly. Model 5 excludes the great financial crisis period of 2008 and 2009. Models 6 and 7 use data before and after January 2001 only. Model 8 uses the Weighted Least Squares regressions in cross-sectional estimation following Asparouhova, Bessembinder and Kalcheva (ABK, 2010). In Model 9, we form decile portfolios sorted by every day, replace each individual firm s with the average of the decile portfolio to which the firm belongs (OIB), and construct other order flow variables using OIB. All independent variables (except R1 and R212) are lagged one month. OIB is the monthly order imbalance defined as (B-S)/(B+S), where B (S) is the number of trades initiated by buyers (sellers). VOIB is the standard deviation of daily order imbalance in a month. POIB is the logistic transform of the ratio of number of days with positive order imbalance and total number of trading days in the month. SVOIB is the difference between VOIB in the current month and the six-month moving average of VOIB in the previous month. SIZE represents the logarithm of market capitalization. BM is the logarithm of the book-to-market ratio. R1 is the lagged one month return. R212 is the cumulative returns over the second through the twelfth months prior to the current month. TURN is the logarithm of the monthly average turnover ratio calculated as the trading volume divided by shares outstanding. StdTURN is the standard deviation of TURN in the past 36 months. ILLIQ represents the Amihud measure of illiquidity. SPRD is the spread measure using the cheap alternative solution by Holden and Jacobsen (2014). ACC represents accruals, measured as in Sloan (1996). AG is the asset growth computed in Cooper, Gulen and Shill (2008). ISSUE represents new issues as in Pontiff and Woodgate (2008). IVOL is the idiosyncratic volatility computed as in Ang, Hodrick, Xing, and Zhang (2006). PROFIT is the profitability variable as in Fama and French (2006). SUE is the standardized unexpected earnings, computed as the most recent quarterly earnings less the earnings four quarters ago, standardized by its standard deviation estimated over the prior eight quarters. MAX is the maximum daily return in the last month. DISP is the analyst dispersion in earnings forecasts and DISPD is a dummy that equals to one if the stock is covered by at least two analysts and zero otherwise. SSTT is the small size trade imbalance as in Hvidkjaer (2008). HiloSprd is the high-low spread estimate of Corwin and Schultz (2012). INSTV is the average of the eight most recent quarterly absolute institutional ownership percentage changes. ILLIQV is the idiosyncratic volatility of liquidity in Akbas, Armstrong and Petkova (2011). PIN is the probability of informed trade measured by Easley, Kiefer, O Hara, and Paperman (1996). Ret_Std is the standard deviation of daily returns in a month. SSPRD, SOIB, SPOIB, STURN, SStdTURN, SIVOL, SILLIQ, SDISP, and SRet_Std are defined similarly as SVOIB. All variables are winsorized