Jonathan A. Milian. Florida International University School of Accounting S.W. 8 th St. Miami, FL

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1 Online Appendix Unsophisticated Arbitrageurs and Market Efficiency: Overreacting to a History of Underreaction? Jonathan A. Milian Florida International University School of Accounting S.W. 8 th St. Miami, FL

2 Online Appendix Figure A1 Hedge Portfolio Returns by Quarter - Earnings Announcements with Actively Traded Stock Options (ATSO) 10.00% 5.00% 0.00% 5.00% 10.00% 15.00% This figure depicts, by quarter, the abnormal returns to two PEAD hedge portfolios at the subsequent earnings announcement for I/B/E/S firms with actively traded stock options. The PEAD hedge portfolio represented by the black series takes long (short) positions in firms in the highest (lowest) decile of earnings announcement abnormal returns from the prior calendar quarter. The PEAD hedge portfolio represented by the gray series takes long (short) positions in firms in the highest (lowest) decile of earnings surprises from the prior calendar quarter. Earnings announcement abnormal returns are measured as the firm s two-day, [0, +1], market-adjusted stock return at the earnings announcement. Earnings surprises are measured as the firm s actual earnings less the mean analyst forecast, scaled by the firm s stock price six days prior to the earnings announcement. The long side and the short side of the hedge portfolio are of equal size each quarter. Within each side of the portfolio, firms abnormal returns are equally weighted. On the day prior to the earnings announcement, these I/B/E/S firms have both positive option volume and open interest in the options necessary to calculate an at-the-money option spread and option skew. 2

3 Online Appendix Figure A2 Hedge Portfolio Returns by Quarter - Earnings Announcements without Actively Traded Stock Options (Non-ATSO) 6.00% 4.00% 2.00% 0.00% 2.00% 4.00% 6.00% This figure depicts, by quarter, the abnormal returns to two PEAD hedge portfolios at the subsequent earnings announcement for I/B/E/S firms without actively traded stock options. The PEAD hedge portfolio represented by the black series takes long (short) positions in firms in the highest (lowest) decile of earnings announcement abnormal returns from the prior calendar quarter. The PEAD hedge portfolio represented by the gray series takes long (short) positions in firms in the highest (lowest) decile of earnings surprises from the prior calendar quarter. Earnings announcement abnormal returns are measured as the firm s two-day, [0, +1], market-adjusted stock return at the earnings announcement. Earnings surprises are measured as the firm s actual earnings less the mean analyst forecast, scaled by the firm s stock price six days prior to the earnings announcement. The long side and the short side of the hedge portfolio are of equal size each quarter. Within each side of the portfolio, firms abnormal returns are equally weighted. On the day prior to the earnings announcement, these I/B/E/S firms meet at least one of the following conditions: no exchange-traded options listed, no option volume, or no open interest in the options necessary to calculate an atthe-money option spread and option skew. 3

4 Online Appendix Figure A3 Average Option Volume around Earnings Announcements 12,000 10,000 8,000 6,000 4,000 ATSO: Q2 ATSO: 2003Q3 Non ATSO: Q2 Non ATSO: 2003Q3 2, This figure depicts the average firm s option volume by day over the 21 trading days around their earnings announcements. Day 0 is the day before the earnings announcement. Option volume is the total option volume across all strike prices for both calls and puts in the options closest to expiration with no more than 40 days to expiration. The black (gray) series presents the average option volume for the ATSO (Non-ATSO) firms during the Q2 and 2003Q3 periods. 4

