Modifying the Mean-Variance Approach to Avoid Violations of Stochastic Dominance

The mean-variance approach is an influential theory of decision under risk proposed by Markowitz (Markowitz, H. 1952. Portfolio selection. J. Finance7(1) 77–91). The mean-variance approach implies violations of first-order stochastic dominance not commonly observed in the data. This paper proposes a new model in the spirit of the classical mean-variance approach without violations of stochastic dominance. The proposed model represents preferences by a functional U(L) − ρ · r(L), where U(L) denotes the expected utility of lottery L, ρ ∈ [−1, 1] is a subjective constant, and r(L) is the mean absolute (utility) semideviation of lottery L. The model comprises a linear trade-off between expected utility and utility dispersion. The model can accommodate several behavioral regularities such as the Allais paradox and switching behavior in Samuelson's example.