Stock Price Levels and Price Informativeness

Transcription

1 Stock Price Levels and Price Informativeness Konan Chan a National Chengchi University Fengfei Li b University of Hong Kong Tse-Chun Lin c University of Hong Kong Ji-Chai Lin d Louisiana State University Abstract: This paper posits that high stock price levels impede informed trading on the stocks, reduce price informativeness, and make listed options more appealing to the informed because uninformed trading is needed for market making and high stock prices may impose budget constraints on uninformed investors and limit their risk sharing capacity. Indeed, we find that stock price informativeness about future earnings is inversely related to stock price levels, and that Roll et al. s (2010) O/S, the relative trading of options over stock, increases with stock price levels. We further use a split sample and find evidence consistent with our second hypothesis that firms can use stock splits to lower stock price levels, improve informed trading on their stocks, and enhance price informativeness. Thus, our study suggests that stock price levels matter in price informativeness and in where informed traders choose to trade. November, 2012 We are grateful to Gurdip Bakshi, Hendrik Bessembinder, Utpal Bhattacharya, Mark Grinblatt, Jiekun Huang, Jingzhi Huang, Neil Pearson, Avanidhar Subrahmanyam, and participants at the Sixth Chulalongkorn Accounting and Finance Symposium, Hong Kong Baptist University, Louisiana State University, Shanghai University of Finance and Economics, and University of Hong Kong for helpful comments. We thank Weimin Liu for making his liquidity factors available to us. Tse-Chun Lin gratefully acknowledges the research support from the Faculty of Business and Economics and the University of Hong Kong and the Research Grants Council of the Hong Kong SAR government. Any remaining errors are ours. a Department of Finance, National Chengchi University, konan@nccu.edu.tw. b School of Economics and Finance, University of Hong Kong, miffiee@gmail.com. c School of Economics and Finance, University of Hong Kong, tsechunlin@hku.hk. d E.J. Ourso College of Business Administration, Louisiana State University, filin@lsu.edu

2 Stock Price Levels and Price Informativeness Abstract This paper posits that high stock price levels impede informed trading on the stocks, reduce price informativeness, and make listed options more appealing to the informed because uninformed trading is needed for market making and high stock prices may impose budget constraints on uninformed investors and limit their risk sharing capacity. Indeed, we find that stock price informativeness about future earnings is inversely related to stock price levels, and that Roll et al. s (2010) O/S, the relative trading of options over stock, increases with stock price levels. We further use a split sample and find evidence consistent with our second hypothesis that firms can use stock splits to lower stock price levels, improve informed trading on their stocks, and enhance price informativeness. Thus, our study suggests that stock price levels matter in price informativeness and in where informed traders choose to trade. JEL classification: G30, G12, G14, G17 Keywords: Stock price level, O/S, stock splits, price informativeness

3 Stock Price Levels and Price Informativeness 1. Introduction Using O/S, the relative trading of options over stock, Roll, Schwartz, and Subrahmanyam (2010) track where investors prefer to trade, the options market or the equity market. The advantages of options are their implicit leverage and usefulness for hedging positions in the underlying stock or other options. However, the liquidity in each market is also a very important factor. Indeed, Roll et al. (2010) find that options delta and trading costs, along with institutional holdings, analyst following, and analyst forecast dispersion are important determinants of O/S. Also, based on the information content of O/S, they find informed trading in the options market prior to earnings announcements. 1 On the other hand, Easley, Hvidkjaer, and O Hara (2002) find evidence that informed traders are active in equity markets. According to Easley, O Hara, and Srinivas (1998), with options and the underlying stock available, informed traders move across markets to maximize trading profits, while the options and equity market makers watch both markets and sets prices in each market to yield zero expected profit. Easley et al. s (1998) multimarket sequential trade model suggests that increasing the depth of the stock market, or reducing the depth of the options market, results in more informed traders using stocks, and the converse induces more informed trading in options. In their model, the market depth is determined by the number of uninformed trades in each market. 1 Roll et al. (2010) show that their O/S measure prior to an earnings announcement is significantly related to absolute cumulative abnormal returns (CARs) after the announcement. Their results provide evidence on the return predictability of O/S and the occurrence of more informed trading in options prior to earnings announcements. Similarly, Cao, Chen, and Griffin (2005) document that options volume is related to takeover announcement returns of target firms and provide evidence that informed traders make trades prior to takeover announcements. These findings are consistent with Pan and Poteshman (2006), who show that put/call ratios reflect fluctuations in informed trading in the options market and are good predictors of future stock returns.

