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On the Cross-Sectional Relation Between Expected Returns, Betas and Size

By Robert R. Grauer and John JanmaatWilliam Ting I Thank, Ray Koopman and John Janmaat


In this paper, I set up scenarios where the mean-variance capital asset pricing model is true and where it is false. Then I investigate whether the coefficients from regressions of population expected excess returns on population betas, and expected excess returns on betas and size, allow us to distinguish between the scenarios. I show that the coefficients from either ordinary least squares or generalized least squares regressions do not allow us to tell whether the model is true or false. EACH OF THE FOLLOWING FIVE statements has implications for how we might judge whether the Sharpe ~1964!–Lintner ~1965! mean-variance capital asset pricing model ~MV CAPM! is true or false. First, the market portfolio is MV efficient. Second, there is at least one positively weighted efficient portfolio. Third, in the riskless asset version of the model, the market portfolio is the tangency portfolio—it is the point of tangency between a ray emanating from the riskless interest rate and the minimum-variance frontier o

Year: 1999
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