The Share Price Puzzle

Transcription

1 The Share Price Puzzle Edward A. Dyl University of Arizona, Tucson, AZ 85721, USA William B. Elliott Oklahoma State University, Stillwater, OK 74078, USA June, 2000 Abstract We document substantial variation in the prices of common stocks in U.S. markets, a phenomenon that apparently results from firms selecting particular price ranges for their stock. We present cross-sectional evidence that variables consistent with Merton s (1987) model of capital market equilibrium explain roughly 45 percent of the variation in share prices. We also find that measures of trading range and share price appreciation are significant predictors of stock splits, that very widely held firms are less inclined to split their stock than less widely held fi rms, and that the investor base of firms splitting their stock increases compared to other firms.

2 2 The Share Price Puzzle A glance at the stock prices published each weekday in The Wall Street Journal and other newspapers reveals a wide range of common stock prices in United States markets. For example, on a given day at the New York Stock Exchange (NYSE), Anheuser-Busch sells for about $75 per share, whereas Boston Beer sells for only $8.75 per share. Similarly, on Nasdaq, Intel sells for $72 per share, but a share of Applied Microsystems costs only $ Why is there so much variation in share prices among firms trading in the same and/or similar markets? Most items in tend to be packaged in ways designed to reduce price dispersion across companies and brands. Bonds typically have a par value of $1,000, most pasta comes in 16-ounce packages, wine bottles generally hold 750 milliliters, and so forth. If the total value of a firm is primarily determined by the firm s future earning power, then the price per share of the firm s stock simply depends on the number of shares outstanding, which the firm controls. Why isn t there more commonality among stock prices? We refer to this heretofore unexplained variation in common stock prices as the Share Price Puzzle. Table I documents the dispersion in prices of common stocks trading in United States markets during Panel A contains aggregate results for the three major U.S. stock markets. The mean and median stock prices of these 6,756 firms are $19.31 and $14.62 per share, respectively, but 33 percent of the firms have average prices lower than $10.00 per share and 19 percent have average prices higher than $30 per share, so more

3 3 than 50 percent of all traded firms have share prices that dif fer considerably from the average. Higher stock prices and the firm s market value are directly associated. This relation is not merely due to higher price, ceteris paribus, causing market higher value. The mean share price of firms in the Greater-than-$70 group is 18 times the mean price of firms in the Less-than -$10 group, whereas the mean market value of firms in the former group is 243 times the mean market value of the firms in the latter group. Panels B, C, and D show the same information sep arately for the three major U.S. stock exchanges. The mean share price of firms trading on the NYSE is roughly twice as high as that of firms trading on the Amex and Nasdaq, and the NYSE firms are much larger. Not surprisingly, both the Amex and Nasdaq have a larger proportion of their firms in the Less-than -$10 category. One apparent anomaly is that, although the Amex and Nasdaq firms in the Greater-than- $70 category have smaller market capitalizations than the corresponding NYSE firms, they have higher stock prices. Evidently stock prices vary all over the place. It is possible that this phenomenon is simply inexplicable, in the sense that stock prices just happen. That is, firms shares begin trading following an Initial Public Offering (IP O), generally priced at an average of about $10.00 per share, 2 and some firms are subsequently more successful than others. Thus, some firms share prices go up over time, and other firms prices go down. These differences in performance over a long period of time may explain the cross- sectional variation in stock prices that we observe in today s markets. The problem with this conjecture is that firms take actions to select a preferred trading range for their shares (i.e., by manipulating the number of shares outstanding). 1 T h e s e p r i c e s r e f e r t o c l o s i n g p r i c e s o n A u g u s t 1 0,

4 4 Consider the evidence in Figure 1, which shows the average annual common stock price of the 1,452 firms having continuous annual data available from the Center for Research in Security Prices (CRSP) for the period from 1976 through The average annual price for each firm is an average of the monthly closing prices for the year, and the solid line depicts the average price over time for the 1,452 firms. The average annual share price for these stocks over the 21 -year period is $24.78, ranging from lows of $18.87 and $19.28 in 1977 and 1976 to highs of $29.74 and $29.84 in 1986 and 1996, respectively. It is remarkable that the average price of these firms shares changes so little during a period when the S&P 500 Composite index appreciated by 692 percent and the NYSE Composite Index appreciated by 785 percent, and it is also prima facie evidence that these firms manage their share prices. 4 The broken line in the figure shows what the average share price would have been in the absence of stock splits. The average price in 1996 would have been $196.01, not $ Clearly stock prices don t just happen! This paper is organized as follows. In the next section we consider the relation between trading range considerations, transaction costs, and share prices, and advance some hypotheses about why it may make sense for some firms to have high share prices and vice versa. Section II presents cross-sectional evidence about share ownership and share price levels from 1976 to 1996 that is consistent with these hypotheses. In Section III, we show that the decisions of the firms in our sample to split their stock, or not to 2 A r e c e n t s t u d y o f 2, I P O s f r o m f i n d s a n a v e r a g e i n t i a l o f f e r i n g p r i c e o f $ p e r s h a r e. S e e A f f l e c k-graves e t. a l. ( ). 3 T h e r a t i o n a l e f o r e x a m i n i n g t h i s s a m p l e o f f i r m s i s d i s c u s s e d b e l o w. 4 O u r s a m p l e c o n t a i n s o n l y s u r v i v o r s, s o t h e s e f i r m s a p p r e c i a t i o n w a s e v e n g r e a t e r t h a n t h e i n d i c e s ( 1, p e r c e n t ).