4 In this study we employ Roll et al. s (2010) O/S to address issues related to high stock price levels and shed light on the nominal share price puzzle, as noted by Weld, Benartzi, Michaely, and Thaler (2009). They review potential explanations including signaling and optimal trading range and find that none of the existing theories are able to explain why firms split their stocks to maintain a price level around $35 since the Great Depression. The intuition that O/S is a useful tool to address drawbacks associated with high stock price levels is that if for some reason a stock s high price causes the depth of the equity market to decrease, then O/S should rise to reflect an increase in traders preference to trade on listed options, relative to the underlying stock. Conversely, if a stock split is an effective way to attract uninformed traders and increase the depth of the stock market, then O/S should fall after the split to reflect an improved venue for trading the stock. Specifically, the first issue we address is: Could high stock prices impede informed trading on the stocks and make listed options more appealing to the informed? Since uninformed or liquidity trading is needed for market making (Kyle (1985) and Glosten and Milgrom (1985)), high stock price levels may discourage uninformed individual traders from participating in trading the stocks because, facing budget constraints, they may not be able to buy a few round lots of high-price stocks. Even if they do, they may not be able to diversify their portfolios. This suggests that high stock price levels may limit uninformed individual investors risk sharing capacity. Thus, we posit that because they discourage uninformed trading, high stock price levels could reduce the market depth and constrain informed trading on the stocks, which may lead more informed traders to use options if listed options are available. 2 2 While a high stock price level may discourage uninformed trading and reduce the stock market depth, it should not affect the options market depth because, due to the nature of leverage in options, the option price is usually a fraction of the underlying stock price and hence uninformed trading in the options market should not be affected by the high stock price level. 2

5 Our hypothesis predicts that, controlling for the determinants identified by Roll et al. (2010), O/S should be positively related to the stock price level and this positive relation should be stronger for firms that have more difficulty to attract small investors, who are more likely to be uninformed. Also, since high stock price levels may constrain informed trading, the price informativeness of high-price stocks would be inversely related to stock price levels. We test these predictions using a comprehensive sample of NYSE/AMEX/Nasdaq firms that also have listed options available. Following Roll et al. (2010), we add trading volume across listed options for each firm for each trading day during our sample period from 1996 through Along with trading volume on common stock, we compute two measures of O/S, one based on share volume and the other dollar volume, for each firm for each day during the sample period. To proxy for the ease in attracting small investors, we use dollar ownership per shareholder, i.e., market value of equity divided by the number of shareholders. If a firm can easily attract small investors, it would have many small investors as shareholders and the dollar ownership per shareholder would be relatively small. Using both Fama-Macbeth regressions and panel regressions and controlling for the known O/S determinants, we find that, indeed, O/S increases with stock price levels and that this positive relation is stronger for firms that have more difficulty in attracting small investors as shareholders. We also find that stock price informativeness about future earnings is inversely related to stock price levels. Our findings illustrate that high stock price levels have drawbacks to attract both uninformed and informed trading to the stocks, and imply that stock price levels matter in price informativeness and in where informed traders choose to trade. Can firms use stock splits to improve informed trading? If our hypothesis that high stock price levels impede informed trading on the stocks is valid, a stock split, which has been shown 3

6 to attract more uninformed trading to the stock, 3 should be able to lessen the constraints on informed trading. Improving informed trading would enhance informational efficiency of stock price, which is valuable. For one thing, it could improve corporate resource allocation (see, e.g., Khanna, Slezak, and Bradley (1994) and Subrahmanyam and Titman (2001)). For another, as Roll, Schwartz, and Subrahmanyam (2009) point out, the risk of investing in a firm is lower when its stock price reflects more information. 4 This leads to our second hypothesis: for firms whose high stock price levels hinder uninformed traders to enter the market, managers can use stock splits to attract more uninformed traders to improve informed trading and enhance informational efficiency of stock prices. This hypothesis predicts that, for splitting firms with listed options, O/S would rise before the stock splits and decline afterwards, and that the informational efficiency of stock prices would increase following the stock splits. Focusing on improving informed trading as a benefit of stock splits, our second hypothesis can also shed light on the debate in the literature on the source of valuation gains from stock splits between the liquidity improvement hypothesis and the signaling hypothesis, and further help us understand the stock split puzzle. As Easley, O Hara, and Saar (2001, p. 25) point out, why a split per se is necessary is unclear 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. If stock splits are initiated to improve informed trading as we postulate, they may not result in a lower bid-ask spread, because market makers need to manage the spread to cover losses to informed traders (Glosten and Milgram (1985)). More informed trading could also lead 3 For example, Schultz (2000) shows a significant increase in small trades following the splits. Also, Easley, O Hara and Saar (2001) document more uninformed trades and more informed trades as well after stock splits. 4 Indeed, Lin, Singh and Yu (2009) find that liquidity risk is significantly lower following stock splits. 4