at the 0.5% and 99.5% levels. N is the average number of stocks per month. Newey- West t-statistics are reported in parentheses. *,**, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively. Model 1 2 3 4 5 6 7 8 9 raw ret o-c ret MA=3 MA=12 ex-crisis post2001 pre2001 ABK OIB Intercept 3.631*** 4.384*** 2.694*** 2.160*** 2.315*** 5.665*** 0.067 2.349*** 2.831*** (3.67) (3.46) (4.04) (2.99) (3.03) (7.86) (0.07) (3.27) (4.06) VOIB 4.013*** 5.375*** 2.798*** 3.079*** 3.097*** 5.910*** 1.935*** 3.543*** 2.295*** (4.39) (4.14) (3.80) (4.08) (3.86) (3.27) (3.74) (4.29) (3.74) SVOIB -5.835*** -7.178*** -4.460*** -4.154*** -4.631*** -8.066*** -3.191*** -5.167*** -3.996*** (-7.35) (-6.33) (-6.63) (-6.16) (-6.65) (-5.32) (-6.38) (-7.03) (-7.11) ILLIQ 0.137 1.637** 1.290 0.015 1.406 0.808 1.820 1.402 1.361 (0.11) (2.38) (1.44) (0.01) (1.21) (1.47) (1.02) (1.30) (1.28) SILLIQ -2.554* -1.495*** -2.648** -1.684-3.492*** -1.100** -4.928** -3.371*** -3.267*** (-1.76) (-3.23) (-2.55) (-1.22) (-2.59) (-2.03) (-2.39) (-2.68) (-2.72) TURN 0.153* 0.228* 0.298*** 0.120 0.162-0.029 0.287** 0.158* 0.114 (1.79) (1.78) (3.87) (1.19) (1.63) (-0.29) (2.03) (1.65) (1.19) STURN 0.770*** 0.611*** 0.498*** 0.653*** 0.639*** 0.727*** 0.609*** 0.658*** 0.706*** (7.06) (5.18) (5.91) (5.90) (6.56) (6.86) (4.35) (7.02) (7.56) SPRD 0.312*** 0.442*** 0.303*** 0.274*** 0.306*** 0.577*** 0.115** 0.303*** 0.317*** (4.83) (4.86) (5.18) (4.67) (4.94) (5.52) (2.28) (5.17) (5.32) SSPRD -23.931***-27.601***-25.386***-18.123***-21.640***-56.607*** -0.239-23.163***-24.459*** (-4.29) (-3.41) (-5.01) (-3.78) (-4.05) (-6.11) (-0.23) (-4.59) (-4.70) 7
Table A5 (Continued) OIB -0.390-1.284** 0.145-1.005* -0.579-2.054** 0.670-0.443-0.044 (-0.87) (-2.04) (0.41) (-1.70) (-1.29) (-2.50) (1.60) (-0.99) (-0.12) SOIB 0.884** 2.053*** 0.423 1.686*** 0.997** 2.362*** 0.020 0.974** 0.744* (2.01) (2.85) (1.21) (3.05) (2.33) (2.85) (0.05) (2.21) (1.93) POIB -0.040 0.131-0.103** -0.072-0.052-0.024-0.103-0.071-0.109** (-0.65) (1.38) (-2.03) (-0.89) (-0.85) (-0.24) (-1.42) (-1.17) (-2.20) SPOIB 0.040-0.070 0.105** 0.039 0.049-0.075 0.152** 0.060 0.152* (0.62) (-0.70) (2.02) (0.47) (0.82) (-0.76) (2.20) (1.01) (1.66) SIZE -0.145** -0.194*** -0.156*** -0.113*** -0.124*** -0.293*** -0.012-0.126*** -0.151*** (-2.49) (-2.79) (-3.88) (-2.72) (-2.82) (-7.07) (-0.20) (-3.03) (-3.74) BM 0.117* 0.073-0.039-0.018-0.035-0.012-0.038-0.028-0.027 (1.65) (0.80) (-0.79) (-0.33) (-0.69) (-0.19) (-0.53) (-0.55) (-0.54) R212 0.131 0.142 0.078-0.192 0.197-0.590 0.336** -0.041-0.037 (0.64) (0.53) (0.42) (-0.96) (1.63) (-1.55) (2.12) (-0.22) (-0.19) R1-0.043*** -0.020*** -0.051*** -0.049*** -0.050*** -0.036*** -0.061*** -0.051*** -0.051*** (-9.11) (-3.84) (-10.16) (-9.97) (-9.91) (-5.80) (-9.28) (-10.48) (-10.46) STDTURN -0.127** -0.174* -0.245*** -0.080* -0.162*** -0.146* -0.158*** -0.153*** -0.147*** (-2.02) (-1.68) (-5.04) (-1.68) (-3.49) (-1.94) (-2.71) (-3.31) (-3.16) SSTDTURN -0.332** -0.388* 