1. Stock Splits, Trading Continuity, and the Cost of Equity Capital Ji-Chai Lin Louisiana State University Ajai K. Singh Case Western Reserve University Wen Yu University of St. Thomas For presentation at NTU, December 2008 Comments welcome

2. "You better cut the pizza in four pieces because I'm not hungry enough to eat six." —Yogi Berra, when asked if he wanted his pizza cut into four or six pieces.

3. Stock Splits: A Simple Corporate Event For example, a firm has 10 million shares outstanding, traded at $50 per share. If the firm announces a 2-for-1 split, Its investors will receive one new share for every old share they have. So, the number of outstanding shares would increase to 20 million; and presumably price per share would decrease to $25. What difference does it make?

4. A Puzzling Issue Managers often indicate that stock splits are intended to improve liquidity. Contrary to Managers’ view, studies find splits induce reduction in liquidity, based on bid-ask spreads and share turnovers. Copeland (1979), Conroy, Harris and Benet (1990), and Easley, O’Hara and Saar (2001), Gray, Smith and Whaley (2003). How to resolve the conflict?

5. “Why a split per se is necessary is unclear.” -- Easley,O’Hara and Saar (2001) “Stock splits remain one of the most popular and least understood phenomena in equity markets… empirical research has documented a wide range of negative effects, such as increased volatility, larger proportional spreads and larger transaction costs following the splits. On balance, it remains a puzzle why companies ever split their shares.”

6. On the Positive Side The market reacts positively to stock split announcements. The average announcement return is about 3.4%. The question is: What are the benefits from stock splits?

7. A New Perspective Our premise: non-trading reflects illiquidity Lesmond, Ogden, and Trzcinka (1999), Lesmond (2005), Liu (2006), and Bekaert, Harvey and Lundbald (2007). Trading decision is endogenous and a function of trading costs Informed investors would trade only if the value of information exceeds trading cost liquidity traders may refrain from trading if trading costs outweigh the improvement in portfolio allocation. This implies firms with greater incidence of no trading face higher (unobservable) trading costs and lower liquidity.

8. Drawbacks of Conventional Liquidity Measures Bid-ask spread: the bid and ask quotes are often for small-size trades whereas a larger transaction size may need to be negotiated. Kyle’s (1985) lambda and Amihud’s (2002) illiquidity measure: because of the endogeneity of the trading decision, these measures may not be able to fully capture the illiquidity of non-trading.

9. The Trading Continuity Hypothesis Our hypothesis posits that, for a firm facing some possibility of trading discontinuity, managers have incentives to use a stock split to attract more uninformed traders to participate in trading their stock. More uninformed trading allows market makers to reduce inventory holding cost and adverse information cost. As liquidity improves, investors face lower liquidity risk and require a lower liquidity premium, which in turn reduces the cost of equity capital for the firm, and increases firm value. We propose this hypothesis to explain how a stock split may improve liquidity and why it could be beneficial to the firm.

10. Measuring Trading Discontinuity To measure trading discontinuity, we use Liu’s (2006) LM12, the standardized turnover adjusted number of days with zero trading volume over the prior 12 months.

11. Liquidity-Augmented CAPM Liu (2006) proposes a two-factor liquidity-augmented CAPM: Similar to Fama and French’s SMB and HML, Liu constructs LIQ as the return difference between a low liquidity portfolio (containing stocks with high LM12) and a high-liquidity portfolio (containing stocks with low LM12). Liu (2006) demonstrates, this model performs better than Fama and French’s three-factor model and Pastor and Stambaugh’s (2003) asset pricing model in explaining the cross-section of stock returns. This model can also explain anomalies associated with firm size, B/M, cash flow-to-price ratio, dividend yield, earnings-to-price ratio, and long-term contrarian investment strategies.

12. Main Findings We use a large sample of stock splits to test our hypothesis. Consistent with our hypothesis, we find that following the splits, incidence of no trading decreases (implying lower latent costs of trading), liquidity risk is mitigated, and the cost of equity capital is reduced. The split announcement returns are correlated with the improvements in both the liquidity level and liquidity risk. On average, the liquidity improvements reduce the cost of equity capital by 17.3 percent, or 2.42% per annum, suggesting that the economic benefits of stock splits are nontrivial.

13. Data Our sample: 3,721 stock splits the CRSP files, ordinary single-class common stocks, a split factor of one or higher, pre-split price of $10 or above, size and B/M available, Trading volume available, 1975-2004 period. By exchange: 2,109 splits from NYSE/AMEX firms, 1,612 splits from Nasdaq firms. By the split factor: 3,399 splits have a split factor equal to one; 267 splits with a split factor between 1 and 2; the remaining 53 with a split factor above two.

14. Stock Splits and Changes in Sample Characteristics

15. Table 3: The Effects of Stock Splits on Trading Continuity For each split firm, we choose a benchmark firm, which is a non-split firm whose price is closest to that of the split firm at month -1, in the same size and the same B/M quartile as the split firm.

16. The effects of stock splits are long term.

17. Split factor and Pre-split Trading Discontinuity Firms appear to choose a higher split factor when their stocks have more trading discontinuity. Firms choosing a higher split factor seem to experience more improvement in trading continuity following the split.

18. Table 4. Cross-Sectional Analysis of the Split Factor

19. Table 5. Cross-Sectional Analysis of Changes in Liquidity

20. Table 6. Changes in Liquidity Risk

21. How much would the cost of equity capital be reduced for the split firms ?

22. Figure 2. Pre-Split and Post-Split Liquidity Risk of the Split Firms vs. Their Benchmark Firms

23. Table 7. Cross-Sectional Analysis of Changes in Liquidity Risk

24. Table 8. Cross-Sectional Analysis of Split Announcement Returns

25. Conclusions: Main Findings Despite extensive research on stock splits, Easley, O’Hara and Saar (2001) note that “it remains a puzzle why companies ever split their shares.” We propose and test the trading continuity improvement hypothesis. We examine a large sample of splits and find that, consistent with our hypothesis, trading continuity improves, liquidity risk is mitigated, and the cost of equity capital is reduced following the splits.

26. Conclusions: Supporting Evidence Firms facing more frequent trading discontinuities choose a higher split factor, and experience greater improvement in trading continuity. The split announcement returns tend to be higher for firms with more liquidity improvements. These results further suggest that reducing the possibility of trading discontinuity is an important factor in firms’ split decisions.

27. Final Comment Overall, our study provides an explanation with economic benefits for why companies split their shares. It is consistent with managers’ view that stock splits are intended for improving liquidity.