7 to higher stock price volatility (Kyle (1985)). With more informed trading, stock prices are more informative, which reduces the risk of investing on the stocks and increases the incentive for investors to hold on the stocks. Thus, stock splits may increase investor base, but they may not increase share turnover (see Copeland (1979) and Lamoureux and Poon (1987)). Consequently, while enhancing informed trading is a form of liquidity improvement, we may not see that stock splits improve liquidity in the dimensions of turnover and bid-ask spread. The premise of the signaling hypothesis is that managers undertake stock splits to reveal favorable private information to the market (Brennan and Copeland (1988)). It emphasizes that investors have less knowledge about firm valuation and that the less they know, the bigger the surprise a split may convey, which may result in a larger signaling effect. However, we will demonstrate in empirical tests that informed investors in fact know that firms are undervalued before stock splits, and that the more they know and trade in options, the larger the split announcement returns. Our findings cast doubt on the validity of the signaling hypothesis. In light of our hypothesis, the more the informed know and trade in options before a stock split, the greater the frictions impede informed trading on the stock, and the more the gains for the firm to use a split to improve informed trading. To test our second hypotheses, we collect 1,687 stock splits undertaken by firms with listed options during the sample period from 1996 through Indeed, we observe that the average O/S of the sample firms gradually increases and reaches the peak the day after the split announcement, and then it declines significantly following the split. Our cross-sectional regression analysis reveals that pre-split O/S is also significantly related to pre-split stock price level and this relation is also stronger for firms with more difficulty in attracting small investors. Also, we find that the higher the pre-split O/S, the higher the split announcement returns. The 5

8 results are largely consistent with our hypothesis that the pre-split high stock price level makes the equity market less favorable to informed trading, causing informed investors to trade more on the options market, and that as stock splits attract more liquidity trading to improve informed trading on the stock, the informed find the equity market again an attractive trading venue. However, one may argue that if some traders are merely aware of the forthcoming split events, which on average receive positive market reactions, they could still profit by trading options regardless of reasons behind splits. 5 To address this concern and to better understand the information content of pre-split O/S, we link pre-split O/S to post-split firm performance. Our empirical results show a close relation between pre-split informed trading and long-term firm performance. Firms with high O/S prior to split announcements produce larger earnings surprises over the year following a split announcement. These results are consistent with the notion that pre-split O/S reflects informed traders preference of options over stock. The results also suggest that the informed have information about the firms future prospects and that they are not merely reacting to forthcoming split announcements. The fact that the information content of pre-split O/S was not fully impounded into stock price until the firms announce to undertake stock splits suggests that the price discovery function in the equity market was impaired by high stock price levels prior to stock splits and that there is a need to improve informed trading. By lowering stock price levels to attract more liquidity trading, stock splits could improve informed trading on the stocks and restore the price discovery function. We provide evidence that post-split stock prices are indeed more informative about future earnings than pre-split stock prices. Furthermore, as stock prices become more informative, 5 In fact, if traders in the options market are merely aware of the occurrence of split events, we would only observe a high O/S ratio before stock split but no positive correlation between pre-split O/S and the split announcement CAR. 6

9 the predictive power of O/S on earnings surprises and earnings announcement returns disappear in the post-split period. The remainder of the paper is organized as follows. Section 2 reviews the literature and develops our hypotheses. Section 3 uses a comprehensive sample of firms with both options and stock trading data available to test our first hypothesis that stock price levels affect O/S and price informativeness. To verify the findings from comprehensive sample, section 4 uses a sample of split firms with listed options to test our second hypothesis that firms can use stock splits to improve informed trading and enhance price informativeness. Section 5 concludes our study. 2. Literature review and hypothesis development Weld, Benartzi, Michaely, and Thaler (2009) point out that It is surprising that firms actively maintained constant nominal price for their shares while general prices in the economy went up more than tenfold. What could motivate managers to do stock splits to keep the price of their stock constant in nominal terms? This question is intriguing and worth further exploration. The two main competing hypotheses proposed in the literature for explaining why firms split their stocks are signaling and liquidity improvement. Brennan and Copeland (1988) propose that since stock splits lower the price levels and increase trading costs, they can serve as a costly signal of managers favorable private information to the market. Asquith, Healy, and Palepu (1989) thus suggest that managers use stock splits to signal that recent earnings growth is permanent. Also, McNichols and Dravid (1990) note that splits can be used to convey information on improvement in future earnings. However, Lin, Singh, and Yu (2009) show evidence of declining latent trading costs after stock splits, which contradict the costly signal hypothesis proposed by Brennan and Copeland (1988). Weld at al. (2009) also argue that stock 7