0.198-0.205* -0.102-0.096-0.174-0.142-0.143 (-2.03) (-1.81) (1.05) (-1.76) (-0.72) (-0.51) (-0.87) (-1.00) (-1.02) IVOL -4.001 15.011-3.525-3.512 6.288 38.588-8.558 10.853 10.587 (-0.16) (0.54) (-0.21) (-0.14) (0.28) (1.40) (-0.28) (0.51) (0.50) SIVOL 2.335-20.784 8.392-0.055-4.376-41.430* 16.146-7.454-8.575 (0.12) (-0.98) (0.67) (-0.00) (-0.23) (-1.79) (0.65) (-0.42) (-0.49) ACC -1.063*** -0.885* -1.089*** -1.049*** -1.036*** -0.605-1.331*** -1.035*** -1.045*** (-2.77) (-1.90) (-3.19) (-3.14) (-2.94) (-1.57) (-2.72) (-3.10) (-3.12) AG -0.180*** -0.205*** -0.173*** -0.152** -0.188*** -0.109-0.241** -0.187*** -0.189*** (-2.70) (-2.74) (-2.72) (-2.29) (-2.75) (-1.54) (-2.50) (-2.90) (-2.90) ISSUE -1.146*** -1.651*** -1.093*** -1.186*** -1.169*** -1.287*** -1.025** -1.130*** -1.119*** (-3.67) (-3.39) (-3.55) (-3.65) (-3.72) (-3.61) (-2.29) (-3.73) (-3.69) PROFIT -0.001 0.092 0.009 0.065 0.030-0.105 0.084 0.008 0.014 (-0.02) (1.06) (0.12) (0.89) (0.40) (-1.21) (0.80) (0.11) (0.20) SUE 0.028** 0.021 0.027** 0.018 0.033*** 0.029 0.023 0.026** 0.026** (2.12) (1.21) (2.27) (1.50) (2.97) (1.57) (1.51) (2.18) (2.23) Max 4.681*** 2.565 4.987*** 6.153*** 5.255*** 3.713** 5.801*** 4.947*** 4.960*** (3.46) (1.64) (3.88) (4.58) (4.02) (2.25) (3.20) (3.88) (3.91) DISP -0.302** -0.030-0.319*** -0.332*** -0.329*** -0.236* -0.366** -0.313*** -0.308*** (-2.47) (-0.16) (-3.36) (-2.68) (-2.93) (-1.90) (-2.34) (-2.97) (-2.93) SDISP 0.015-0.058 0.108 0.051 0.074 0.224-0.031 0.072 0.070 (0.12) (-0.25) (0.98) (0.40) (0.62) (1.42) (-0.20) (0.63) (0.61) DISPD -0.277*** -0.246* -0.124-0.127-0.128-0.213* -0.111-0.150* -0.142* (-2.97) (-1.91) (-1.61) (-1.52) (-1.57) (-1.79) (-1.05) (-1.89) (-1.80) SSTT -2.561-32.725* 5.592-2.792 9.469-5.615 17.303 8.133 8.714 (-0.18) (-1.93) (0.40) (-0.19) (0.59) (-0.75) (0.70) (0.54) (0.57) HiLoSprd 10.947 17.182 10.835 13.088* 9.998-2.407 16.892* 8.939 7.814 (1.36) (1.53) (1.44) (1.89) (1.32) (-0.25) (1.69) (1.24) (1.08) INSTV 0.148 0.009-0.005 0.093 0.105-0.170*** 0.266 0.088 0.105 (1.07) (0.05) (-0.05) (0.80) (0.90) (-3.10) (1.52) (0.81) (0.92) ILLIQV -0.103-0.056-0.104* -0.085-0.116* 0.035-0.222*** -0.118* -0.093 (-1.58) (-0.52) (-1.70) (-1.36) (-1.82) (0.38) (-2.88) (-1.93) (-1.51) PIN -5.899*** -8.541*** -4.504*** -4.977*** -4.363*** -13.710*** 0.500-5.278*** -4.748*** (-4.17) (-4.67) (-3.81) (-4.08) (-3.51) (-6.60) (0.64) (-4.15) (-4.11) Ret_Std -47.226* -45.589*** -44.943** -47.226* -55.820***-64.777*** -48.021* -54.913***-54.873*** (-1.74) (-3.22) (-2.08) (-1.74) (-2.84) (-2.75) (-1.80) (-2.97) (-2.98) SRet_Std 15.500 3.375 3.716 15.500 13.224 40.920** -6.793 12.660 13.372 (0.79) (0.32) (0.18) (0.79) (0.79) (2.17) (-0.30) (0.80) (0.85) Adj. R-sq 0.087 0.087 0.060 0.061 0.060 0.050 0.068 0.061 0.060 N 1499 1486 1516 1455 1462 2069 1102 1497 1497 8