5 5 split their stock, are also consistent with these hypotheses. Conclusions are summarized in Section IV. I. Stock Splits, Trading Ranges, and Transaction Costs The notion that there is an optimal (or, at least preferable) trading range for a firm s common stock is widely accepted among finance practitioners. In a survey of 100 chief financial officers of NYSE - listed firms, Baker and Gallagher (1980) find almost universal agreement with the statement that Stock splits keep a firm s stock price in an optimal price range. In a similar vein, the New York Stock Exchange Listed Company Manual contains the following statements: Exchange statistics indicate a preferential price range within which a significant percentage of Exchange round lot volume is generated.... Today, liquidity is probably the most important element in the investment decision, other than the financial condition or suitability of the security under consideration.... Consideration of a stock split is therefore justified when a company s shares are selling at a relatively high price, and when such action is accompanied by healthy operating results and a strong financial condition. (page 7-11) Apparently firms heed the NYSE s advice. Numerous empirical studies report that firms tend to announce a stock split when their share price is higher than usual, and that stock splits convey positive information about the firms future prospects. 5 5 L a k o n i s h o k a n d L e v ( ), L a m o u r e u x a n d P o o n ( ), M c N i c h o l s a n d D r a v i d ( ) a n d I k e n b e r r y e t. a l. ( ). W h e t h e r o r n o t t h e c o n v e y a n c e o f i n f o r m a t i o n i s i n t e n t i o n a l ( i. e., s o -c a l l e d s i g n a l l i n g ) o r s i m p l y i n a d v e r t e n t b e c a u s e m a n a g e r s b e h a v e a c c o r d i n g t o t h e g u i d e l i n e s i n t h e N Y S E L i s t e d C o m p a n y M a n u a l i s, f o r t u n a t e l y, o u t s i d e t h e s c o p e o f t h i s p a p e r.

6 6 Despite the NYSE s assertion regarding the importance of liquidity, however, stock splits and lower trading ranges do not necessarily result in increased liquidity for a firm s shares, at least in any traditional meaning of the word. Traditionally, liquidity is associated with low transaction costs and high trading volume. Several studies document that stock splits actually increase percentage bid-ask spreads. 6 In fact, lower share prices are generally associated with higher transaction costs, such as percentage bid-ask spreads and commissions, and not vice versa. 7 In a market that specifies a minimum price variation between quotes (i.e., a tick size), an inverse relation between share prices and b i d -ask spreads is almost inevitable. 8 For example, if the minimum price variation in a market is one-eighth of a dollar ($.125), as it was in U.S. stock markets for most of this century, then the smallest percentage bid-ask spread that can occur for a stock priced at $5.00 is 2.5 percent, whereas the smallest percentage spread possible for a stock priced at $12.50 is 1.0 percent and 0.25 percent for a $50 stock. Also, the dollar volume of trading in a stock frequently declines following stock splits. 9 This inverse relation between transaction costs and trading volume is not unexpected; an extensive amount of literature addresses this issue. 1 0 Amihud and Mendelson (1986) document that such illiquidity is costly, in the sense that, ceteris paribus, it reduces the value of the firm. Why, then, do firms voluntarily use stock splits to move their share price to a less liquid trading range? 6 C o p e l a n d ( ), C o n r o y e t. a l. ( ), a n d S c h u l t z ( ). 7 B e n s t o n a n d H a g e r m a n ( ), S t o l l a n d W h a l e y ( ), B r e n n a n a n d C o p e l a n d ( ), B r e n n a n a n d H u g h e s ( ), a n d H a r r i s ( ). 8 H a r r i s ( ), A n s h u m a n a n d K a l a y ( ), a n d A n g e l ( ). A n g e l ( ) d o c u m e n t s a n i n t r i g u i n g r e l a t i o n b e t w e e n a v e r a g e s h a r e p r i c e s a n d t i c k s i z e s a c r o s s m a r k e t s w o r l d w i d e, b u t d o e s n o t a d d r e s s t h e i s s u e o f p r i c e v a r i a t i o n w i t h i n t h e s e m a r k e t s. 9 C o p e l a n d ( ), L a k o n i s h o k a n d L e v ( ), L a m o u r e u x a n d P o o n ( ), a n d C o n r o y e t. a l. ( ). 1 0 D e m s e t z ( ), T i n i c ( ), B e n s t o n a n d H a g e r m a n ( ) S t o l l ( ), A m i h u d a n d M e n d e l s o n ( ), C o n s t a n t a n i d e s ( ), a n d A t k i n s a n d D y l ( ).

