The Center for Research in Security Prices

The value premium in U.S. stock returns is robust. The positive relation between average return and book-to-market equity is as strong for 1929-63 as for the subsequent period studied in previous papers. A three-factor risk model explains the value premium better than the hypothesis that the book-to-market characteristic is compensated irrespective of risk loadings. * College of Business, Kansas State University (Davis), Graduate School of Business, University of Chicago (Fama) and Sloan School of Management, Massachusetts Institute of Technology (French). Support for data collection from Dimensional Fund Advisors and the comments of Kent Daniel, John Heaton, Ren Stulz, Sheridan Titman, and two referees are gratefully acknowledged. Firms with high ratios of book value to the market value of common equity have higher average returns than firms with low book-to-market ratios (Rosenberg, Reid, and Lanstein (1985)). Because the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) does not explain this pattern in average returns, it is typically called an anomaly. There are four common explanations for the book-to-market (BE/ME) anomaly. One says that the positive relation between BE/ME and average return (the so-called value premium) is a chance result unlikely to be observed out of sample (Black (1993), MacKinlay (1995)). Out-ofsample evidence is, however, provided by Chan, Hamao, and Lakonishok (1991), Capaul, Rowley, and Sharpe (1993), and Fama and French (1998). They document strong relations between average return and BE/ME in markets outside the U.S. Using a rather small sample of firms, Davis (1994) finds that the relation between average return and BE/ME observed in recent U.S. returns extends back to 1941. We extend DavisÕ data back to 1926, and we expand the coverage to all NYSE industrial firms. We find that the value premium in pre-1963 returns is close to that observed for the subsequent period in earlier work. These results argue against the sample-specific explanation for the value premium. The second story for the value premium is that it is not an anomaly at all. The higher average returns on high BE/ME stocks are compensation for risk in a multifactor version of MertonÕs (1973) intertemporal capital asset pricing model (ICAPM) or RossÕs (1976) arbitrage pricing theory (APT). Consistent with this view, Fama and French (1993) document covariation in returns related t o BE/ME beyond the covariation explained by the market return. Fama and French (1995) show that there is a BE/ME factor in fundamentals (earnings and sales) like the common factor in returns. The acid test of a multifactor model is whether it explains differences in average returns. Fama and French (1993, 1996) propose a three-factor model that uses the market portfolio and mimicking portfolios for factors related to size (market capitalization) and BE/ME to describe returns. They find that the model largely captures the average returns on U.S. portfolios formed on size, BE/ME, and other variables known to cause problems for the CAPM (earnings/price, cashflow/price, past sales growth, and long-term past return). Fama and French (1998) show that an international version of