Table A6: Fama-MacBeth Regressions Using Randomly Formed Portfolios We perform an alternative test that accounts for measurement error in OIB. In this test, we use 20 randomly formed portfolios as test assets every month, and use the portfolios average order flows to compute their VOIB and SVOIB. We then run Fama-MacBeth regressions for the 20 portfolios, using equally-weighted open-close quote midpoint returns to account for non-synchronous trading. We repeat this procedure 100 times. This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates between July 1983 and December 2012. SHR NUM Intercept 0.210 0.354 (0.57) (1.05) VOIB 2.684*** 2.894*** (6.82) (7.30) SVOIB -5.988*** -7.026*** (-9.39) (-10.57) 9
Table A7: Bivariate Portfolio Sorts Controlling for Limits to Arbitrage Proxies (Contemporaneous Relationship) Each month between July 1983 and December 2012, stocks are first sorted into high and low groups based on one of the control variables, and then into SVOIB_SHR or SVOIB_NUM quintile portfolios within each control variable group. Then the quintile portfolio returns, the return differences between high and low quintile SVOIB portfolios, and the alphas using the Fama and French (1993) model along with the momentum factor and the Pastor and Stambaugh (2003) liquidity factor are reported with the Newey-West t-statistics in parentheses. VOIB is the standard deviation of daily order imbalance in a month, where order imbalance is defined as (B S)/(B+S) with B (S) being the trades initiated by buyers (sellers). SVOIB is the difference between VOIB in the current month and the six-month moving average of VOIB in the previous month. The order imbalance is calculated using the number of shares traded in Panel A and using the number of trades in Panel B. SIZE represents the logarithm of market capitalization. INST is the percentage of shares held by institutional investors. IVOL is the idiosyncratic stock return volatility. *,**, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively. Panel A: SVOIB_SHR Controlling for SIZE Controlling for INST Controlling for IVOL Small- SVOIB Small Large Large Low High Low-High Low High Low-High Low 3.652 2.776 3.887 1.967 1.027 4.906 2 1.043 1.704 1.694 1.292 0.869 2.209 3 0.423 1.423 1.163 1.066 0.778 1.427 4 0.146 1.378 0.763 0.929 0.647 1.067 High 0.157 1.402 0.604 0.797 0.389 0.782 High-Low -3.495*** -1.374*** -2.121*** -3.283*** -1.170*** -2.112*** -0.638*** -4.124*** 3.486*** (-8.24) (-6.75) (-8.02) (-8.12) (-9.25) (-6.41) (-6.31) (-8.70) (8.24) Alpha -3.369*** -1.359*** -2.010*** -3.163*** -1.199*** -1.964*** -0.651*** -3.980*** 3.329*** (-8.45) (-7.38) (-7.23) (-8.25) (-9.69) (-6.01) (-6.55) (-9.11) (8.60) Panel B: SVOIB_NUM Controlling for SIZE Controlling for INST Controlling for IVOL Small- SVOIB Small Large Large Low High Low-High Low High Low-High Low 3.204 2.655 3.498 1.756 0.943 4.363 2 1.035 1.596 1.749 1.215 0.848 2.099 3 0.341 1.407 1.030 1.106 0.838 1.387 4 0.173 1.422 0.829 1.010 0.677 1.153 High 0.668 1.603 1.005 0.965 0.404 1.390 High-Low -2.535*** -1.052*** -1.484*** -2.493*** -0.791*** -1.702*** -0.540*** -2.973*** 2.433*** (-5.83) (-5.62) (-4.93) (-6.08) (-5.55) (-4.91) (-5.35) (-6.36) (5.80) Alpha -2.449*** -1.062*** -1.387*** -2.432*** -0.815*** -1.617*** -0.539*** -2.861*** 2.322*** (-5.89) (-6.00) (-4.58) (-6.20) (-5.38) (-4.67) (-5.11) (-6.51) (5.88) 10
