The Cross-Section of Expected Stock Returns Part 1

The Cross-Section of Expected Stock Returns ABSTRACT Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market 3. size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the tests allow for variation in @ that is unrelated to size, the relation between market and average return is flat, even when is the only explanatory variable. THE ASSET-PRICING MODEL OF Sharpe (1964), Lintner (1965), and Black (1972) has long shaped the way academics and practitioners think about average returns and risk. The central prediction of the model is that the market portfolio of invested wealth is mean-variance efficient in the sense of Markowitz (1959). The efficiency of the market portfolio implies that (a) expected returns on securities are a positive linear function of their market Bs (the slope in the regression of a security's return on the market's return), and (b) market ẞs suffice to describe the cross-section of expected returns. There are several empirical contradictions of the Sharpe-Lintner-Black (SLB) model. The most prominent is the size effect of Banz (1981). He finds that market equity, ME (a stock's price times shares outstanding), adds to the explanation of the cross-section of average returns provided by market 68. Average returns on small (low ME) stocks are too high given their estimates, and average returns on large stocks are too low. Another contradiction of the SLB model is the positive relation between leverage and average return documented by Bhandari (1988). It is plausible that leverage is associated with risk and expected return, but in the SLB model, leverage risk should be captured by market 3. Bhandari finds, how-ever, that leverage helps explain the cross-section of average stock returns in tests that include size (ME) as well as 3. Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) find that aver-age returns on U.S. stocks are positively related to the ratio of a firm's book value of common equity, BE, to its market value, ME. Chan, Hamao, and Lakonishok (1991) find that book-to-market equity, BE/ME, also has a strong role in explaining the cross-section of average returns on Japanese stocks. Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, IL 60637. We acknowledge the helpful comments of David Booth, Naifu Chen, George Constan tinides, Wayne Ferson, Edward George, Campbell Harvey, Josef Lakonishok, Rex Sinquefield, René Stulz. Mark Zmijeweski, and an anonymous referee. This research is supported by the National Science Foundation (Pama) and the Center for Research in Security Prices (French). Finally, Basu (1983) shows that earnings-price ratios (E/P) help explain the cross-section of average returns on U.S. stocks in tests that also include size and market 3. Ball (1978) argues that E/P is a catch-all proxy for unnamed factors in expected returns; E/P is likely to be higher (prices are lower relative to earnings) for stocks with higher risks and expected returns, whatever the unnamed sources of risk. Ball's proxy argument for E/P might also apply to size (ME), leverage, and book-to-market equity. All these variables can be regarded as different ways to scale stock prices, to extract the information in prices about risk and expected returns (Keim (1988)). Moreover, since E/P, ME, leverage, and BE/ME are all scaled versions of price, it is reasonable to expect that some of them are redundant for describing average returns. Our goal is to evaluate the joint roles of market 3, size, E/P, leverage, and book-to-market equity in the cross-section of average returns on NYSE, AMEX, and NASDAQ stocks. Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) find that, as predicted by the SLB model, there is a positive simple relation between average stock returns and ẞ during the pre-1969 period. Like Reinganum (1981) and Lakonishok and Shapiro (1986), we find that the relation between ẞ and average return disappears during the more recent 1963-1990 period, even when 3 is used alone to explain average returns. The appendix shows that the simple relation between ẞ and average return is also weak in the 50-year 1941-1990 period. In short, our tests do not support the most basic prediction of the SLB model, that average stock returns are positively related to market 3s. Unlike the simple relation between and average return, the univariate relations between average return and size, leverage, E/P, and book-to-market equity are strong. In multivariate tests, the negative relation between size and average return is robust to the inclusion of other variables. The positive relation between book-to-market equity and average return also persists in competition with other variables. Moreover, although the size effect has attracted more attention, book-to-market equity has a consistently stronger role in average returns. Our bottom-line results are: (a) ẞ does not seem to help explain the cross-section of average stock returns, and (b) the combina-tion of size and book-to-market equity seems to absorb the roles of leverage and E/P in average stock returns, at least during our 1963-1990 sample period. If assets are priced rationally, our results suggest that stock risks are multidimensional. One dimension of risk is proxied by size, ME. Another dimension of risk is proxied by BE/ME, the ratio of the book value of common equity to its market value. It is possible that the risk captured by BE/ME is the relative distress factor of Chan and Chen (1991). They postulate that the earning prospects of firms are associated with a risk factor in returns. Firms that the market judges to have poor prospects, signaled here by low stock prices and high ratios of book-to-market equity, have higher expected stock returns (they are penalized with higher costs of capital) than firms with strong prospects. It is for variation in ẞ that is unrelated to size, the relation between and average return is flat, even when 3 is the only explanatory variable. B. Fama-MacBeth Regressions Table III shows time-series averages of the slopes from the month-by-month Fama-MacBeth (FM) regressions of the cross-section of stock returns on size, ẞ, and the other variables (leverage, E/P, and book-to-market equity) used to explain average returns. The average slopes provide standard FM tests for determining which explanatory variables on average have non-zero expected premiums during the July 1963 to December 1990 period. Like the average returns in Tables I and II, the regressions in Table III say that size, In(ME), helps explain the cross-section of average stock returns. The average slope from the monthly regressions of returns on size alone is -0.15%, with a 1-statistic of -2.58. This reliable negative relation persists no matter which other explanatory variables are in the regressions; the average slopes on In(ME) are always close to or more than 2 standard errors from 0. The size effect (smaller stocks have higher average returns) is thus robust in the 1963-1990 returns on NYSE, AMEX, and NASDAQ stocks. In contrast to the consistent explanatory power of size, the FM regressions show that market 8 does not help explain average stock returns for 1963-1990. In a shot straight at the heart of the SLB model, the average slope from the regressions of returns on ẞ alone in Table III is 0.15% per month and only 0.46 standard errors from 0. In the regressions of returns on size and B, size has explanatory power (an average slope 3.41 standard errors from 0), but the average slope for ẞ is negative and only 1.21 standard errors from 0. Lakonishok and Shapiro (1986) get similar results for NYSE stocks for 1962-1981. We can also report that & shows no power to explain average returns (the average slopes are typically less than 1 standard error from 0) in FM regressions that use various combinations of 3 with size, book-to-market equity, leverage, and E/P. C. Can B Be Saved? What explains the poor results for 3? One possibility is that other explana-tory variables are correlated with true ßs, and this obscures the relation between average returns and measured ẞs. But this line of attack cannot explain why ẞ has no power when used alone to explain average returns. Moreover, leverage, book-to-market equity, and E/P do not seem to be good proxies for 3. The averages of the monthly cross-sectional correlations be-tween and the values of these variables for individual stocks are all within. 0.15 of 0. Another hypothesis is that, as predicted by the SLB model, there is a positive relation between and average return, but the relation is obscured by noise in the ẞ estimates. However, our full-period post-ranking ẞs do not seem to be imprecise. Most of the standard errors of the ßs (not shown) are