5 Online Appendix Table A1 Predicting Earnings Announcement Returns for ATSO Firms Expected Announcements (1) (2) (3) Prior Multivariate Multivariate Multivariate Literature Q2 2003Q3- Intercept % ** 0.43% ** 0.13% [1.98] [2.65] [0.87] LagEARet % ** -0.01% -1.10% *** [-2.08] [-0.01] [-2.89] LagESurp % *** -0.50% -1.21% *** [-4.30] [-1.22] [-4.09] Spread % *** 1.64% ** 0.96% ** [3.12] [2.59] [2.15] Skew % 0.23% 0.52% [1.07] [0.40] [1.45] O/S % -0.44% 0.55% * [0.91] [-1.40] [1.83] PreEA5DayRet % *** -1.93% *** -1.55% *** [-7.22] [-4.57] [-5.29] Size % -0.57% -0.17% [-0.98] [-1.05] [-0.39] M/B % -0.30% 0.10% [-0.19] [-0.55] [0.22] Accruals % 0.36% -0.08% [0.20] [0.70] [-0.27] R % 0.89% 1.00% N 13,973 4,586 9,387 This table presents the results of multivariate regressions with EARet as the dependent variable. It repeats the analysis in Table 5 for earnings announcements that are near their expected announcement date given a firm s earnings announcement history. Earnings announcements are excluded from this analysis, if the earnings announcement is more than 5 calendar days away from the expected earnings announcement date. The expected earnings announcement date is the median announcement date of the prior four earnings announcements for that same fiscal quarter. Results are presented for three time periods: the full sample period ( ), the first half of the sample period ( Q2), and the second half of the sample period (2003Q3 - ). All independent variables are transformed into decile rankings and scaled to have a range of 1, [-0.5, 0.5], and a mean of zero. EARet is the firm s two-day abnormal return at the earnings announcement. Specifically, it is the compounded return for the firm less the compounded return for the CRSP value-weighted index over the two-day earnings announcement period, [0, +1], where day 0 is the earnings announcement date in I/B/E/S (adjusted for after-hours announcements). LagEARet is the firm s EARet from the previous calendar quarter. ESurp is the firm s earnings surprise. Specifically, it is the firm s actual earnings less the mean analyst forecast, scaled by the firm s stock price six days prior to the earnings announcement. LagESurp is the firm s ESurp form the previous calendar quarter. The option variables: Spread, Skew, O/S, and OpenInt are calculated on the day prior to the earnings announcement based on a single set of the firm s options with the same expiration. The set of options examined are the ones closest to expiration with no more than 40 days to expiration. Spread is calculated as the implied volatility of a call for a given strike price and expiration less the implied volatility of the put with the same strike price and expiration as the call, these differences are then weighted by the amount of open interest in all strike price pairs with the same expiration. Skew is the implied volatility of an out-of-the-money put (i.e., delta closest to -0.25, given a delta of [-0.375, ]) less the implied volatility on an at-the-money call (i.e., delta closest to 0.5, given a delta of [0.375, 0.625]). O/S is the ratio of option market volume to stock market volume on the day prior to the firm s earnings announcement. PreEA5DayRet is the firm s abnormal return over the five trading days prior to their earnings announcement. Size is the firm s market capitalization six days prior to the earnings announcement in billions of dollars. M/B is the firm s Size divided by the firm s book value. Accruals is the firm s income before extraordinary items less cash flow from operating activities, scaled by average total assets (all from the prior quarter). Coefficients are presented in percentage format for presentation purposes. Standard errors are clustered on two dimensions, firm and quarter. t-statistics are in brackets. ***, **, and * indicate significance at 1%, 5%, and 10% levels, respectively. 5

6 Online Appendix Table A2 Predicting Earnings Announcement Returns for ATSO Firms Continuous Independent Variables (1) (2) (3) (4) (5) (6) Prior Multivariate Multivariate Multivariate Univariate Univariate Univariate Literature Q2 2003Q Q2 2003Q3 - Intercept *** *** ** [3.10] [4.70] [0.25] [1.03] [2.16] [-0.35] LagEARet *** *** *** *** [-2.61] [-0.72] [-3.10] [-3.03] [-0.76] [-3.48] LagESurp *** *** *** *** [-3.70] [-0.84] [-3.31] [-3.87] [-1.01] [-3.52] Spread * *** ** [1.81] [1.03] [1.63] [2.67] [2.35] [1.40] Skew ** ** [-0.30] [-0.93] [0.90] [-2.01] [-2.50] [-0.28] O/S ** [-0.38] [-1.37] [0.64] [-0.58] [-2.26] [0.46] PreEA5DayRet *** *** * *** *** *** [-3.30] [-3.29] [-1.90] [-3.54] [-3.43] [-2.12] Size * [-1.78] [-1.40] [-1.17] [-1.41] [-1.59] [-0.83] M/B ** ** [-0.80] [-2.04] [-0.12] [-1.13] [-2.24] [0.30] Accruals ** ** * [2.23] [1.57] [1.48] [2.34] [1.63] [1.64] R 2 N 0.63% 18, % 6, % 12,037 18,805 6,768 12,037 This table presents the results of multivariate and univariate regressions with EARet as the dependent variable. Results are presented for three time periods: the full sample period ( ), the first half of the sample period ( Q2), and the second half of the sample period (2003Q3 - ). To conserve space, univariate results for regressions over the same time period are presented in the same column. EARet is the firm s two-day abnormal return at the earnings announcement. Specifically, it is the compounded return for the firm less the compounded return for the CRSP value-weighted index over the two-day earnings announcement period, [0, +1], where day 0 is the earnings announcement date in I/B/E/S (adjusted for after-hours announcements). LagEARet is the firm s EARet from the previous calendar quarter. ESurp is the firm s earnings surprise. Specifically, it is the firm s actual earnings less the mean analyst forecast, scaled by the firm s stock price six days prior to the earnings announcement. LagESurp is the firm s ESurp form the previous calendar quarter. The option variables: Spread, Skew, and O/S are calculated on the day prior to the earnings announcement based on a single set of the firm s options with the same expiration. The set of options examined are the ones closest to expiration with no more than 40 days to expiration. Spread is calculated as the implied volatility of a call for a given strike price and expiration less the implied volatility of the put with the same strike price and expiration as the call, these differences are then weighted by the amount of open interest in all strike price pairs with the same expiration. Skew is the implied volatility of an out-of-themoney put (i.e., delta closest to -0.25, given a delta of [-0.375, ]) less the implied volatility on an at-the-money call (i.e., delta closest to 0.5, given a delta of [0.375, 0.625]). O/S is the ratio of option market volume to stock market volume on the day prior to the firm s earnings announcement. PreEA5DayRet is the firm s abnormal return over the five trading days prior to their earnings announcement. Size is the firm s market capitalization six days prior to the earnings announcement in billions of dollars. M/B is the firm s Size divided by the firm s book value. Accruals is the firm s income before extraordinary items less cash flow from operating activities, scaled by average total assets (all from the prior quarter). Standard errors are clustered on two dimensions, firm and quarter. t-statistics are in brackets. ***, **, and * indicate significance at 1%, 5%, and 10% levels, respectively. 6