7 7 Part of the answer to this question lies with Merton s (1987) model of capital market equilibrium with incomplete information. Merton assumes that investors generally are aware of only a subset of all available securities, that these subsets differ among investors, and that investors can only invest in securities that they know about. He shows that an increase in the relative size of a firm s investor base (i.e., the group of investors and potential investors who are aware of the firm) increases the market value of the firm. Firms may select a trading range for their shares that enlarges the firm s investor base, perhaps resulting in an increase in value that more than offsets the costs of the higher bid-ask spreads following stock splits noted by the studies cited in footnote 6. Muscarella and Vetsuypens (1996) provide evidence that splits of American Depository Receipts (ADRs) are to move the price of the ADRs to a particular trading range, and Conroy and Harris (1999) show that managers apparently design stock splits to return their firms stock prices to a desired trading range (i.e., the price level after the firms s last stock split). It is also well documented that the number of shareholders in a firm generally increases following a stock split, which is akin to an increase in the firm s investor base. 1 1 The specific mechanism through which a particular trading range for a firm s shares increases its investor base is not clear. The simplest explanation derives from a combination of investors revealed preferences for trading in round lots, the benefits of holding a diversified portfolio (Markowitz (1952)), and the limited wealth of most investors. In particular, a diversified portfolio of common stocks may require as many as 1 1 L a m o u r e u x a n d P o o n ( ), M a l o n e y a n d M u l h e r i n ( ), a n d M u k h e r j i e t. a l. ( ) r e p o r t t h i s f i n d i n g f o r c o m m o n s t o c k s p l i t s. F e r n a n d o e t. a l. ( ) r e p o r t a s i m i l a r r e s u l t f o r m u t u a l f u n d s p l i t s.

8 8 30 different stocks. 1 2 The NYSE s Shareownership 1998 publication indicates that the median and mean values of the common stock portfolios of all adult shar eholders are $15,500 and $95,000, respectively. 1 3 Thus, the median (mean) investor can only invest in about two (12) round lots of stocks in the Annheuser Busch/Intel trading range of $70- $75 per share, whereas he/she could invest in ten (more than 60) rounds lots of stocks priced at around $15 per share. It is likely that stock splits increase the number of shareholders simply because the lower price facilitates and, therefore, attracts investment by individual investors. Schultz (2000), for example, documents a large number of small buy orders following stock splits. Other explanations linking stock splits and the firm s investors have also been suggested. Brennan and Hughes (1991) observe that brokerage commissions are inversely related to share price and suggest that, in a world with incomplete information, brokers produce and disseminate more information (e.g., research reports and recommendations) about lower-priced firms, so firms are able to use stock splits to increase their investor base. Angel (1997) suggests that a single tick size in a market means that stock splits increase the minimum percentage bid-ask spread for a stock, consequently encouraging more market makers to both make a market in the firm s stock and to promote that stock to investors. Amihud et.al. (1999), however, find support for the simplest explanation. They investigate reductions in the minimum trading unit (MTU) in Japan, which is the minimum number of a firm s shares required for a transaction on an exchange in Japan, an d report an increase in the number of shareholders following a reduction in a firm s 1 2 S t a t m a n ( ). E a r l i e r w o r k b y E v a n s a n d A r c h e r ( ) s u g g e s t s a s m a l l e r n u m b e r.

9 9 MTU. They also observe a concomitant increase in stock price that is related to the increase in the number of shareholders. In Japan, brokerage commissions are a function of the value of the transaction, not the share price, and the reduction in the MTU does not change the stock price, so the Brennan and Hughes (1991) and Angel (1997) conjectures do not apply. The driving force behind the increase in shareholders and market value found in Japan following a reduction in a firm s MTU is apparently new investment by the small investors whose limited wealth did not permit them to purchase these stocks previously. The explanation of the dispersion in share prices in U.S. markets that emerges from Merton s model and from these other studies is that firms whose owners are primarily individual investors are most concerned with the trading range issue, and so these firms opt for lower share prices to expand their investor bases. Merton s model also implies the converse. Large, well-known, widely- held firms already have a very large investor base, with a high percentage of institutional and/or wealthy investors, and changes in the investor base of these firms have essentially no effect on the firm s market value. 1 4 For these firms, the qualitative predictions of Merton s model and Black s (1972) zero -beta Capital Asset Pricing Model coincide. These firms may therefore care little about share price levels in the trading range sense, but rather place a higher value on liquidity and low transaction costs, explaining why large firms tend to have higher share prices. 1 3 T h e s e d a t a a r e b a s e d o n t h e S u r v e y o f C o n s u m e r F i n a n c e s, a n o n g o i n g s u r v e y c o n d u c t e d b y t h e S u r v e y R e s e a r c h C e n t e r a t t h e U n i v e r s i t y o f M i c h i g a n f o r t h e F e d e r a l R e s e r v e B o a r d. 1 4 B a d r i n a t h e t. a l. ( ) d o c u m e n t t h e p e n c h a n t o f i n s t i t u t i o n a l i n v e s t o r s f o r t h i s t y p e o f s t o c k.