10 splits cannot be motivated by signaling because post-split prices are usually centered on those of peer firm prices and rejoining the herd is not consistent with a separating equilibrium. We add to this line of questioning by showing that informed investors trade more options prior to stock splits, suggesting that, instead of being informed by the split announcement, some traders seem to know beforehand that the firms stock prices do not fully reflect relevant information and that they trade options to profit from their knowledge. It is an indication that the stocks price discovery function does not work properly prior to stock splits. While managers often claim that stock splits are intended to attract more investors and to improve stock liquidity, 6 liquidity on the dimensions of bid-ask spread and turnover does not seem to improve after stock splits. 7 This leads Easley, O Hara and Saar (2001, p.25) to note that stock splits remain one of the most popular and least understood phenomena in equity markets. However, consistent with the liquidity improvement hypothesis, Lin, Singh, and Yu (2009) show that incidence of no trading decreases and liquidity risk is lower after stock splits. Recently, Baker, Greenwood, and Wurgler (2009) propose a catering theory of nominal stock prices, which predicts that when investors place higher valuations on low-price firms, managers respond by supplying shares at lower price levels, and vice versa. While firms may have catering incentives, it is possible that when investors place higher valuations on low-price firms, low prices increase individual investors risk sharing capacity, which allows low-price firms to take more risky projects and, as we will discuss below, make their stock prices more informative. At which time, firms are also more likely to split their stocks to capture the benefits of enlarging investors risk sharing capacity. 6 See, for example, Dolley (1933), Baker and Gallagher (1980), and Baker and Powell (1993). 7 Copeland (1979), Conroy, Harris, and Benet (1990), Easley, O Hara, and Saar (2001), and Gray, Smith, and Whaley (2003) all document that relative bid-ask spread increases following stock splits. 8

11 Nevertheless, none of previous studies have explored the possibility that high stock price levels may create problems for informed trading and make stock prices less informative. The reason we suspect such problems could arise is that market microstructure theories have suggested that informed trading is a key element of the price discovery function of the market and that uninformed trading is needed to facilitate informed trading (Kyle (1985) and Glosten and Milgrom (1985)). As Admati and Pfleiderer (1988) point out, informed traders tend to camouflage their trades among uninformed trades. If high stock price levels create barriers for uninformed investors to enter the market because of budget constraints and limited risk sharing capacity, they could have negative impacts on informed trading as well. In fact, several studies have discussed the budget constraint issue. For example, Amihud, Mendelson and Uno (1999) show that when companies in Japan reduce their stock s minimum trading unit, i.e., the number of shares in a round lot, to better facilitate trading by small investors, the number of their individual shareholders significantly increases. Similarly, Fernando, Krishnamurthy, and Spindt (1999) analyze mutual fund share splits and find that, relative to nonsplitting matched funds, split funds experience significant increases in net assets and shareholders. Also, Schultz (2000) shows a significant increase in small trades following the splits; and Easley, O Hara and Saar (2001) document more uninformed trades (and more informed trades as well) after stock splits. The evidence from these studies clearly suggest that small individual investors have limited risk sharing capacity and are likely subject to budget constraints. Consequently, they could be excluded from participating in trading stocks with high price levels. When informed traders cannot effectively camouflage their trades among uninformed trades in the equity market, their private information would not be efficiently impounded into stock prices; and the informational role of stock price could diminish. 9

12 When stock price becomes less informative, informed traders may find listed options an attractive vehicle for profiting from their private information. Because of the nature of implicit leverage in options, option prices are usually fractions of the underlying stock price. The relatively low prices of options could attract speculative trading and hedging trading as well. Easley, O Hara, and Srinivas (1998) measure the depth of the stock market or the options market by the number of uninformed traders in each market, and suggest that decreasing the depth of the stock market could result in more informed traders using options. Thus, if high stock price levels unfavorably affect uninformed trading and reduce the depth of the stock market, we should see that more informed traders migrate their trades to the options market. We summarize the above reasoning in the following hypothesis: H1: High stock price levels would impede informed trading on the stocks, reduce price informativeness, and make listed options more appealing to the informed because uninformed trading is needed for market making and high stock price levels may impose budget constraints on uninformed traders and limit their risk sharing capacity. Since informed trading with private information in each market is not easily observable, we test our hypothesis using Roll, Schwartz, and Subrahmanyam s (2010) O/S as a relative measure of informed trading, i.e., more informed trading in options relative to the underlying stock when O/S is high; and vice versa. Roll et al. (2010) have identified a set of important determinants of O/S, including the costs of trading, the size of the firm, the available degree of leverage in options, institutional holdings, and proxies for the availability of private information and the diversity of opinions. Based on three observations that Roll et al. (2010) infer that O/S is a good informed trading measure in options: (i) O/S increases significantly in the few days around an earnings announcement; (ii) high O/S predicts high absolute CARs after the earnings 10