7 Online Appendix Table A3 Predicting Earnings Announcement Returns for ATSO Firms So and Wang s (2014) PAR variable replaces PreEA5DayRet (1) (2) (3) (4) (5) (6) Prior Multivariate Multivariate Multivariate Univariate Univariate Univariate Literature Q2 2003Q Q2 2003Q3 - Intercept % 0.33% ** -0.04% 0.10% 0.34% ** -0.04% [0.95] [2.09] [-0.35] [1.03] [2.16] [-0.35] LagEARet % ** -0.25% -1.04% *** -1.00% *** -0.27% -1.41% *** [-2.49] [-0.44] [-2.95] [-3.33] [-0.49] [-4.30] LagESurp % *** -0.34% -1.09% *** -1.06% *** -0.37% -1.43% *** [-3.78] [-0.95] [-3.77] [-4.83] [-1.14] [-5.18] Spread % *** 1.68% *** 1.01% ** 1.11% *** 1.72% *** 0.77% * [3.59] [3.33] [2.28] [3.67] [4.44] [1.91] Skew % 0.06% 0.42% -0.44% * -1.01% *** -0.11% [0.70] [0.12] [1.19] [-1.79] [-2.94] [-0.37] O/S % -0.74% ** 0.31% -0.12% -0.86% ** 0.30% [-0.35] [-2.22] [1.21] [-0.55] [-2.46] [1.16] PAR % *** -1.76% *** -0.84% ** -1.25% *** -1.85% *** -0.91% *** [-4.09] [-3.36] [-2.48] [-4.30] [-3.56] [-2.65] Size % -0.12% 0.25% 0.21% -0.11% 0.39% [0.20] [-0.24] [0.71] [0.83] [-0.24] [1.29] M/B % -0.07% 0.23% -0.19% -0.30% 0.14% [0.27] [-0.16] [0.51] [-0.06] [-0.72] [0.31] Accruals % 0.61% 0.12% 0.33% 0.67% 0.14% [1.33] [1.28] [0.58] [1.49] [1.40] [0.68] R % 0.80% 0.63% N 18,805 6,768 12,037 18,805 6,768 12,037 This table presents the results of multivariate and univariate regressions with EARet as the dependent variable. Results are presented for three time periods: the full sample period ( ), the first half of the sample period ( Q2), and the second half of the sample period (2003Q3 - ). To conserve space, univariate results for regressions over the same time period are presented in the same column. All independent variables are transformed into decile rankings and scaled to have a range of 1, [-0.5, 0.5], and a mean of zero. EARet is the firm s two-day abnormal return at the earnings announcement. Specifically, it is the compounded return for the firm less the compounded return for the CRSP value-weighted index over the two-day earnings announcement period, [0, +1], where day 0 is the earnings announcement date in I/B/E/S (adjusted for after-hours announcements). LagEARet is the firm s EARet from the previous calendar quarter. ESurp is the firm s earnings surprise. Specifically, it is the firm s actual earnings less the mean analyst forecast, scaled by the firm s stock price six days prior to the earnings announcement. LagESurp is the firm s ESurp form the previous calendar quarter. The option variables: Spread, Skew, and O/S are calculated on the day prior to the earnings announcement based on a single set of the firm s options with the same expiration. The set of options examined are the ones closest to expiration with no more than 40 days to expiration. Spread is calculated as the implied volatility of a call for a given strike price and expiration less the implied volatility of the put with the same strike price and expiration as the call, these differences are then weighted by the amount of open interest in all strike price pairs with the same expiration. Skew is the implied volatility of an out-of-the-money put (i.e., delta closest to -0.25, given a delta of [-0.375, ]) less the implied volatility on an at-the-money call (i.e., delta closest to 0.5, given a delta of [0.375, 0.625]). O/S is the ratio of option market volume to stock market volume on the day prior to the firm s earnings announcement. PAR is the firm s abnormal return over three trading days prior to their earnings announcement, [-4, -2], where day 0 is the earnings announcement date. Size is the firm s market capitalization six days prior to the earnings announcement in billions of dollars. M/B is the firm s Size divided by the firm s book value. Accruals is the firm s income before extraordinary items less cash flow from operating activities, scaled by average total assets (all from the prior quarter). Coefficients are presented in percentage format for presentation purposes. Standard errors are clustered on two dimensions, firm and quarter. t-statistics are in brackets. ***, **, and * indicate significance at 1%, 5%, and 10% levels, respectively. 7