10 10 II. Ownership Characteristics and Share Prices Merton s (1987) model leads to two testable hypotheses about the dispersion of share prices in U.S. markets: (1) lower share prices are characteristic of firms owned by s o -called small investors and the converse; and (2) higher share prices are characteristic of large firms and the converse. In this section we present cross-sectional evidence regarding these hypotheses. A. Methodology and Data We test the hypotheses posed above by estimating the regression parameters associated with the following variables: SharePrice j,t = δ 0 + δ 1 TotalAssets j,t + δ 2 AvgHldg j,t + δ 3 InstPct j,t + ε j,t (1) where the dependent variable, SharePrice j,t, is the average price per share of firm j s common stock during year t, measured as the average of its monthly closing prices, the δ s are the parameters to be estimated, and ε j,t is an error term. The first independent variable, TotalAssets j,t, is the logarithm of the book value of firm j s assets at the end of year t. We use the book value of the firm s assets, rather than the firm s market capitalization, as the measure o f firm size in Equation (1) to avoid any spurious correlation that might arise with the latter measure (since the dependent variable is share price and market capitalization is share price times the number of shares outstanding). The book value of the firm s assets is obtained from Compustat.

11 11 The next independent variable, AvgHldg j,t, is the average dollar investment per shareholder in firm j during year t. The average dollar holding per shareholder is a measure of whether the firm s ownership clientele consists of small or large investors, at least on average. The number of shareholders per firm is also from Compustat. The final variable, InstPct j,t, is the percentage of firm j owned by institutional investors during year t. Institutional ownership is an alternative measure of the nature of the firm s ownership structure. Institutional investors are large investors, who are generally especially interested in liquidity and low transaction costs, and they are increasingly important participants in U.S. stock markets over the period of our study. Data regarding institutional ownership are from Compact Disclosure. Our initial data include all firms listed in the Center for Research in Security Prices (CRSP) database that have both continuous data available over the 21-year period from 1976 to 1996 and a share price of at least $1.25 at the end of January, We examine only firms with continuous data over the whole period to eliminate firms whose share price is largely a consequence of either circumstance (e.g., newly public firms) or vicissitude (e.g., firms experiencing financial distress). The initial sample consists of 1,426 firms. In 1976, 74.8 percent of the firms were listed on the NYSE and 26.2 percent were listed on the Amex. 1 6 In 1996, 84.6 percent of the firms are listed on the NYSE, 13.7 percent on the Amex, and 1.7 percent on Nasdaq. Even survivors do not all prosper. Table II shows summary statistics regarding our sample at five- year intervals from 1976 to Panel A contains data on share prices. The mean and median share 1 5 T h e m i n i m u m p r i c e o f $ w a s c h o s e n a r b i t r a r i l y t o e l i m i n a t e s o -c a l l e d p e n n y s t o c k s. I t i s s i m p l y t e n t i m e s t h e t i c k s i z e t h a t w a s i n e f f e c t d u r i n g t h i s p e r i o d.

12 12 prices are slightly higher in the later years than in the earlier years, although, as we have already noted in our discussion of Figure 1, the increase in share prices pales in comparison to the increase in the value of these firms during the period. The slight differences between the mean figures reported in Table II and the values for the same years in Figure 1 are because the data in Table II exclude common stocks with a price of less than $1.25 per share in 1976 whereas these firms are included in Figure 1. Panel B shows the mean and median market values of the firms (i.e., the year-end market capitalization reported by CRSP). The mean and median market values increase by 793 percent and 1,046 percent, respectively, from 1976 to Panels C and D report the number of shareholders per firm and the average investment per shareholder, respectively. Although the value of these firms increases greatly over the period, the average number of shareholders remains remarkably constant at roughly 21,000 shareholders per firm. The median number of shareholders per firm increases from just under 4,000 in 1976 to about 4,800 in 1996, a 20 percent increase. The mean number of shareholders is almost five times the median, indicating that the distribution of shareholders across the firms in our sample is very skewed. Overall, the combination of no meaningful increase in the average number of shareholders per firm and a substantial increase in the average market value of the firms results in a very large increase in the average investment per shareholder from 1976 to The mean investment increases from $24,600 per shareholder in 1976 to $235,840 in 1996, and the median shareholding also increases roughly tenfold during the period, from $12,090 in 1976 to $116,020 in Again, skewness is evident in the distribution of this variable 1 6 D a t a f o r N a s d a q f i r m s a r e n o t a v a i l a b l e o n C R S P u n t i l a f t e r

13 13 across firms. The substantial increase in the average dollar holdings per shareholder may be largely driven by increasing institutional ownership from 1976 to Finally, Panel E shows mean and median percentage institutional ownership beginning in 1986, as reported by Compact Disclosure. 1 7 These data are from Securities and Exchange Commission (SEC) reports (Form 13 -F) required of all institutions with equity holdings of $100 million or more, including banks, insurance companies, investment companies, pension funds, and foundations. The mean and median holding of these institutions averages about 42 percent of the firms shares in each year. Note, however, that whereas large institutions report holdings in only 305 of the firms in 1986, they report holdings in 1,228 of the firms in 1996 a 400 percent increase. B. Regression Results The results of our regression analysis are summarized in Table III. Panel A shows the coefficients of the share price regression when the independent variables are firm size and average dollar holding per shareholder. The numbers in parentheses are White (1980) heteroskedasticity-consistent t-statistics, and the double and single asterisks denote statistical significance at the.01 and.05 levels, respectively. The coefficient on firm size (δ 1 ) is positive and significant in each annual cross-sectional regression, a finding consistent with the hypothesis that larger, well-known firms have high share prices and vice versa. The coefficient on average investment per shareholder (δ 2 ) is also positive and significant at the.01 level in each regression, consistent with the hypothesis 1 7 T h e s e d a t a a r e n o t a v a i l a b l e f r o m t h i s s o u r c e f o r a n d

