The Fama and French (1992) study has itself been challenged. The study's claims most attacked are these: that beta has no role for explaining cross-sectional variation in returns, that size has an important role, and that the book-to-market equity ratio has an important role. The studies responding to the Fama and French challenge generally take a closer look at the data used in that study. Kothari, Shahken, and Sloan (1995) argue that Fama and French's (1992) findings depend critically on how one interprets their statistical tests. Kothari, Shanken, and Sloan focus on Fama and French's estimates for the coefficient on beta [gamma1 in equation (15)], which have high standard errors and therefore imply that a wide range of economically plausible risk premiums cannot be rejected statistically. For example, if the estimate of gamma1 is 0.24 percent per month with a standard error of 0.23 percent, then 0 and 50 basis points per month are both statistically plausible. This view, that the data are too noisy to invalidate the CAPM, is supported by Amihud, Christensen, and Mendelson (1992) and Black (1993). In fact, Amihud, Christensen, and Mendelson (1992) find that when a more efficient statistical method is used, the estimated relation between average return and beta is positive and significant. The widely accepted capital asset pricing model (henceforth CAPM) developed by Sharpe (1964), Lintner (1965) and Mossin (1966) postulates a simple linear relationship between a stock’s expected return and its risk. Basu (1977) finds that price-earnings ratios and risk adjusted returns are related. A study performed by Litzenberger and Ramaswamy (1979) shows a significant positive relationship between dividend yield and returns on common stock. One of the most discussed relationships, and the main focus of this study, is the one between a company’s size and the return on its stock.
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