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Table 1 Summary Statistics
This table reports summary statistics of firm characteristics for split firms (Panel A) and matched non-split firms (Panel B). We consider all stock split announcements from the CRSP with a split factor of at least 0.25 during 1996 to 2012 and require split firms to be covered by OptionMetrics and have common shares (CRSP share code 10 or 11). Matched non-split firms are matched by size and book-to-market ratio (B/M) and have no stock split in a two-year window centered around the split announcement. Price is the average stock price from day –22 to –3 relative to the split announcement date. Ln(price) is the natural logarithm of Price. Size is the natural logarithm of pre-split market capitalization in millions measured at day –23. B/M is the pre-split book-to-market ratio from Compustat.
Runup is the pre-split 11-month cumulative stock return from month –12 to day –23 before splits. Age is the number of years that the firm exists in the CRSP. Common shareholders is the number of common shareholders at previous year end (in thousands). Institutional investors is the number of institutional investors in the previous three months.
Percentage holding is average percentage holding of institutional investors in the three months prior to split.
Institutional ownership is a firm’s shares held by institutions from Thomson Reuters scaled by shares outstanding from the CRSP. Analyst is the number of I/B/E/S analysts who provide one-year earnings forecasts in the previous three months. Analyst dispersion is the standard deviation across earnings forecasts in previous three months. ShO/S is the average ratio of total options trading volume to the corresponding stock trading volume. $O/S is the average ratio of dollar options trading volume to the corresponding dollar stock trading volume, expressed in percentage.
Ln(ShO/S)and Ln($O/S)are natural logarithms of ShO/S and $O/S, respectively. Implied volatility is from OptionMetrics, which is calculated with American or European models (as appropriate). Delta is the delta of the option, which indicates the change in option premium for a $1.00 change in underlying price. Spread is the average bid-ask spread divided by the midpoint of all options traded. For each day, a firm’s average Spread, Implied volatility and Delta (put deltas are reversed in sign) are value-weighted based on options trading volume. ShO/S,
$O/S, Spread, Implied volatility, and Delta are based on the average values from day –22 to –3 relative to the split announcement date. CAR is (–2,+2) five-day abnormal returns around the split announcement date, with the CRSP value-weighted index returns as the benchmark. N is the number of observations.
Mean Median Q1 Q3 Std Min Max N
Table 1 (continued)
Panel B: Matched non-split firms
Mean Median Q1 Q3 Std Min Max N
Price 38.165 34.285 22.599 49.156 24.791 2.903 407.246 1,636
Ln(price) 3.476 3.535 3.118 3.895 0.591 1.066 6.009 1,636
Size 8.001 7.880 7.076 8.797 1.238 5.160 12.517 1,636
B/M 0.320 0.269 0.156 0.431 0.252 –0.390 3.831 1,621
Runup 0.325 0.169 –0.053 0.416 1.074 –0.892 24.431 1,636
Age 22 15 7 31 20 2 88 1,636
Common shareholders 28 5 1 20 121 0.002 3,367 1,574
Institutional investors 215 169 103 280 168 1 1,116 1,635
Percentage holding 0.004 0.004 0.002 0.005 0.002 0.0003 0.021 1,631 Institutional ownership 0.647 0.680 0.493 0.818 0.227 0.001 1.000 1,635
Analyst 9 8 5 13 6 0 39 1,636
Analyst dispersion 0.122 0.061 0.024 0.134 0.229 0.000 3.342 1,512
ShO/S 0.095 0.055 0.021 0.126 0.130 0.0001 2.694 1,636
Ln(ShO/S) –3.052 –2.897 –3.855 –2.069 1.317 –9.259 0.991 1,636
$O/S (%) 0.805 0.390 0.149 0.963 1.388 0.003 28.626 1,636
Ln($O/S) –5.606 –5.548 –6.511 –4.643 1.321 –10.317 –1.251 1,636
Implied volatility 0.442 0.393 0.296 0.533 0.208 0.065 1.483 1,621
Delta 0.459 0.453 0.415 0.496 0.071 0.080 0.965 1,621
Spread 0.253 0.221 0.168 0.294 0.149 0.049 2.000 1,636
Table 2
Changes in common shareholders and their holdings following stock splits
This table shows changes in the number of common shareholders (institutional investors) and in the average percentage holding per common shareholder (per institutional investor) following stock splits, based on 1,636 stock splits and their matched non-split firms. Common shareholders, institutional investors, analyst and analyst dispersion are defined as in Table 1. Number of insiders and percentage holding of insiders are from Thomson Reuters. Change in number of institutional investors, change in average percentage holding per institutional investor, change in number of analysts, change in analyst dispersion, change in number of insiders, and change in average percentage holding per insider are calculated based on the difference in each variable between three months after and three months before stock splits. Change in number of common shareholders and Change in average percentage holding per common shareholder are calculated based on the difference between post-split and pre-split one year. Average percentage holding per common shareholder is calculated as 100% divided by the number of common shareholders. Average percentage holding per institutional investor is the total institutional percentage holdings divided by the number of institutional investors. All the changes are calculated as the natural logarithm of post-split values minus the natural logarithm of pre-split values. Difference is the mean of paired differences between split firms and their non-split counterparts.