14 14 that lower share prices are preferred by firms owned by small investors and vice versa. 1 8 The average R 2 of the five regressions is Panel B shows estimates of the regression coefficients when the independent variables in the regression are firm size and institutional ownership. The coefficient on firm size (d 1 ) remains positive and significant in each year. The coefficient on institutional ownership (d 3 ) is also positive in each year, consistent with firms owned by large institutional investors having higher share prices and vice versa, but it is not significant in the 1986 regression. The R 2 s of the three regressions average 0.30, much lower than the 0.45 average for the five regressions in Panel A. Panel C shows the results when all three independent variables are included in the regression. The findings regarding firm size and average investment per shareholder remain unchanged. The significance of the coefficient on institutional ownership drops in each regression, however, and the adjusted R 2 s are actually slightly lower that those of the comparable regressions in Panel A. Apparently the size of the average dollar shareholding, indicating the general wealthiness of the firm s ownership clientele per se, is paramount, and the distinction between large individual inv estors and institutional investors is irrelevant. C. Summary The cross-sectional regression estimates in Table III provide strong support both for the hypothesis that lower share prices characterize firms owned largely by small 1 8 T h e m a g n i t u d e o f t h e c o e f f i c i e n t o n AvgHldg j,t d e c l i n e s s t e a d i l y o v e r t h e p e r i o d, a n d t h e v a l u e i n i s only one-t e n t h t h e v a l u e i n T h i s d e c r e a s e i s s i m p l y a m a t t e r o f s c a l e, a n d h a s n o e c o n o m i c i n t e r p r e t a t i o n. R e c a l l f r o m T a b l e I I t h a t t h e a v e r a g e i n v e s t m e n t p e r s h a r e h o l d e r i n c r e a s e s r o u g h l y t e n f o l d f r o m t o

15 15 investors and vice versa, and for the hypothesis that higher share prices are associated with large, well- known firms and vice versa. When interpreted in the light of Merton (1987), these findings are consistent with the widespread belief among finance practitioners that the choice of an appropriate trading range for a firm s shares affects the value of the firm. III. Share Prices and Stock Splits If firms manage the price of their shares in an attempt to keep the price within an appropriate trading range, where appropriate is defined in terms of the size of the firm and the characteristics of its owners as per Panel A in Table III, then firms whose share prices rise above this range are presumably more likely to split their stock than are firms whose share prices remain at or below the appropriate trading range. We investigate this issue by testing whether firms whose share prices are in some sense too high are more likely to split their stock than are firms whose share prices are not too high. Merton s model also indicates that additional shareholders provide only negligible increases in firm value for firms with very large shareholder bases, which may reduce the likelihood that a firm will split their stock. We incorporate this possibility into the tests described in the next section. A. Methodology We examine the propensity of firms to split their stock by estimating the parameters of the following logit model:

16 16 StockSplit j,t = F (ß 0 + ß 1 TradeRange j,t + ß 2 StockApprec j,t + ß 3 Shareholders j,t ) (2) where StockSplit j,t is the probability that firm j will split its stock during time period T a binary variable with a value of 1 if firm j splits its stock during time interval T and 0 otherwise, F is the logistic cumulative density function, TradeRange j,t measures the location of firm j s share price in year t relative to the stock s predicted trading range an indication of whether or not the price of the stock is too high, StockApprec j,t measures the proportionate increase in the firm s stock price over the five years preceding year t, Shareholders j,t is a binary variable based on the relative size of the firm s investor base in year t, and the ß s are the parameters of the logit model. 1 9 The dependent variable, StockSplit j,t, equals 1 if firm j has a stock split of 1.25-t o- 1 or greater during time interval T, and 0 otherwise. 2 0 These data are identified for two - year and four-year intervals following the years 1976, 1981, 1986, and 1991 by examining the stock split factors reported in CRSP. The proportion of firms in our sample having common stock splits during each four-year interval is shown in Table IV. Panel A shows the incidence of 2 -for -l or greater splits, and Panel B shows for-1 or greater splits. Clearly stock splits are not exactly a rare event for the firms in our sample in any of the four sub-periods. Roughly 23 percent of the firms had at least a 2 -for-1 s p l i t during each of the four-year periods, and roughly 34 percent had at least a 1.25-for-l split. The first independent variable, TradeRange j,t, is defined as follows: 1 9 U s i n g a n o r m a l c u m u l a t i v e d e n s i t y f u n c t i o n ( i. e., p r o b i t ) y i e l d s q u a l i t a t i v e l y s i m i l a r r es u l t s. 2 0 T h e r e s u l t s a r e n o t s e n s i t i v e t o t h e m i n i m u m l e v e l u s e d t o d e f i n e w h e t h e r o r n o t a f i r m h a s s p l i t i t s s t o c k. W e c h o s e t o -1 a s a m i n i m u m s i m p l y t o e x c l u d e f i r m s t h a t u s e s m a l l s t o c k d i s t r i b u t i o n s i n l i e u o f c a s h d i v i d e n d s.

