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

Starting from the reward-risk model for portfolio selection introduced in De Giorgi (2004), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. The reward-risk portfolio selection arises froman 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, investors optimal allocations are comonotonic and therefore the capital market equilibrium model can be reduced to a representative investor model. Moreover, the pricing kernel is an explicitly given, monotone function of the market portfolio return, corresponding to the increments of the distortion function characterizing the representative investors risk perceptions. 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.