Split firms Matched non-split firms
Difference t-value
Mean t-value Mean t-value
Change in number of common shareholders(in thousands) 0.177 8.43 0.005 0.29 0.171 6.21
Change in average percentage holding per common shareholder –0.177 –8.43 –0.005 –0.29 –0.171 –6.21
Change in number of institutional investors 0.137 21.43 0.081 7.57 0.056 4.51
Change in average percentage holding per institutional investor –0.169 –26.17 –0.008 –1.66 –0.161 –20.56
Change in number of analysts 0.095 8.46 0.039 2.58 0.056 3.08
Change in analyst dispersion 0.160 4.64 –0.033 –0.98 0.192 4.37
Change in number of insiders –0.034 –1.36 –0.044 –1.60 0.010 0.29
Change in average percentage holding per insider –0.127 –2.38 –0.152 –2.45 0.024 0.30
Table 3
The association between change in average percentage shareholding and stock price run-ups
This table shows the results of regressing change in the average percentage shareholding per common shareholder and per institutional investor on Runup and control variables. The dependent variable is change in average percentage holding per common shareholder in Models 1 and 3 and change in average percentage holding per institutional investor in Models 2 and 4. Change in average percentage holding per common shareholder is calculated based on the difference between post-split and pre-split one year. Average percentage holding per common shareholder is calculated as 100% divided by the number of common shareholders. Change in average percentage holding per institutional investor is calculated based on the difference between post-split and pre-split three months as defined in Table 2. Average percentage holding per institutional investor is the total institutional percentage holdings divided by the number of institutional investors. Runup is the pre-split 11-month cumulative stock return from month –12 to day –23 before the split announcement date. Size is the natural logarithm of pre-split market capitalization in millions measured at day –23. B/M is the pre-split book-to-market ratio from Compustat. Illiquidity is Amihud’s (2002) illiquidity measure defined as the average ratio of the daily absolute return to its dollar trading volume. Illiquidity is previous one-year average. Numbers in parentheses are t-statistics based on White (1980) heteroskedasticity-adjusted standard errors. ***, **, and * indicate the significance levels of 1%, 5%, and 10%, respectively.
Table 4
The momentum effect on split firms’ share turnover
This table shows cross-sectional regressions of turnover on Runup and control variables from month –6 to month 0 relative to the split announcement month and month 0 to month +6 relative to the ex-distribution month. Panel A reports results for split firms, and Panel B reports results for matched non-split firms. The dependent variable is average turnover in each month. Turnover is stock trading volume divided by shares outstanding. Runup is the cumulative return from months –12 to month –2. Size is the natural logarithm of market capitalization in millions measured at the previous month end. B/M is the book-to-market ratio from Compustat. Illiquidity is Amihud’s (2002) illiquidity measure defined as the average ratio of the daily absolute return to its dollar trading volume. Illiquidity is previous one-month average. Analyst is the number of I/B/E/S analysts who provide one-year earnings forecasts in the previous three months. Dispersion is the standard deviation across earnings forecasts in the previous three months. Ioship is institutional ownership defined as a firm’s shares held by institutions from Thomson Reuters scaled by shares outstanding from the CRSP. Panel C reports the panel regression results based on all the months excluding month 0 (split announcement month and ex-distribution month). Post-split dummy and an interaction term Post-split dummy × Runup are added into the regression. Post-split dummy equals one for month +1 to month +6. The coefficients of Analyst are multiplied by 100. Numbers in parentheses are t-statistics based on White (1980) heteroskedasticity-adjusted standard errors. ***, **, and * indicate the significance levels of 1%, 5%, and 10%, respectively.