13 announcement; and (iii) some options traders execute orders in the right direction for the upcoming earnings surprise. Our H1 predicts that there would be more informed trading in options relative to the underlying stock when the stock price level is higher, and that the effect of stock price level on the relative informed trading should be larger for firms that have more difficulty in attracting small investors. Thus, our H1 extends Roll et al. (2010) by proposing that, in addition to the O/S determinants they identify, stock price levels and the interaction between stock price levels and dollar ownership per shareholder, which is a proxy for the ease in attracting small investors, are also important determinants of O/S. If high stock price levels constrain informed trading, stock splits, which are an effective mechanism to allow firms to adjust their price levels lower and attract more uninformed trading, should improve informed trading and make stock prices more informative. As we mentioned in the introduction, when stock price becomes more informative, it helps corporate investment decisions and reduces the risk of holding the stock. Since enhancing the informational role of stock price is valuable, we believe that it is a compelling factor for motivating firms to split their stocks when their stock price levels are relatively high. below. We summarize our thought on why firms split their stocks in the second hypothesis H2: For firms whose high stock price levels hinder uninformed traders to enter the market, managers can use stock splits to attract more uninformed traders to improve informed trading and enhance informational efficiency of stock prices. Similarly to H1, this hypothesis predicts that, for splitting firms with listed options, O/S would rise before stock splits since pre-split high stock price levels make informed trading in the stocks less favorable, causing more informed traders move to the options market. This implies 11

14 that pre-split O/S would be informative about splitting firms future prospects. Furthermore, O/S should decline after stock splits because as stock splits lower stock price levels and attract more informed trading to the stocks, they should result in more informed traders using the stocks. As stock price becomes more informative after stock splits, post-split O/S would contain less information, compared to pre-split O/S. Thus, based on the behavior of O/S surrounding the stock split event, we test whether high stock price levels impede informed trading on the stocks prior to stock splits and whether splitting the stocks improves informed trading on the stock. 3. Testing the first hypothesis Our first hypothesis posits that high stock price level may impede informed trading on the stock and make listed options more appealing to the informed. To test this hypothesis, we use a comprehensive sample of firms with trading data available on both listed options and the underlying stock. This section first discusses the sample we use in the test and then present empirical results The comprehensive sample Our sample period is from 1996 to 2010 with options data from OptionMetrics and data on the stock from the CRSP. The number of firms in our sample varies over time, with the average number of firms in a given year ranging from 960 in 1996 to 1967 in 2007, with a total of 4702 firms in our sample. Follow Roll et al. (2010), we use two measures of daily O/S, the ratio of the total trading volume of options in the options market to the trading volume of the corresponding underlying stock in the stock market on a given trading day for each firm -- ShO/S based on daily share 12

15 volume and $O/S based on daily dollar volume. 8 Roll et al. (2010) show that O/S is higher around earnings announcements and that O/S prior to earnings announcements is significantly related to absolute earnings announcement returns. They thus argue that O/S fairly represents informed trading on listed options, relative to the underlying stock. Roll et al. (2010) show that the determinants of O/S include firm size, options spreads, implied volatility, options deltas, number of analysts following the firm, analysts earnings forecast dispersion, and institutional holdings. Table 1 report summary statistics and correlations of the variables used in analysis. The variables include O/S and the known O/S determinants, along with the two key variables for testing our first hypothesis -- Price, the log stock price level, and the interaction between Price and Small, where Small is a dummy variable equal to one if the dollar ownership per shareholder is greater than the cross-sectional median, and zero otherwise. We assume that firms with Small=1 have more difficulty in attracting small investors than those with Small=0. Table 1 Panel A reports summary statistics of the variables based on the pooled 4,812,117 daily observations. The mean of ShO/S is 0.1 and its standard deviation is 0.31, while the same statistics of $O/S are and 0.068, respectively. We also report summary statistics of log ShO/S and log $O/S since we use them in most of our regression analysis. The means of Ln(ShO/S) and Ln($O/S) are and -6.12, respectively. Among the 4.8 million daily observations in our sample, the highest stock price level is $ while the lowest is $0.88. Panel B, which reports the firm-level statistics, shows that the average stock price level across our sample firms ranges from $11.37 to $52.76, with a mean of $ This wide stock price range should give us sufficient power to test whether O/S and price informativeness are related to stock price levels. 8 Given the fact that each options contract is for 100 shares of the underlying stock, we compute the O/S as the ratio of total options trading volume multiplied by 100 to stock trading volume. We also adjust trading volume for firms listed on Nasdaq according to Gao and Ritter (2010). 13

