Robustness Checks

We perform additional tests on our trading strategies based on splits and SUEs as a robustness check. First, we regress returns of long–short calendar-time portfolios generated from our trading strategies on asset pricing factors. We examine whether the trading strategies survive with the control of important factors in explaining cross-section returns. Second, we repeatedly roll over our long–short portfolios for the long run and compare their long-term performance

with major market benchmarks, such as the small firm portfolio and the value firm portfolio. We investigate whether our strategies dominate the major index that people watch closely. Third, we construct a quarterly rebalanced portfolio and check whether its return performance persists over time. Finally, we use the new approach proposed by Bessembinder and Zhang (2013) to test whether the abnormal returns to split firms and high SUE firms can be explained by firm characteristics.

Table 7 reports the abnormal returns generated from the long–short calendar-time strategies based on stock splits and SUEs. We form a long–short portfolio by buying firms that had a split announcement and experienced a high SUE in the past x months and selling their corresponding size, B/M, and momentum matched control firms that had no stock splits and experienced a low SUE in the past x months, where x is equal to 3, 6, or 12.⁵ As the sample size gets smaller when requiring both stock split status and extreme SUE ranks, we pool the bottom two SUE quintiles as low SUE firms, and top two SUE quintiles as high SUE firms. To determine whether our long–short portfolio works, we compare its returns with those of long–

short strategies formed solely based on whether firms announce stock splits or whether firms experience extreme SUEs.

[TABLE7 ABOUT HERE]

5 We re-form the portfolio every month and regress its returns on five factors: Carhart’s (1997) four factors plus the liquidity factor based on Pastor and Stambaugh (2003). The abnormal return is measured by the alpha of the WLS regressions where the weight is the number of firms in each month. Our results are very similar with different factor models (i.e., Fama–French three-factor; Carhart four-factor) and different weighting schemes (i.e., OLS; WLS).

We find that the long–short strategy combining splits and extreme earnings surprises generate remarkably large abnormal returns. The average monthly alpha is 1.63% (0.96%) in the equal-weighted long–short portfolio over a three-month horizon, even with the control of important asset pricing factors, such as size, B/M, momentum, and liquidity. Over a year, the abnormal monthly return amounts to 0.84 % and 0.72% for the equal-weighted and value-weighted portfolios, respectively. These abnormal returns using two-way sorts on splits and SUEs are larger than those by one-way sort portfolios based on splits only (equal-weighted:

0.45%; weighted: 0.37%) and based on SUEs only (equal-weighted: 0.24%; value-weighted: 0.17%). This result is consistent with Table 5 and confirms that both splits and SUEs have incremental power to predict stock returns.

To avoid the short-sale constraint and potential high short-selling costs in implementing the long–short strategies, we repeat a similar analysis by focusing on the long positions only and report the results in Table 8. We find that the two-way sort portfolio based on splits and high SUEs generates a monthly alpha of 1.26% (0.54%) in the equal-weighted (value-weighted) case over the three post-event months. Consistent with Table 7, this abnormal return is larger than that of the portfolio formed based on splits only or based on high SUEs only. Next, we examine the long-run performance of our long–short portfolio by rolling over the long–short trading strategy.

We take the monthly value-weighted raw returns and compound these returns over the entire sample period (1984–2011) for both the long and short positions. The abnormal return for the long–short portfolio is the difference in compounded returns between long and short positions.

We compare the return performance with that of the market index based on CRSP value-weighted index returns, of the Small portfolio, which includes small firms with a bottom size quintile rank using NYSE cutoffs, and of the Value portfolio, which includes firms with a top B/M quintile rank. Figure 2 plots the return performance of our trading strategies and major market benchmarks. Our long–short portfolio based on splits and SUEs simultaneously generates an enormous return of 504% and outperforms the major market benchmarks.