Month –6 to month 0 relative to the announcement month Month 0 to month +6 relative to the ex-distribution month
Month –6 –5 –4 –3 –2 –1 0 0 +1 +2 +3 +4 +5 +6
Table 4 (continued)
Runup Post-split dummy Size B/M Illiquidity Analyst Dispersion Ioship Constant Obs. Adj. R2 Split firms 0.004*** –0.002* 0.001** –0.003*** –0.002*** –0.297*** 0.031*** 0.010*** 0.004*** 0.023*** 18,120 0.131
(5.46) (–1.93) (2.12) (–20.78) (–5.40) (–12.75) (24.12) (12.54) (4.07) (16.34)
Non-split firms 0.002*** –0.001 0.0004 –0.002*** –0.002** –0.100*** 0.037*** 0.005*** 0.010*** 0.015*** 17,712 0.221
(3.28) (–0.65) (1.54) (–13.12) (–2.12) (–7.67) (10.11) (3.13) (11.30) (8.50)
Table 5
The momentum effect on split firms’ stock returns
This table shows cross-sectional regressions of split firms’ stock returns on Runup and control variables from month –6 to month 0 relative to the split announcement month and month 0 to month +6 relative to the ex-distribution month. Panel A reports results for split firms, and Panel B reports results for matched non-split firms. The dependent variable is monthly excess return with CRSP value-weighted index returns as the benchmark. Runup is the cumulative return from month –12 to month –2. Size is the natural logarithm of market capitalization in millions measured at the previous month end. B/M is the book-to-market ratio. Illiquidity is Amihud’s (2002) illiquidity measure defined as the average ratio of the daily absolute return to its dollar trading volume. Illiquidity is previous month average. Panel C reports the panel regression results based on all the months excluding month 0. split dummy and an interaction term Post-split dummy × Runup are added into the regression. Post-Post-split dummy equals one for month +1 to month +6. Numbers in parentheses are t-statistics based on White (1980) heteroskedasticity-adjusted standard errors. ***, **, and * indicate the significance levels of 1%, 5%, and 10%, respectively.
Month –6 to month 0 relative to the announcement month Month 0 to month +6 relative to the ex-distribution month
Table 5 (continued) Panel C: Panel regression
Runup
Post-split dummy ×
Runup Post-split dummy Size B/M Illiquidity Constant Obs. Adj. R2
Split firms 0.016*** –0.008** –0.037*** –0.005*** –0.022*** 0.571*** 0.082*** 19,197 0.038
(5.79) (–2.33) (–14.48) (–6.06) (–4.59) (4.22) (10.38)
Non-split firms 0.004 –0.009 –0.009*** –0.006*** –0.013*** 0.358* 0.057*** 18,603 0.009
(0.99) (–1.57) (–4.38) (–5.19) (–2.59) (1.88) (5.45)
Table 6
The momentum effect and predictive power of O/S on split firms’ stock returns
This table shows cross-sectional regressions of split firms’ stock returns on Ln(ShO/S) and control variables from month –6 to month 0 relative to the split announcement month and month 0 to month +6 relative to the ex-distribution month. Panel A reports results for split firms, and Panel B reports results for matched non-split firms. The dependent variable is monthly excess return with CRSP value-weighted index returns as the benchmark. Ln(ShO/S) is the natural logarithm of average ShO/S in previous month. Runup is the cumulative return from month –12 to month –2. Size is the natural logarithm of market capitalization at previous month end. B/M is the book-to-market ratio. Illiquidity is previous one-month average. Panel C reports the panel regression results based on all the months excluding month 0 (split announcement month and ex-distribution month). Post-split dummy and an interaction term Post-split dummy × Ln(ShO/S) are added into the regression. Post-split dummy equals one for month +1 to month +6. Numbers in parentheses are t-statistics based on White (1980) heteroskedasticity-adjusted standard errors. ***, **, and * indicate the significance levels of 1%, 5%, and 10%, respectively.