16 3.2. The relationship between O/S and stock price levels Table 2 reports the results from both Fama-Macbeth cross-sectional regressions and panel data regressions. Panel A presents the regression results with Ln(ShO/S) as the dependent variable; and in Panel B the dependent variable is Ln($O/S). Since the results are virtually the same, we focus our discussion on the results based on Ln(ShO/S). In models (1) and (4), we replicate Roll et al. s (2010) analysis on the determinants of O/S. The results are largely consistent with theirs. That is, O/S is positively related to firm size, implied volatility, number of analysts, analyst forecast dispersion, but negatively related to spread, options delta and institutional ownership. In Models 2 and 4, we add Price, the log stock price level, to the set of explanatory variables. Price is very significant with an average coefficient of 0.62 (t-value=87.73) from Fama-Macbeth regressions; and its coefficient is 0.55 (tvalue=10.40) under the panel regressions. Interestingly, adding Price to the panel regressions makes firm size insignificant, and the adjusted-r 2 increases to from Models 3 and 6 further add the interaction between Price and Small to see whether the effect of Price on O/S depends on the ease to attract small investors. Since our hypothesis posits that high stock price levels discourage uninformed trading and reduce the depth on the stocks and make listed options more appealing to the informed, suggesting that this high price effect on O/S would be stronger for firms that have difficulty in attracting small investors to provide liquidity in the stock market. Indeed, Models 3 and 6 show that O/S is significantly related to both Price and the interaction of Price and Small. The results are consistent with our theory that high stock price levels make the stocks less attractive to traders, and increase the attractiveness 14

17 of the options market to the informed. Thus, the evidence illustrates that stock price levels matter in where traders choose to trade The relationship between price informativeness and stock price levels Table 3 shows that stock price levels also matter in price informativeness. To link stock price levels to price informativeness, we follow Gelb and Zarowin (2002), who define price informativeness by the association between current stock returns and future earnings changes: more informative stock price changes contain more information about future earnings changes. Gelb and Zarowin s (2002) methodology is largely based on the multiple regression model of Collins, Kothari, Shanken and Sloan (CKSS, 1994), who argue that the more the current return reflects information about future earnings, the higher the future earnings response coefficient (ERC) is expected to be. However, instead of expected future earnings, which are unobservable, their model uses actual future earrings and suggests future returns as an instrumental variable to correct the measurement error and eliminate the bias in estimating future ERC. The rationale is that returns have little autocorrelation, but future returns are correlated with unexpected future earnings changes. CKSS further suggest that including earnings-price ratio and the contemporaneous asset growth rate may help reduce the measurement error problem. Following Gelb and Zarowin (2002), we also include firm size to control for possible differences in firms information environment. Model 1 in Panel A of Table 3 reports the estimation results based on Gelb and Zarowin s (2002) specification. The results show that stock returns in a given year are positively related to 9 One may argue that the odd-lots trading becomes easier due to online trading system, which might mitigate the budget constraint faced by the uninformed traders. However, even though odd lots are more available, that would not help much in market making and facilitating informed trading in the equity market unless informed traders also use odd lots to capitalize on their information frequently. 15

18 future earnings changes in the next two years, with an estimated future ERC of (tvalue=5.54). Consistent with CKSS (1994) and Gelb and Zarowin (2002), stock returns are negatively related to future returns and firm size, but positively related to E/P and asset growth rate. Model 2 adds Price, the log of the average price during the same year as stock returns (the dependent variable), and interaction of Price with future earnings changes. The interaction term is significantly negative, with an estimated coefficient of (t-value=-9.43). The estimated future ERC remains significant and increases to (t-value=9.71). The results of Model 2 suggest that future ERC is reversely related to stock price levels. Model 3 further includes the interaction terms of Price with other control variables and shows that future ERC remains a negative function of stock price levels. Thus, price informativeness about future earnings decreases as stock price levels increase. Panel B of Table 3 reports the subsample analysis, comparing low-priced vs. high-prices stocks. Specifically, we sort all Compustat firms into quintiles in each year by their average stock price in the fiscal year t. We then keep only firms in the top and bottom price quintiles. Model 1 includes firms in the bottom price quintile (i.e., low-priced stocks), Model 2 includes firms in the top price quintile (i.e., high-prices stocks), and Models 3 includes both extreme price quintiles. Models 1 and 2 show that the future ERC is (t-value=5.06) for the low-priced stocks, and (t-value=-3.84) for the high-priced stocks. The future ERC for high price stocks is significantly lower than that for high price stocks, as shown in Model 3 (the coefficient of the interaction of future ERC and high price dummy is with a t-value of -5.41), confirming that price informativeness about future earnings is inversely related to stock price levels. 16