Table A8: Dynamic Effects of Liquidity Shocks: Robustness Checks This table presents robustness checks for the effects of SVOIB on returns in the next 1, 2-4, 5-7, 8-10, 11-13, 14-16, 17-19, 20-22, 23-25, 26-28, 29-31 months. We calculate OIB as the monthly order imbalance defined as (B-S)/(B+S). VOIB is the standard deviation of daily order imbalance in a month. SVOIB is the difference between VOIB in the current month and the six-month moving average of VOIB in the previous month. SILLIQ is the shock to the Amihud illiquidity measure defined similarly as SVOIB. Panel A reports the raw return differences and the alphas with respect to the Fama-French three-factor along with the momentum and liquidity factors of portfolios that buy stocks in the highest quintile of illiquidity shocks and sell stocks in the lowest quintile of illiquidity shocks, and the time-series averages of the coefficient estimates for the illiquidity shocks from cross-sectional regressions as in Table 5. In Panel B, we divide the sample into two groups based on the institutional holding (INST) or idiosyncratic volatility (IVOL), and report for each group the time-series averages of the coefficient estimates of SVOIB_SHR and SILLIQ from cross-sectional regressions. In Panel C, we divide the sample into two groups based on SIZE, the institutional holding or idiosyncratic volatility, and report the results for SVOIB_NUM. All cross-sectional regressions control for the same variables as those in Column 3 of Table 5. For brevity, coefficient estimates are reported only for the illiquidity shock variables. All variables are winsorized at the 0.5% and 99.5% levels. Newey-West t-statistics are reported in parentheses. *,**, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively. Panel A: Price impact in the long run Return difference Alpha FM coefficient SVOIB_NUM SILLIQ SVOIB_NUM SILLIQ SVOIB_NUM SILLIQ Month1-0.945*** -1.530*** -0.968*** -1.534*** -0.216-3.249** (-7.49) (-8.94) (-7.84) (-9.08) (-0.41) (-2.51) Month2-4 -0.050-1.615*** -0.092-1.506*** -1.665-4.556** (-0.20) (-4.56) (-0.32) (-3.73) (-1.42) (-2.50) Month5-7 0.131-0.839** 0.167-0.657* 0.017-7.570* (0.63) (-2.45) (0.71) (-1.95) (0.01) (-1.93) Month8-10 0.613*** -0.435 0.609*** -0.367 0.855 2.392 (2.79) (-1.18) (2.72) (-0.92) (0.44) (0.84) Month11-13 0.587*** 0.287 0.568** 0.431 1.793 2.613 (2.71) (0.73) (2.34) (0.99) (1.07) (0.69) Month14-16 0.604*** 0.961** 0.674*** 1.077*** 2.482* -5.153 (2.71) (2.35) (2.94) (2.62) (1.82) (-1.34) Month17-19 0.324** 0.651** 0.320** 0.742*** 3.260** 8.684** (2.21) (2.55) (1.97) (2.79) (2.18) (2.01) Month20-22 0.618*** 0.405 0.603** 0.377 3.748** 3.069 (2.62) (1.38) (2.53) (1.21) (2.40) (0.84) Month23-25 0.450** 0.445 0.371* 0.499 2.315 4.121 (2.04) (1.36) (1.78) (1.50) (1.62) (1.12) Month26-28 0.024 0.366 0.057 0.337 0.944 6.060 (0.14) (1.11) (0.33) (1.05) (0.69) (1.63) Month29-31 -0.088 0.402-0.103 0.362-0.216-3.249** (-0.43) (1.56) (-0.51) (1.39) (-0.41) (-2.51) 11
