A Note on Stochastic Dominance Criteria for Mixture Distributions

Abstract

This paper extends the stochastic dominance rules for normal mixture distributions derived by Levy and Kaplanski (2015). First, the portfolios under consideration are allowed to follow different regime-switching processes. Second, the results are extended from second- to fourth-order stochastic dominance, which is known to be closely related to kurtosis aversion in financial markets and allows to compare mixture distributions with the same overall variance. In particular, when a risk-free asset is available, checking for fourth-order stochastic dominance turns out to amount to a comparison of the regime-specific and overall Sharpe ratios of the portfolios under consideration.