19 Given the results, we expect that good firms that have significant price run-ups would be interested in reducing the unfavorable effects of high stock price levels on price informativeness. In the sections that follow, we present evidence that firms use stock splits to accomplish the task. 4. Testing the second hypothesis Our second hypothesis posits that, for firms whose high stock price levels impede informed trading, managers can use stock splits to attract more uninformed traders to improve informed trading and enhance informational efficiency of stock prices. This section tests this hypothesis using a sample of splitting firms with listed options. Again, we first describe the split sample and make sure that the O/S of the splitting firms behaves similarly to that of the comprehensive sample, and then focus on how stock splits affect O/S itself and the information content of O/S The split sample We collect firms that made announcements of stock splits with a split factor of at least 0.25 during 1996 to 2010 from the CRSP. 10 The sample starts in 1996 because the coverage of options in OptionMetrics begins that year. We require split firms to be covered by OptionMetrics and to have options trading volume data available prior to and after the stock splits. Our split sample consists of 1,687 splits over the period of 1996 through Table 4 reports summary statistics and correlations of the variables for the split sample. The pre-split stock price, averaged over days -22 to -3 before the split announcement date, 10 We exclude stock splits with split factors less than 0.25 and drop all stock dividends to be consistent with prior research (e.g., Ikenberry, Rankine, and Stice (1996) and Ikenberry and Ramnath (2002)). 17

20 ranges from $10.48 to $ The mean pre-split stock price is $70.29, which is 2.7 times higher than the average stock price in the comprehensive sample reported in Table 1 Panel B. Consistent with the literature, our sample firms on average enjoy 3% abnormal returns (i.e., excess returns over the CRSP value-weighted market index returns) during the five days surrounding the split announcement date. These firms are generally growth firms with low bookto-market ratios that have experienced enormous price run-up (100%) prior to the split announcements. The average options trading volume is 14% of the stock trading volume in the sample. To control for liquidity, we use Liu s (2006) LM, the standardized turnover-adjusted number of days with zero trading volume. This measure takes into account the notion that trading decision is endogenous and depends on trading costs. In particular, non-trading reflects illiquidity. Lin, Singh, and Yu (2009) show that after stock splits, the incident of non-trading significantly decreases. Thus, to see how splitting firms stock price level affect trading on options relative to the stocks, we use changes in LM to control for potential liquidity improvement on the stock associated with stock splits. 11 Note that since our split sample consists of firms with listed options, they are likely to be relatively large and actively traded, suggesting that non-trading is probably not a critical issue to our sample firms, compared with firms in Lin et al. s (2009) sample. For robustness checks, we also examine changes in Amihud s (2002) ILLIQ and share turnover around stock splits Split firms O/S and stock price level 11 We try different windows to measure changes in liquidity, such as one year before and one year after the split announcement date, or one year before and one year after the effective date of splits. The results are similar. 18

21 Table 5 shows that, similar to the results from the comprehensive sample, both split firms ShO/S and $O/S prior to stock splits are positively related to pre-split Price and pre-split Price Small, suggesting that pre-split high stock price levels lead traders to trade options more relative to the underlying stocks and that the effect of high stock price levels on O/S is larger for split firms that do not attract many small investors. Thus, in light of Easley et al. s (1998) multimarket sequential trade model, the findings suggest that high stock price levels reduce the depth of the stock market prior to stock splits, resulting in more traders using options. If high stock price levels induce more trading on options over stocks, then pre-split price run-ups should lead to an increasing trend in O/S prior to stock splits. Figure 1 clearly shows such a trend for split firms starting 12 months prior to split announcements--the average O/S rises from around in month -12 to about around split announcements. While comparable non-split firms, matched by firm size and B/M, also exhibit a slightly upward trend in O/S, the pre-split increases in the average O/S of split firms are much more substantial and visible. Later on, we will show that pre-split O/S contains useful information about split firms future prospects. Interestingly, the figure shows that the average O/S of split firms declines remarkably over the three month period after stock splits and then stabilizes afterwards at the level observed around month -12 before the splits. For the matched firms, we do not observe any significant changes in their average O/S during the post-split period, suggesting that the declines in the average O/S of split firms are likely associated with lower stock price levels induced by stock splits. To confirm our conjecture, Table 6 reports the results of regressing changes in O/S from before to after the stock splits on changes in stock price levels, controlling for changes in the O/S 19

22 determinants identified by Roll et al. (2010). Indeed, the results show that changes in O/S surrounding the split event are significantly related to changes in stock price levels induced by stock splits, and that the effect of lowering stock prices on changes in O/S is stronger for split firms that had more difficulty to attract small investors before stock splits. In sum, the evidence suggests that stock price levels matter in where informed traders choose to trade. The lower post-split O/S implies that, by lowering stock price levels to attract more uninformed trading to the stocks, stock splits also make the stocks more attractive to informed traders. We next turn to show that pre-split O/S is informative about split firms future prospects, reflecting informed traders preference to use options prior to stock splits, and that stock splits improve informed trading on the stocks, causing the information content of O/S to decline in the post-issue period The information content of pre-split O/S To first show the information content of pre-split O/S, Table 7 reports the results of regressing the five-day split announcement returns on pre-split O/S, the natural logarithm of average O/S over days -22 to -3, and a set of control variables, including firm size, B/M, pre-split price run-up, pre-split stock price level, the split factor, and changes in stock liquidity. The regression results show that the O/S is very significant, with a coefficient ranging from 0.53 (tvalue=3.05) to 0.77 (t-value=4.20) in various specifications. The finding suggests that pre-split O/S is very informative, indicating that the higher the pre-split O/S, the higher the split announcement returns. This finding has two implications. First, it implies that the rise in pre-split O/S reflects more informed trading in the options over the stocks. Second, split firms with more pre-split O/S 20