17 17 TradeRange j,t = SharePrice j,t / E (SharePrice j,t TotalAssets j,t, AvgHldg j,t ), (3) where E(SharePrice j,t ) is estimated for each of the four years (1976, 1981, 1986, and 1991) using the regression relation shown in Panel A of Table III. 2 1 That is, E( SharePrice j,t ) = d 0 + d 1 TotalAssets j,t + d 2 AvgHldg j,t, (4) s o TradeRange j,t is the ratio of a firm s actual share price in year t to its predicted share price given the firm s size and average holdings per shareholder. A value greater than 1 for TradeRange j,t suggests that firm j s share price is too high for the firm s size and average investment per shareholder, and a value less than or equal to 1 indicates that the firm s share price is below or close to its appropriate trading range, respectively. The second independent variable, StockApprec j,t, is the proportional increase in the jth firm s split-adjusted average stock price over the four years ending with the estimation year, computed as follows: StockApprec j,t = SharePrice j,t / SharePrice j,t-4. (5) We include share price appreciation as an explanatory variable in our logit model of stock splits because numerous studies report an increase in stock prices (in excess of market 2 1 W e r e q u i r e t h a t E (S h a r e P r i c e j,t ) b e g r e a t e r t h a n f i v e d o l l a r s f o r t h e f i r m t o b e i n c l u d e d i n t h e l o g i t a n a l y s i s. I n c l u s i o n o f a l l o b s e r v a t i o n s d o e s n o t q u a l i t a t i v e l y a l t e r t h e r e s u l t s o f t h e l o g i t a n a l y s i s.

18 18 returns) preceding splits that begins up to five years before the announcement of the stock split. 2 2 The last independent variable, Shareholders j,t, is a binary variable created by ranking all firms in descending order based on the number of shareholders. Shareholders j,t has a value of 1 when the number of shareholders is in the top five percent, otherwise it is 0. We include this variable because Merton s model implies that the size of the firm s investor base is not a concern for firms that already have a great many shareholders. B. Logit Results The results of the logit analysis are shown in Table V, when the time interval T in StockSplit j,t is the four-year period following year t. 2 3 Panel A shows the findings when TradeRange j,t and ShareApprec j,t are the only variables in the model. The coefficients on TradeRange j,t (i.e., the ß 1 s) are positive and significant, indicating that a firm whose share price in year t is above its predicted trading range is more likely to split its stock in the next four years than is a firm whose price is near or below its predicted trading range. When the actual share price is twice the predicted price, a firm is between 1.8 and 4 times (depending on the cross section) more likely to split its stock than is a firm whose actual and predicted prices are equal. For example, in the logit, a firm is 2.6 times more likely to split its stock when its actual share price is double the predicted price, F a m a e t. a l. ( ), L a k o n i s h o k a n d L e v ( ), L a m o u r e u x a n d P o o n ( ), a n d M c N i c h o l s a n d D r a v i d ( ). 2 3 U s e o f a t w o -y e a r p e r i o d y i e l d s s i m i l a r r e s u l t s. 2 4 T h i s i n t e r p r e t a t i o n o f a l o g i t p a r a m e t e r e s t i m a t e i s k n o w n a s a n o d d s r a t i o, a n d i s c o m p u t e d a s e x p { ß 1 } ( s e e D e m a r i s ( ) ).

19 19 strong evidence that trading range considerations are important to firms and that they use stock splits to manage share price levels. The coefficients on StockApprec j,t (i.e., the ß 2 s) are also positive and generally significant, indicating that firms are more likely to split their stock after a period of price appreciation, consistent with the findings of earlier studies (see footnote 22). This result is not surprising, since an increase I share prices is likely to be the primary cause of share prices becoming too high relative to their appropriate trading range. The trading range variable is, however, more important than the price appreciation variable as a predictor of a firm s propensity to split its stock. Panel B in Table V reports the results of the logit model when the variable measuring the firm s relative investor base, Shareholders j,t, is included. The results for TradeRa n g e j,t and StockApprec j,t are similar to those reported in Panel A, and the overall significance levels are slightly higher. In three of the four cross-sections, firms with relatively large shareholder bases (i.e., the number of shareholders is in the 95 th percentile) are less likely to split than are firms with smaller shareholder bases, a result significant at the.01 level for the 1976 and 1981 cross-sections. 2 5 The results in both Panels A and B of Table V suggest that when stock prices exceed some preferred trading range, firms are more likely to split their stock to move prices back toward a desired share price habitat, but that firms with very large shareholder bases are less likely to split. C. Do Stock Splits Increase the Number of Shareholders? A basic theme of this paper is that firms manage share price levels to make the 2 5 T h e c o e f f i c i e n t o n S h a r e h o l d e r s j,t i n t h e c r o s s -s e c t i o n i s p o s i t i v e, b u t i n s i g n i f i c a n t.

