A simple moment-ordering condition is shown to be necessary for stochastic dominance. Closely related results on generalizations of the geometric and harmonic means are also provided. An ordering of the moment-generating functions is shown to be necessary and sufficient for stochastic dominance. The results have a straightforward and useful interpretation in terms of constant relative and absolute risk aversion utility functions. These results are used to provide necessary and sufficient conditions for optimality of distributions on an important class of utility functions.

In a recent study, Tinic and West (1986) empirically reexamine the risk-return relationship posited by the traditional mean-variance CAPM. They find a positive nonlinear relationship between risk and return, except during January when the market rewards bearing nonsystematic risk. This study examines the hypothesis that nonnormality of return distributions may account for some of these anomalous results. We compare Shalit and Yitzhaki's (1984) mean-extended Gini CAPM—an equilibrium asset pricing relation that is independent of the form of the underlying asset distribution—with the traditional CAPM. Our results indicate that the nonlinear risk-return relationship and the size and January effects are robust to nonnormality of return distributions.