Month –6 to month 0 relative to the announcement month Month 0 to month +6 relative to the ex–distribution month
Table 6 (continued)
Month –6 to month 0 relative to the announcement month Month 0 to month +6 relative to the ex–distribution month
Month –6 –5 –4 –3 –2 –1 0 0 +1 +2 +3 +4 +5 +6
Panel B：Non-split firms
Ln(ShO/S) –0.002 0.001 –0.003 0.007** 0.003 0.004 –0.005* –0.005* –0.005** –0.001 –0.001 0.002 –0.003 –0.007**
(–0.62) (0.48) (–1.01) (2.57) (1.08) (1.36) (–1.89) (–1.74) (–2.16) (–0.37) (–0.44) (0.75) (–0.98) (–2.43) Runup –0.002 0.007 –0.006 –0.010 0.009 –0.006 0.007 0.008 0.001 –0.010 –0.003 –0.019* –0.017 0.007 (–0.19) (0.67) (–0.60) (–0.97) (0.96) (–0.81) (0.88) (0.82) (0.13) (–0.98) (–0.24) (–1.73) (–1.61) (0.62) Size –0.006* –0.003 –0.010*** –0.010*** –0.012*** –0.014*** –0.003 0.007** 0.002 –0.004 –0.001 0.002 –0.004 –0.002 (–1.70) (–1.01) (–3.27) (–3.24) (–3.96) (–4.63) (–1.09) (2.42) (0.76) (–1.32) (–0.31) (0.51) (–1.15) (–0.73)
B/M 0.006 –0.009 –0.011 –0.011 –0.000 0.012 –0.002 0.020 0.008 –0.010 –0.013 –0.012 –0.021 –0.031*
(0.38) (–0.67) (–0.80) (–0.73) (–0.02) (0.74) (–0.15) (1.25) (0.51) (–0.67) (–0.77) (–0.85) (–1.39) (–1.73) Illiquidity –0.099 0.664 0.561 2.068* 0.651 0.280 –0.170 0.596 0.130 0.039 0.001 –0.083 0.248 –0.007 (–0.28) (1.58) (0.97) (1.94) (0.73) (0.39) (–0.28) (0.82) (0.17) (0.06) (0.00) (–0.22) (0.40) (–0.01) Constant 0.050 0.037 0.077** 0.109*** 0.120*** 0.124*** 0.006 –0.091*** –0.044 0.029 0.009 –0.001 0.030 0.006 (1.23) (1.17) (2.48) (3.19) (3.75) (3.81) (0.22) (–2.91) (–1.44) (0.90) (0.27) (–0.02) (0.87) (0.17)
Obs. 1,396 1,414 1,442 1,475 1,512 1,546 1,569 1,562 1,543 1,538 1,532 1,520 1,508 1,496
Adj. R2 0.001 0.006 0.019 0.029 0.020 0.021 0.001 0.004 0.000 0.000 0.001 0.002 0.005 0.004
Panel C: Panel regression
Ln(ShO/S)
Post–split dummy ×
Ln(ShO/S) Post–split dummy Runup Size B/M Illiquidity Constant Obs. Adj. R2
Split firms 0.009*** –0.010*** –0.070*** 0.008*** –0.006*** –0.021*** 0.348*** 0.120*** 18,118 0.035
(6.84) (–5.75) (–11.70) (4.76) (–6.45) (–4.76) (2.62) (11.20)
Non–split firms 0.001 –0.003* –0.019*** –0.003 –0.006*** –0.010** 0.213 0.060*** 17,922 0.006
(0.89) (–1.75) (–3.43) (–1.19) (–6.37) (–2.30) (1.50) (6.10)
Table 7
Predictability of O/S on Earnings Announcement Returns around Splits
This table presents the regressions of absolute earnings announcement returns and of earnings announcement returns on Ln(ShO/S) before and after splits. Earnings announcement return is five-day (–2,+2) abnormal return (CRSP value-weighted index return as the benchmark) around quarterly earnings announcements. Regressions are run separately before splits and after splits. Ln(ShO/S) is the natural logarithm of average ratio of total options trading volume to the corresponding stock trading volume from day –22 to day –3 relative to the earnings announcement date. Following Denis and Sarin (2001), we include the following control variables: Size is the natural logarithm of market capitalization in millions measured at day –23; B/M is the book-to-market ratio before earnings announcements; Change in earnings is the difference of earnings between quarter t and quarter t–4, expressed as a percentage of the firm’s market value at day –23; and, Accruals is calculated as the change in non-cash current assets less the change in current liabilities excluding the change in debt included in current liabilities and the change in income taxes payable, minus depreciation and amortization expense. Accruals are scaled by average total assets from the beginning to the end of a quarter. Numbers in parentheses are t-statistics based on White (1980) heteroskedasticity-adjusted standard errors. ***, **, and * indicate the significance levels of 1%, 5%, and 10%, respectively.