20 20 firm s common stock more attractive to investors. Why might one share price be more attractive than another to a particular firm s current and potential shareholders? We have already summarized the explanations offered by Merton (1987), Brennan and Hughes (1991), Angel (1997) and the NYSE Listed Company Manual (undated) and have presented various reasons why the preferences of so-called small investors might differ markedly f rom those of large institutional investors. Indeed, it is likely that all of these explanations at least partially account for the differences in share price preferences among firms. Although a unified theory of share price levels and stock splits is b eyond the scope of this paper, we can document whether or not stock splits by the firms in our sample are associated with subsequent increases in the number of shareholders (for whatever reason). These findings are summarized in Table VI. Firms that have at least a 2 -for-1 stock split average a 50 percent increase in shareholders during the four years, whereas firms that do not split their stock or have a smaller split average a 0.5 percent decrease in shareholders. Similarly, firms that have a 1.25-to-1 or greater split exhibit an average increase in shareholders of 42 percent and the other firms average a 5 percent decrease in shareholders. The results for our sample are thus consistent with those of earlier studies (see footnote 11). If the purpose o f stock splits is to increase a firm s socalled investor base, it appears that, on average, they accomplish this goal (even if the mechanism is not entirely clear).

21 21 IV. Conclusions We observe wide variations among share prices in U.S. stock markets, and it i s evident that these differences in share prices do not just happen. That is, apparently firms manage their share prices. We present cross-sectional evidence that variables consistent with Merton s (1987) model of capital market equilibrium with incomplete information explain 45 percent of the variation among firms share prices. In particular, firms owned by small investors have lower share prices and vice versa, and large, wellknown firms have higher share prices and vice versa. We also find that trading range, share price appreciation, and shareholder base are significant predictors of subsequent stock splits, and that firms splitting their stock experience an increase in shareholders compared to non -splitting firms. We conclude that the Share Price Puzzle is not so puzzling after all. Rather, it is a matter of the optimal design of a security. The high dispersion in stock prices in U.S. markets is largely a manifestation of firms tailoring their share prices to reflect the desires of the firm s owners.

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24 24 Mukherji, Sandip, Yong H. Kim, and Michael C. Walker, 1997, The effect of stock splits on the ownership structure of firms, Journal of Corporate Finance 3, Muscarella, Chris J., and Michael R. Vetsuypens, 1996, Stock splits: Signaling or liquidity? The case of ADR solo-splits, Journal of Financial Economics 42, Schultz, Paul, 2000, Stock splits, tick size and sponsorship, Journal of Finance 5 5, Statman, Meir, 1987, How many stocks make a diversified portfolio? Journal of Financial and Quantitative Analysis 22, Stoll, Hans R., 1978, The pricing of security dealer services: An empirical study of Nasdaq stocks, Journal of Finance 33, Stoll, Hans R., and Robert E. Whaley, 1983, Transactions costs and the small firm effect: A comment, Journal of Financial Economics 1 2, Tinic, Seha M., 1972, The economics of liquidity services, Quarterly Journal of Economics 86, White, Halbert, 1980, A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica 48,

25 25 $250 $200 $150 Price $100 $50 Average Price w/o Splits Average Price $ Year Figure 1. Average Common Stock Prices from 1976 to Average annual stock prices for 1,452 firms with continuous data available on CRSP for 1976 through The annual price for each firm is the average of monthly closing prices. The solid line shows actual prices. The broken line shows what the prices would have been in the absence of stock splits that occurred during this period.

26 26 Table I Stock Prices on the NYSE, Amex, and Nasdaq in 1996 I n c l u d e s a l l f i r m s r e p o r t e d i n t h e C R S P d a t a b a s e f o r h a v i n g a n a v e r a g e p r i c e o f a t l e a s t $ p e r s h a r e. I n d i v i d u a l f i r m s s t o c k p r i c e s a r e t h e a v e r a g e o f m o n t h l y c l o s i n g p r i c e s i n M a r k e t v a l u e i s t h e year-e n d m a r k e t c a p i t a l i z a t i o n r e p o r t e d i n t h e C R S P d a t a b a s e. All Prices Less than $ 1 0 $ 1 0 to $30 $ 3 0 t o $ 5 0 $ 5 0 t o $ 7 0 Greater than $70 Panel A: All Firms Listed on the NYSE, Amex, and Nasdaq Share Price Mean $ $ $ $ $57.84 $ Median $ $ $ $ $56.81 $ Number of Firms 6, , , Proportion of Firms % 33.2% % % 3. 5 % 1. 7 % Market Value (000,000) Mean $ 1, $ 8 4 $ $ 2, $8,545 $ 2 0, Median $149 $ 3 3 $ $ 1, $4,259 $ 7, Panel B: NYSE Firms Share Price Mean $ $ $ $ $57.68 $ Median $ $ $ $ $56.62 $ Number of Firms 2, , Proportion of Firms % 15.6% % % 6. 9 % 3. 5 % Market Value (000,000) Mean $ 2, $ $ $ 3, $ 1 0, $ 2 2, Median $531 $ $ $ 1, $4,963 $ 1 3, Panel C: Amex Firms Share Price Mean $ $ $ $ $58.95 $ Median $ $ $ $ $ Number of Firms Proportion of Firms % 46.4% % 5.4% 0. 4 % 1. 1 % Market Value (000,000) Mean $209 $ 5 9 $ $ 1, $1,045 $ Median $ 5 8 $ 2 9 $ 9 0 $ $ Panel D: Nasdaq Firms Share Price Mean $ $ $ $ $58.27 $ Median $ $ $ $ $57.49 $ Number of Firms 3, , , Proportion of Firms % 43.3% % 9.4% 1. 7 % 0.1 Market Value (000,000) Mean $366 $ 4 8 $ $ 1, $3,667 $ 1 5, Median $ 7 9 $ 2 7 $ $ $1,982 $ 1, 0 9 7

