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Second-Order Stochastic Dominance, Reward-Risk Portfolio Selection, and the CAPM

Published online by Cambridge University Press:  06 April 2009

Enrico De Giorgi  and
Thierry Post
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Abstract

Starting from the reward-risk model for portfolio selection introduced in De Giorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on a few basic principles, including consistency with second-order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and, therefore, our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM captures the cross section of U.S. stock returns better than the mean-variance CAPM does.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 43 , Issue 2 , June 2008 , pp. 525 - 546
Copyright
Copyright © School of Business Administration, University of Washington 2008

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