THE JOURNAL OF FINANCE. VOL XLVII. 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 equity, combine to capture the cross-sectional variation in average stock returns associated with market a size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the ests allow for variation in e that is unrelated to size the relation between market B and average return is flat, even when a 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 as(the slope in the regression of a security's return on the market,s return), nd (b) market &s suffice to describe the cross-section of expected returns G There are several empirical contradictions of the Sharpe-Lintner-Black LB)model. The most prominent is the size effect of Banz(1981). He finds hat market equity, Me (a stock's price times shares outstanding), adds to the explanation of the cross-section of average returns provided by market estimates, and average returns on large stocks are too low. gh given their B Bs. Average returns on small (low ME) stocks are too hig 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 ts 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 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, Nai-fu Chen, George Constan tinides, Wayne ferson, Edward George, Campbell Harvey, Josef Lakonishak, 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)