27 27 Table II Descriptive Statistics for Sample Firms, T h e s h a r e p r i c e s a m p l e i n c l u d e s a l l f i r m s w i t h a s h a r e p r i c e g r e a t e r t h a n o r e q u a l t o $ i n a n d w i t h c o n t i n u o u s i n f o r m a t i o n a v a i l a b l e o n C R S P f r o m t o A n n u a l s h a r e p r i c e i s t h e a v e r a g e o f m o n t h l y c l o s i n g p r i c e s f r o m C R S P. M a r k e t v a l u e i s t h e y e a r -e n d c a p i t a l i z a t i o n r e p o r t e d o n C R S P. N u m b e r o f s h a r e h o l d e r s i s f r o m C o m p u s t a t, a n d i n s t i t u t i o n a l o w n e r s h i p i s f r o m C o m p a c t D i s c l o s u r e P a n e l A : S h a r e P r i c e M e a n $ $ $ $ $ ( S t a n d a r d D e v i a t i o n ) ( ) ( ) ( ) ( ) ( ) M e d i a n $ $ $ $ $ N u m b e r o f F i r m s 1, , , , , P a n e l B : M a r k e t V a l u e ( 0 0 0, ) M e a n $ $ $ 1, $ 1, $ 3, ( S t a n d a r d D e v i a t i o n ) ( 2, ) ( 2, ) ( 3, ) ( 6, ) ( 1 1, ) M e d i a n $ 5 2 $ $ $ $ N u m b e r o f F i r m s 1, , , , , P a n e l C : N u m b e r o f S h a r e h o l d e r s ( ) M e a n ( S t a n d a r d D e v i a t i o n ) ( ) ( ) ( ) ( ) ( ) M e d i a n N u m b e r o f F i r m s , , , P a n e l D : A v e r a g e I n v e s t m e n t p e r S h a r e h o l d e r ( ) M e a n $ $ $ $ $ ( S t a n d a r d D e v i a t i o n ) ( ) ( ) ( ) ( ) ( ) M e d i a n $ $ $ $ $ N u m b e r o f F i r m s , , , P a n e l E : I n s t i t u t i o n a l O w n e r s h i p M e a n n.a. n.a % % % ( S t a n d a r d D e v i a t i o n ) n.a. n.a. ( ) ( ) ( ) M e d i a n n.a. n.a % % % N u m b e r o f F i r m s n.a. n.a , 2 2 8

28 28 Table III Share Prices, Firm Size, and Ownership Characteristics T h i s t a b l e r e p o r t s c r o s s -s e c t i o n a l e s t i m a t e s o f t h e p a r a m e t e r s o f t h e f o l l o w i n g r e g r e s s i o n v a r i a b l e s : S h a r e P r i c e j,t = δ 0 + δ 1 T o t a l A s s e t s j,t + δ 2 A v g H l d g j,t + δ 3 I n s t P c t j,t + ε j,t w h e r e S h a r e P r i c e j,t i s t h e a v e r a g e p r i c e p e r s h a r e o f f i r m j s c o m m o n s t ock during year t, T o t a l A s s e t s j,t i s t h e l o g a r i t h m o f t h e b o o k v a l u e o f f i r m j s a s s e t s a t t h e e n d o f y e a r t, A v g H l d g j,t i s t h e a v e r a g e d o l l a r i n v e s t m e n t p e r s h a r e h o l d e r i n f i r m j d u r i n g y e a r t, a n d I n s t P c t j,t i s t h e p e r c e n t a g e o f f i r m j o w n e d b y i n s t i t u t i o n a l i n v e s t o r s d u r i n g y e a r t. T h e n u m b e r s i n p a r e n t h e s e s a r e W h i t e ( ) h e t e r o s k e d a s t i c i t y c o n s i s t e n t t -s t a t i s t i c s, a n d * * ( * ) d e n o t e s s i g n i f i c a n c e a t t h e. 0 1 (. 0 5 ) l e v e l. Year δ 0 δ 1 δ 2 δ 3 Adj. R 2 F- test Number of Firms Panel A: The Independent Variables are T o t a l A s s e t s a n d A v g H l d g (-4.63**) (10.57**) (8.24**) ( ) (15.12**) (9.16**) (-3.54**) (15.41**) (4.27**) , (-5.21**) (16.61**) (8.49**) , (-6.38**) (15.05**) (4.93**) , Panel B: The Independent Variables are T o t a l A s s e t s a n d InstPct (- 2.29*) (6.65**) ( ) (-6.88**) (14.47**) (6.19**) (-8.94**) (16.81**) (4.69**) , Panel C: The Independent Variables are T o t a l A s s e t s, A v g H l d g, and I n s t P c t ( ) (7.63**) (4.95**) ( ) (-4.99**) (13.10**) (7.06**) (2.42*) (-6.46**) (13.72**) (4.45**) ( *) , 1 0 1