O/S and price momentum

If undervaluation is the common underlying factor for the O/S trend and for the price momentum during the pre-split period, the two should be related to each other. To demonstrate such a relation and to show which one is more informative about undervaluation, we add Ln(O/S), the natural logarithm of average O/S in month t–1, to the cross-sectional regression model in Table 5 as an explanatory variable for stock returns in month t. Panels A and B of Table 6 report the regression results for the split sample and the non-split sample, respectively. Note that we use the predictability of O/S on future stock returns to illustrate stock undervaluation. It is different from the predictability of O/S on the absolute values of future stock returns, which essentially predicts the volatility of future stock returns.

<<TABLE 6 ABOUT HERE>>

The results in Panel A of Table 6 show that O/S is significantly positive during the pre-split period. Its coefficient ranges from 0.008 (t-value = 2.61) in month –4 to 0.019 (t-value = 3.84) in month –1. In contrast, Runup, which is significant during the five months prior to stock splits in Table 5, becomes insignificant during the pre-split period, except for month –3. In month –3, the coefficient of Runup declines from 0.021 value = 2.87) in Table 5 to 0.013 (t-value = 2.06) in Table 6. The results suggest that split firms’ Runup and O/S contain some common information about their future stock returns and that the latter has stronger predictive power on their future stock returns than the former. This evidence is consistent with the notion that informed traders are more inclined to use listed options than the underlying stock to take advantage of stock undervaluation, causing O/S to have stronger predictive power on future stock returns than Runup. Furthermore, Runup is likely a noisy proxy for the extent of existing shareholders’ portfolio rebalancing needs induced by price run-ups because the composition of shareholders changes as trades occur.

The predictive power of split firms’ O/S on future stock returns also prevails in the split announcement month, with a coefficient of 0.017 (t-value = 4.57). However, the predictive power of split firms’ O/S on future stock returns becomes insignificant in the post-split period, except for months +2 and +4 in which the coefficients of O/S are significantly negative, unlike those in the pre-split period. Similarly, Panel B of Table 6 shows that, unlike split firms’ O/S in the pre-split period, non-split firms’ O/S does not have consistent predictive power on future stock returns either in the pre-split or the post-split period.

Thus, the predictive power of O/S in the pre-split period and in the split announcement month confirms that stock undervaluation exists prior to stock splits and that informed traders use listed options to exploit such undervaluation. The declining of the predictive power of O/S in

the post-split period implies that firms are able to use stock splits to attract more investors and resolve the undervaluation problem. Consequently, following stock splits, the appeal of trading on options declines, and it becomes more difficult to predict future stock returns.

To reiterate, the finding that stock returns in the pre-split period are predictable using the previous month’s O/S implies that split firms’ stock prices do not efficiently impound the information content of the previous month’s options trading volume relative to the stock’s trading volume. This result is consistent with our earlier argument that the market does not function well in price discovery in the pre-split period and that stock splits improve this function of the market. That is, by attracting more new investors to offset the selling pressure from existing shareholders who are rebalancing their portfolios after significant price run-ups, stock splits, as a corporate tool, improve market efficiency.

To further demonstrate that the market is less efficient before stock splits, Table 7 reports the results of using O/S, averaging over days –22 to –3 relative to the earnings announcement date, to predict earnings announcement returns in the quarter before and the quarter after stock splits.⁸

8 We measure earnings announcement returns as the five-day (–2,+2) abnormal returns, using the CRSP value-weighted index returns over the same five-day period as the benchmark. Following Denis and Sarin (2001), we control for firm size, B/M, the standardized changes in earnings, and accruals in earnings announcement return regression. The change in earnings in each quarter t is measured as the difference between earnings in quarter t and earnings in quarter t–4, expressed as a percentage of the market value of the firm.

The results show that O/S can predict upcoming earnings announcement returns prior to stock splits, suggesting that informed investors tend to increase their trading of listed options the more that the market underprices the firms’ earnings potentials. However, the predictive power of O/S on earnings announcement returns disappears after stock splits. This evidence is consistent with our hypothesis that, weighed down by the selling pressure from existing shareholders’ portfolio rebalancing needs, the stocks are undervalued prior to stock splits, which provides room for informed traders to exploit their information advantage using listed options.

After stock splits, the equity market becomes more efficient as more new investors are attracted to meet existing shareholders’ portfolio rebalancing needs, and listed options become less appealing.

<<TABLE 7 ABOUT HERE>>

Roll, Schwartz, and Subrahmanyam (2010) suggest that O/S is informative about the absolute values of earnings announcement returns. In this case, instead of underpricing the firms’

earnings potentials, the market is uncertain about the outcomes of the upcoming earnings announcements, and such uncertainty provides room for informed investors to use options to exploit their information advantage. Because uncertainty about the outcomes of the upcoming earnings announcements would exist even if the market becomes more efficient, we expect that the predictability of O/S on the absolute values of earnings announcement returns will not be affected by stock splits. Indeed, consistent with Roll, Schwartz, and Subrahmanyam, Table 7 reports that O/S has such predictive power in both the quarter before and the quarter after stock splits. Thus, while stock splits improve market efficiency and take away the usefulness of O/S in predicting earnings announcement returns, they do not alter the predictability of O/S on the absolute values of earnings announcement returns, as reported by Roll, Schwartz, and Subrahmanyam (2010).