Dependent variable Absolute earnings announcement return Earnings announcement return Before splits After splits Before splits After splits
Ln(ShO/S) 0.009*** 0.011*** 0.006*** –0.004
Table 8
Cross-Sectional Regressions of Split Announcement Returns on O/S
This table shows the regressions of split announcement returns on pre-split O/S and various control variables. The dependent variable is (–2,+2) five-day abnormal returns (CRSP value-weighted index return as the benchmark) around split announcements. Ln(ShO/S) is the natural logarithm of the average ratio of total options trading volume to the corresponding stock trading volume from day –22 to day –3 relative to the stock split announcement date. Size is the natural logarithm of pre-split market capitalization in millions measured at day –23. B/M is the pre-split book-to-market ratio from Compustat. Ln(price) is the natural logarithm of the average stock price from day –22 to day –3.
Runup is the pre-split 11-month cumulative stock return from month –12 to day –23 before splits. Turnover is stock trading volume divided by shares outstanding. Illiquidity is Amihud’s (2002) illiquidity measure defined as the average ratio of the daily absolute return to its dollar trading volume. LM is Liu’s (2006) liquidity measure defined as the standardized turnover-adjusted number of days with zero trading volumes. Pre-split turnover, pre-split illiquidity, and re-split LM are estimated over days –22 to day –3 before the split announcement date; post-split turnover, post-split illiquidity, and post-split LM are estimated over day +3 to day +22 after the ex-distribution date.
Change in turnover, Change in illiquidity, and Change in LM are the differences between post-split estimates and pre-split estimates. Pre-split LM, post-split LM and change in LM are benchmark-adjusted (the difference between a split firm’s LM and that of its matched non-split firm) as in Lin et al (2009). Numbers in parentheses are t-statistics based on White (1980) heteroskedasticity-adjusted standard errors. ***, **, and * indicate the significance levels of 1%, 5%, and 10%, respectively.
Figure 1. Pre-Split and Post-Split Turnover of Split Firms vs. Matched Non-split Firms
Notes: This figure shows the pre-split average share turnover from month –12 to month –1 relative to the stock split announcement month and the post-split share turnover from month 1 to month 12 relative to the ex-distribution month for the split firms and their matched non-split firms, matched on size and B/M.
0.005 0.006 0.007 0.008 0.009 0.010
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12
turnover split firm turnover matching firm Declaration Month Ex-Distribution Month
Relative Month
Figure 2. Pre-Split and Post-Split O/S of Split Firms vs. Matched Non-split Firms
Notes: This figure shows the pre-split average ShO/S from month –12 to month –1 relative to the stock split announcement month and the post-split average ShO/S from month 1 to month 12 relative to the ex-distribution month for the split firms and their matched non-split firms, matched on size and B/M.
0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 O/S split firm O/S matching firm Declaration Month Ex-Distribution Month
Relative Month