8 Online Appendix Table A4 Predicting Earnings Announcement Returns for Non-ATSO Firms Continuous Independent Variables (1) (2) (3) (4) (5) (6) Prior Multivariate Multivariate Multivariate Univariate Univariate Univariate Literature Q2 2003Q Q2 2003Q3 - Intercept *** [1.39] [2.63] [0.06] [0.99] [1.37] [0.30] LagEARet [1.57] [0.96] [1.14] [1.22] [0.86] [0.84] LagESurp * ** * [-1.89] [0.78] [-2.06] [-1.38] [0.53] [-1.55] PreEA5DayRet *** *** *** *** *** *** [-9.26] [-7.53] [-5.75] [-8.83] [-7.55] [-5.24] Size [1.29] [0.72] [1.31] [0.96] [0.59] [0.79] M/B ** ** * ** ** [-2.46] [-2.36] [-1.66] [-2.31] [-2.12] [-1.47] Accruals * *** * *** [-0.53] [1.67] [-2.72] [-0.36] [1.81] [-2.59] 0.57% 1.17% 0.39% N 76,462 25,639 50,823 76,462 25,639 50,823 This table presents the results of multivariate and univariate regressions with EARet as the dependent variable. Results are presented for three time periods: the full sample period ( ), the first half of the sample period ( Q2), and the second half of the sample period (2003Q3 - ). To conserve space, univariate results for regressions over the same time period are presented in the same column. EARet is the firm s two-day abnormal return at the earnings announcement. Specifically, it is the compounded return for the firm less the compounded return for the CRSP value-weighted index over the two-day earnings announcement period, [0, +1], where day 0 is the earnings announcement date in I/B/E/S (adjusted for afterhours announcements). LagEARet is the firm s EARet from the previous calendar quarter. ESurp is the firm s earnings surprise. Specifically, it is the firm s actual earnings less the mean analyst forecast, scaled by the firm s stock price six days prior to the earnings announcement. LagESurp is the firm s ESurp form the previous calendar quarter. PreEA5DayRet is the firm s abnormal return over the five trading days prior to their earnings announcement. Size is the firm s market capitalization six days prior to the earnings announcement in billions of dollars. M/B is the firm s Size divided by the firm s book value. Accruals is the firm s income before extraordinary items less cash flow from operating activities, scaled by average total assets (all from the prior quarter). Standard errors are clustered on two dimensions, firm and quarter. t-statistics are in brackets. ***, **, and * indicate significance at 1%, 5%, and 10% levels, respectively. R 2 8

