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


  • Robert R. Grauer

    1. Department of Economics, Faculty of Business Administration, Simon Fraser University
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    • * Department of Economics, Faculty of Business Administration, Simon Fraser University. Financial support from the Social Sciences and Humanities Research Council of Canada is greatly appreciated as is the capable assistance of Maciek Kon, John Janmaat, and William Ting. I thank Reo Audette, Avi Bick, George Blazenko, Peter Clarkson, Wayne Ferson, John Heaney, Burton Hollifield, Avi Kamara, Peter Klein, Andy Siegel, Simon Wheatley, and especially John Herzog, Ray Koopman, John Janmaat, two anonymous referees, and the editor René Stulz for extremely helpful comments. But, naturally, I am responsible for both interpretation and errors. The paper was presented at Simon Fraser University, the Pacific Northwest Finance Conference in Seattle, and the Northern Finance Association Meetings in Vancouver. It was originally titled: “Tests of the Capital Asset Pricing Model Based on the Cross-Section of Expected Returns.”


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.