[FIGURE 2 ABOUT HERE]

We then examine the quarter-by-quarter BHARs of our long–short portfolio. At the beginning of each calendar quarter, we implement the long–short strategy by buying firms that have both high SUEs (in the top two SUE quintiles) and split announcements in the past quarter and selling firms that have low SUEs (in the bottom two SUE quintiles) and no split announcements in the past quarter. We hold the portfolio for a quarter and rebalance it in each quarter. To measure abnormal returns, for both the long and the short positions, we subtract the return of size, B/M, and momentum-matched control firms and then get the difference in abnormal returns between long and short positions. In other words, we perform the difference-in-difference between winners (splits and high SUEs) and losers (non-splits and low SUEs).

Figure 3 plots BHARs over the quarters from 1984 to 2011. Over the 108 quarters, the long–short portfolio generates positive BHARs with about 70% chance (75 quarters).⁶ The average quarterly BHAR is 4.31%, which is close to the abnormal return of the two-way sort portfolio in Table 5. When we separate the analysis into two subsample periods, 1984 to 1997 and 1998 to 2011, the percentage of quarters with positive BHARs is similar, 71% and 68%, respectively. The average BHAR is 5.24% and 3.34%, separately, for the two subperiods. We conclude that our long–short portfolio based on both splits and SUEs earns a positive return drift with a high probability.

[FIGURE 3 ABOUT HERE]

In addition, following Hou, Xue, and Zhang (2012), we repeat the analysis in Tables 2, 7, and 8 by using a q-factor model to check the robustness of our findings. The results are report in Appendix Tables I and II.⁷ The q-factor model consists of the market factor, size factor, investment factor, and return-on-equity factor. All these robustness tests yield consistent results.

6. Conclusions

The literature reports two anomalies that are related to future earnings: post-split drift and PEAD. We explore the relation between these two anomalies and test whether they are driven by

6 We do not have sufficient sample firms to construct the long–short portfolio for three quarters (the first three quarters of 2009) from the second quarter of 1984 to the fourth quarter of 2011.

7 We thank Chen Xue for making the q-factors available to us.

the same source of information. In examining the connection between the anomalies, we check whether stock splits continue to generate abnormal returns as some prior studies raise a concern that the post-split drift is spurious. We also investigate the duration of post-split drift to determine whether splits and earnings surprises evoke abnormal returns over the same horizon.

Using splits announced from 1984 to 2011, we show an abnormally positive return in the one-year following stock splits. Consistent with the literature, we find that the post-split drift holds under different approaches and over different sample periods. We then examine the month-by-month return performance during the post-split 12-month horizon and find that the significantly positive abnormal return occurs mainly in the first few post-split months and disappears after seven months of stock splits, suggesting that the post-split drift is a short-term phenomenon.

To the extent that PEAD is also a short-term anomaly, lasting for up to six months, we test whether the post-split drift can be explained by PEAD. We find that abnormal returns following splits are indeed related to earnings surprises, but other factors, such as liquidity improvement, are also important. We further show that both splits and earnings surprises can explain cross-section variation of stock returns. As a result, although both the post-split drift and PEAD are related to future earnings changes, they are two distinct anomalies.

Because splits and earnings surprises represent different pieces of information, we explore a trading strategy based on split announcements and extreme earnings surprises simultaneously. The long–short portfolio formed by buying split firms with positive earnings surprises and selling non-split firms with negative earnings surprises generates an abnormal

return of 4.9% over a three-month horizon or about 20% in an annual basis. This result is fairly robust under different approaches.

This study makes important contributions to the literature. First, we address the debate about whether a real return drift exists following stock splits. We find that firms yield positive abnormal returns in the post-split period not only in the 1970s and 1980s but also in recent years.

Second, we shed light on the relation between post-split drift and PEAD. While both share the information of future earnings, splits, and earnings surprises, each has incremental return predictability. Finally, we design a profitable trading strategy that exploits the post-split drift and PEAD. The strategy generates remarkably large returns. This finding has important implications to both investors and researchers.

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