9 Online Appendix Table A5 Propensity to Have Actively Traded Stock Options at Earnings Announcements (1) (2) (3) Q2 2003Q3 - Intercept *** *** [5.15] [0.85] [8.24] Size *** *** *** [5.44] [4.65] [3.06] Volume *** *** *** [10.74] [10.21] [23.40] AbVolume *** *** *** [8.83] [12.32] [3.54] Volatility ** *** [-1.58] [2.41] [-5.46] AbVolatility [-0.76] [-0.37] [-0.72] Avg. Adj. R % 16.84% 10.14% N This table presents the results of Fama-MacBeth regressions with ActiveOptions as the dependent variable. ActiveOptions is an indicator variable equal to one for earnings announcements from the ATSO sample, and zero otherwise. Results are presented for three time periods: the full sample period ( ), the first half of the sample period ( Q2), and the second half of the sample period (2003Q3 - ). Size is the firm s market capitalization six days prior to the earnings announcement in billions of dollars. Volume is the firm s average trading volume over the 250 trading days prior to the earnings announcements in millions of shares. AbVolume is the firm s average trading volume over the 30 trading days prior the earnings announcement in millions of shares divided by Volume. Volatility is the standard deviation of the firm s stock return over the 250 trading days prior to the earnings announcements. AbVolatility is the standard deviation of the firm s stock return over the 30 trading days prior to the earnings announcement divided by Volatility. t-statistics are in brackets. ***, **, and * indicate significance at 1%, 5%, and 10% levels, respectively. 9

10 Online Appendix Table A6 Time-series Mean of Portfolio Returns Propensity Matched Non-ATSO Firms Time Period Quarters Q2 30 Quarters 2003Q3 30 Quarters Panel A: Earnings Announcement Returns to Decile Portfolios of LagEARet Low (Past Losers) -0.26% [-0.26%] -0.76% [-0.58%] 0.25% [-0.22%] % [0.12%] 0.08% [0.10%] -0.03% [-0.10%] % [0.35%] -0.03% [0.23%] 0.38% * [0.47%] % [0.23%] 0.56% [0.81%] -0.05% [0.05%] % [0.04%] 0.05% [0.22%] -0.09% [-0.08%] % [0.20%] 0.08% [-0.13%] 0.16% [0.32%] % [0.10%] 0.29% [0.32%] 0.11% [-0.19%] % [-0.10%] 0.20% [0.14%] -0.07% [-0.19%] % [0.08%] 0.22% [0.43%] -0.25% [-0.15%] High (Past Winners) -0.34% [-0.48%] -0.33% [-0.45%] -0.36% [-0.48%] High Low -0.09% [0.25%] 0.43% [0.99%] -0.61% [-0.37%] Panel B: Earnings Announcement Returns to Decile Portfolios of LagESurp Low (Past Losers) -0.05% [0.35%] -0.06% [-0.30%] -0.04% [0.57%] % [-0.14%] -0.69% * [-0.66%] 0.23% [0.35%] % [0.10%] 0.26% [0.01%] 0.26% [0.37%] % [-0.09%] -0.20% [-0.47%] 0.21% [0.07%] % [0.13%] 0.16% [0.25%] 0.18% [0.07%] % ** [0.37%] 0.35% [0.33%] 0.28% ** [0.37%] % [0.30%] 0.25% [0.43%] -0.11% [0.13%] % [0.37%] 0.83% ** [0.92%] -0.24% [-0.17%] % [-0.56%] -0.38% [-0.14%] -0.32% [-0.67%] High (Past Winners) -0.21% [-0.67%] 0.13% [-0.21%] -0.55% [-1.05%] High Low -0.16% [-0.58%] 0.19% [0.20%] -0.51% [-1.67%] This table presents mean and median (in brackets) earnings announcement abnormal returns for decile portfolios created based on prior earnings announcement news for the propensity matched sample (i.e., the firms from the Non-ATSO sample that are most similar to the firms from the ATSO sample). Portfolio returns are presented for three time periods: the full sample period ( ), the first half of the sample period ( Q2), and the second half of the sample period (2003Q3 - ). The High - Low portfolios are hedge portfolios that take long positions in firms in the highest decile of the prior quarter s earnings announcement news and short positions in firms in the lowest decile of the prior quarter s earnings announcement news. In Panel A, the prior quarter s earnings news is determined by LagEARet. LagEARet is the firm s two-day abnormal return at the earnings announcement from the prior calendar quarter. In Panel B, the prior earnings news is determined by LagESurp. LagESurp is the firm s earnings surprise from the prior calendar quarter. ***, **, and * indicate that the mean is significant at 1%, 5%, and 10% levels, respectively. 10

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