23 benefit more from announcing a stock split. These two implications build on the notion that when pre-split high stock price level discourages uninformed trading on a stock, it constrains informed trading on the stock and weakens the stock s price discovery function as well. The weakened price discovery on the stock market is evident by the increasing option trading activities, whose information content is not fully reflected in pre-split stock price. Furthermore, the more the informed trading on the stock is constrained prior to the stock split, the higher the benefit to the split firm. To show that the pre-split increases in trading options over stocks do not merely reflect that informed traders anticipate the upcoming stock split announcements, Table 8 shows that presplit O/S can also predict earnings surprises from one quarter to four quarters after the stock splits. Since the earnings surprises are based on I/B/E/S reported analyst forecasts and actual earnings, the regression results suggest that options traders prior to stock splits are informed about future earnings surprises. Moreover, Table 9 reports that pre-split O/S also contains information about future stock performance. To show that, we first sort split firms into five quintile groups based on their presplit O/Ss and, for each group, form a calendar-time portfolio every month from January 1996 to December 2010 that consists of firms that had stock split announcements in the past 12 months. Then, we use three pricing models to measure abnormal stock performance: Fama-French threefactor model, Carhart s (1997) four-factor model, and a five-factor model that further adds Liu s (2006) liquidity factor. The reason we use the calendar-time portfolio regression approach is that it offers better statistical properties and mitigates the cross-sectional correlation in observations (Fama (1998)). To address the concern that the calendar-time approach may have low power to detect abnormal returns (Loughran and Ritter (2000)), we perform both ordinary least squares 21

24 (OLS) and weighted least squares (WLS) regressions where the weight for WLS regressions is based on the number of sample firms in a given month. Both methods show that the abnormal returns on the calendar-time portfolios from all three models increase monotonically with presplit O/S. The evidence indicates that firms with more trading in options over stock perform better in the year after the stock splits, suggesting that options traders prior to stock splits are also informed about split firms future stock performance. Thus, the evidence suggests that informed traders seem to know split firms future prospects before stock splits and that the better the future prospects, the more they trade listed options over the stocks. The finding that the informed know in advance casts doubts the validity of the signaling hypothesis that managers use stock splits to signal their firms future prospects. Rather, the evidence is consistent with our hypothesis that high stock price levels impede informed trading on the stocks and make listed options more appealing to the informed prior to stock splits Post-split stock price informativeness Our second hypothesis suggests that managers use stock splits to improve informed trading and make stock price more informative. To empirically examine changes in the price informativeness associated with stock splits, we again follow Gelb and Zarowin s (2002) specification to capture the notion that more informative stock price changes contain more information about future earnings changes. Table 10 shows that, indeed, stock prices become more informative following stock splits. The table reports the results of regressing annual returns on contemporaneous earnings change, future earnings change for the next two years and a set of control variables, and the interactions 22

25 of these variables with a post-split dummy. Before stock splits, the future ERC, i.e., the coefficient on future earnings changes, ranges from (t-value=2.59) to (t-value=4.56) in three model specifications. After stock splits, the future ERC increases by an amount ranging from (t-value=4.03) to (t-value=7.21). Thus, the increase in stock price informativeness associated with stock splits is relatively large and significant. The finding is interesting because the common impression in the literature is that, by lowering stock price levels, stock splits attract more small and uninformed traders, who seem likely to create more noises in stock prices rather than making stock prices more informative. Instead, the evidence is consistent with our hypothesis that firms use stock splits to attract more uninformed trading to improve informed trading. Meanwhile, out result is also consistent with the information production theory of stock split in Brennan and Hughes (1991) and Chemmanur, Hu, and Huang (2012) who argue that information production increases after stock splits and hence may lead to more informed trading. Table 11 further compares the information content of O/S before and after stock splits. We expect the information content of O/S declines after stock splits since stock price reflects more information, which reduces room for the informed to use options to exploit private information. The results show that, before stock splits, the average O/S over days -22 to -3 relative to the earnings announcement date can predict earnings surprises and earnings announcement returns (Models 1 and 3). However, the predictive power of O/S disappears after stock splits (Models 2 and 4). The evidence that post-split trading of options contains less information compliments our finding that stock splits make stock price more informative. To further support the argument that options volume contains information, we use call options trading volume divided by stock trading volume to estimate pre- and post-split informed 23