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

Abstract

Starting from the reward-risk model for portfolio selection introduced in DeGiorgi (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 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 better captures the cross-section of US stock returns than the mean-variance CAPM does.

Keywords: Stochastic dominance, mean-risk models, portfolio optimization, CAPM

JEL Classification: G11, D81