The Cross-Section of Expected Stock Returns TORIo Eugene F Fama: Kenneth R. french The Journal of Finance, Vol. 47, No. 2. ( Jun, 1992), pp. 427-465 Stable url: http://links.jstor.org/sici?sici=0022-1082%028199206%294793a2%03c427%03atcoesr%3e2.0.c0%3b2-n The Journal of finance is currently published by American Finance Association Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://wwwjstor.org/journals/afina.html Each copy of any part of a jSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission jStOR is an independent not-for-profit organization dedicated to creating and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor. org http://www」]stor.or Wed mar2900:49:062006
THE JOURNAL OF FINANCE VOL. XLVIL. NO. 2. JUNE 1992 The Cross-Section of Expected Stock Returns euGene F FAMA and KENNETH R. FreNch ABSTRACT Two easily measured variables, size and book-to-market combine to capture ted with market B, ize, leverage, book-to-market equity, and earnings-price Moreover. when the tests allow for variation in b that is unrelated to size, the relation between market B and average return is flat, even when B 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 Bs 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 Bs. Average returns on small (low ME) stocks are too high given their B 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 B. Bhandari finds, how ever, that leverage helps explain the cross-section of average stock returns in tests that include size (mE)as well as B 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 firms 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 Stree 60637. We acknowledge the helpful comments of David Booth, Nai-fu Chen, George Constan tinides, Wayne Ferson, Edward George, Campbell Harvey, Josef Lakonishok, Rex Sinquefield, Rene Stulz, Mark Zmijeweski, and an anonymous referee. This research is supported by the National Science Foundation(Fama)and the Center for Research in Security Prices(French)
The Journal of finance 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 B. Ball(1978) argues that E/P is tch-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 Balls 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 B, 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 p during the pre-1969 period. Like Reinganum (1981) and Lakonishok and Shapiro (1986), we find that the relation between B and average return disappears during the more recent 1963-1990 period, even when B is used alone to explain average returns. The appendix shows that the simple relation between B 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 Bs Unlike the simple relation between 8 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)B 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 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
The Cross-Section of Expected Stock Returns also possible, however, that BE /ME just captures the unraveling(regression toward the mean) of irrational market whims about the prospects of firms Whatever the underlying economic causes, our main result is straightfor ward. Two easily measured variables, size (ME)and book-to-market equity (BE /ME), provide a simple and powerful characterization of the cross-section of average stock returns for the 1963-1990 period In the next section we discuss the data and our approach to estimating B Section II examines the relations between average return and B and between average return and size. Section Ill examines the roles of E /P, leverage, and book-to-market equity in average returns, In sections IV and v, we summa rize, interpret, and discuss applications of the results I. Preliminaries A. Data use all nonfinancial firms in the intersection of (a) the NYSE, AMEX, and NASDAQ return files from the Center for Research in Security Prices (CRSP)and(b) the merged COMPUSTAT annual industrial files of income statement and balance-sheet data, also maintained by CRSP. We exclude financial firms because the high leverage that is normal for these firms high leverage more likely indicates distress. The CRSP returns cover NESN probably does not have the same meaning as for nonfinancial firms, whe and AMEX stocks until 1973 when NASDAQ returns also come on line. The comPustat data are for 1962-1989. The 1962 start date reflects the fact that book value of common equity(COMPUSTAT item 60), is not generally available prior to 1962. More important, COMPUSTAT data for earlier years have a serious selection bias; the pre-1962 data are tilted toward big histori ally successful firms To ensure that the accounting variables are known before the returns they are used to explain, we match the accounting data for all fiscal yearends in calendar year t-1(1962-1989)with the returns for July of year t to June of t+1. The 6-month (minimum) gap between fiscal yearend and the return tests is conservative. Earlier work (e.g, Basu(1983) often assumes that ccounting data are available within three months of fiscal yearends. Firms are indeed required to file their 10-K reports with the SEC within 90 days of their fiscal yearends, but on average 19.8% do not comply. In addition, more than 40% of the December fiscal yearend firms that do comply with the 90-day rule file on March 31, and their reports are not made public until April.(See Alford, Jones, and Zmijewski (1992).) We use a firms market equity at the end of December of year t-1 to compute its book-to-market, leverage, and earnings-price ratios for t-1 we use its market equity for June of year t to measure its size. Thus included in the return tests for July of year t, a firm must have a CRSP price for December of year t-1 and June of year t. It must also have monthly returns for at least 24 of the 60 months preceding July of year t(for
430 The Journal of finance ings(E), for its fiscal year ending in(any month of) calendar year /->ar pre-rankin estimates, discussed below). And the firm must have comPUSTaT data on total book assets(A), book equity(BE), and ea Our use of December market equity in the E/P, BE/ME, and leverage ratios is objectionable for firms that do not have December fiscal yearends because the accounting variable in the numerator of a ratio is not aligned h the market value in the denominator Using ME at fiscal yearends is lso problematic; then part of the cross-sectional variation of a ratio for a given year is due to market-wide variation in the ratio during the year. For xample, if there is a general fall in stock prices during the year, ratios measured early in the year will tend to be lower than ratios measured later We can repo however, that the use of fiscal-yearend MEs, rather than December MEs, in the accounting ratios has little impact on our return tests Finally, the tests mix firms with different fiscal yearends. Since we match accounting data for all fiscal yearends in calendar year t-1 with returns for July of t to June of t+ 1, the gap between the accounting data and the matching returns varies across firms. We have done the tests using the smaller san of firms with December fiscal yearends with similar results B. Estimating Market Bs Our asset-pricing tests use the cross-sectional regression approach of Fama and MacBeth(1973). Each month the cross-section of returns on stocks is regressed on variables hypothesized to explain expected returns. The time- series means of the monthly regression slopes then provide standard tests of whether different explanatory variables are on average priced Q Since size, E/P, leverage, and BE/ME are measured precisely for individ l stocks, there is no reason to smear the information in these variables by using portfolios in the Fama-MacBeth(FM)regre Most previous tests use portfolios because estimates of market Bs are more precise for portfolios Our approach is to estimate Bs for portfolios and then assign a portfolios p to each stock in the portfolio. This allows us to use individual stocks in the FM asset-pricing tests B.1. B Estimation: Details n June of each year, all NYSE stocks on CRSP are sorted by size (me) to determine the NYSe decile breakpoints for ME. NYSE, AMEX, and NASdAQ stocks that have the required CRSP-comPUSTaT data are ther allocated to 10 size portfolios based on the NYSE breakpoints. (If we used stocks from all three exchanges to determine the ME breakpoints, mos portfolios would include only small stocks after 1973, when NASDAQ stocks are added to the sample.) We form portfolios on size because of the evidence of Chan and Chen(1988) and others that size produces a wide spread of average returns and Bs. Chan and Chen use only size portfolios. The problem this creates is that size and the Bs of size portfolios are highly correlated (-0.988 in their data),so