A8 (continued) Panel B: Fama-MacBeth regression coefficient estimates conditioning on INST and IVOL INST IVOL Low High Low High SVOIB_SHR SILLIQ SVOIB_SHR SILLIQ SVOIB_SHR SILLIQ SVOIB_SHR SILLIQ Month1-3.093*** -0.364-1.040** -5.578-1.645*** -0.832-3.923*** -0.281 (-4.14) (-1.13) (-2.35) (-1.60) (-6.23) (-0.48) (-8.45) (-1.26) Month2-4 -2.599*** -2.122** 1.027-10.01*** -0.988 0.274-2.771*** -2.441** (-2.99) (-2.57) (0.56) (-2.65) (-0.95) (0.04) (-2.90) (-2.23) Month5-7 2.730* -4.664-0.533-3.507 1.267-3.737 1.140-1.692 (1.87) (-1.43) (-0.33) (-0.39) (1.14) (-0.46) (0.74) (-1.20) Month8-10 3.729** -3.564 1.743* -3.733 0.952 2.615 1.546-3.560** (1.97) (-0.89) (1.94) (-0.74) (0.80) (0.33) (0.79) (-2.02) Month11-13 4.605** 3.863 2.065-4.673 1.754* 0.991 3.262* 2.973* (1.99) (1.26) (1.14) (-0.97) (1.81) (0.13) (1.83) (1.68) Month14-16 5.334*** 2.239-0.266-2.627 1.928-7.388 5.285*** 2.090 (3.12) (0.71) (-0.12) (-0.08) (1.46) (-1.01) (3.21) (1.18) Month17-19 4.975*** -5.904 3.755** -5.538 0.072 0.063 5.667** -3.727* (3.02) (-1.44) (2.41) (-0.50) (0.06) (0.01) (2.54) (-1.82) Month20-22 5.608*** 4.919-1.777 3.118 1.968* -6.385 6.628** 3.963* (2.68) (1.27) (-0.80) (0.27) (1.79) (-1.44) (2.52) (1.70) Month23-25 6.053** 7.209* 1.759-9.533** 2.443** -7.474* 6.074** 3.978 (2.50) (1.94) (0.93) (-2.13) (1.99) (-1.86) (2.49) (1.37) Month26-28 4.642** 6.240 1.647-5.369 1.547-4.770 4.692** 4.816* (2.09) (1.57) (1.09) (-0.74) (1.18) (-0.80) (2.25) (1.68) Month29-31 3.107 4.271 1.044-7.109 0.296-4.852 3.321 4.287 (1.50) (1.16) (0.81) (-1.58) (0.25) (-0.71) (1.35) (1.47) Panel C: Fama-MacBeth regression coefficient estimates for SVOIB_NUM conditioning on SIZE, INST and IVOL SIZE INST IVOL Small Large Low High Low High Month1-4.151*** -1.508*** -3.675*** -1.863*** -2.236*** -4.711*** (-5.73) (-2.73) (-5.93) (-3.25) (-3.91) (-10.31) Month2-4 -2.990*** -1.071-2.367** 0.917-2.641-2.645** (-2.63) (-1.17) (-2.10) (0.54) (-1.38) (-2.31) Month5-7 1.438-2.193 1.277-2.907 0.367-1.205 (1.04) (-0.79) (0.95) (-1.54) (0.33) (-0.75) Month8-10 1.904-1.674 1.428-1.127 0.545 0.336 (1.11) (-0.53) (0.83) (-0.43) (0.41) (0.18) Month11-13 2.731-2.358 2.872 1.306 0.510 2.086 (1.26) (-0.70) (1.16) (0.53) (0.45) (0.72) Month14-16 3.553** 4.633** 4.931*** -2.020 1.531 2.565 (2.08) (2.04) (2.78) (-0.63) (1.08) (1.21) Month17-19 4.047** 9.532** 4.714*** -6.031 0.670 3.540** (2.23) (2.37) (2.88) (-1.38) (0.49) (2.02) Month20-22 5.556** 6.676** 6.060*** 6.610* 0.443 5.800** (2.48) (2.25) (2.86) (1.87) (0.33) (2.41) Month23-25 4.809** -1.984 6.120** 3.703** 2.160 5.619** (2.06) (-0.79) (2.47) (2.21) (1.59) (2.12) Month26-28 3.152-2.952 3.276* -0.362 0.661 3.164 (1.57) (-1.30) (1.75) (-0.14) (0.46) (1.42) Month29-31 1.919-3.520 2.505-0.186-1.192 1.786 (1.01) (-1.42) (1.44) (-0.09) (-1.04) (0.84) 12