Portfolio choice based on third-degree stochastic dominance

Abstract

We develop an optimization method for constructing investment portfolios that dominate a given benchmark portfolio in terms of third-degree stochastic dominance. Our approach relies on the properties of the semivariance function, a refinement of an existing "superconvex" dominance condition, and quadratic constrained programming. We apply our method to historical stock market data using an industry momentum strategy. Our enhanced portfolio generates important performance improvements compared with alternatives based on mean-variance dominance and second-degree stochastic dominance. Relative to the Center for Research in Security Prices all-share index, our portfolio increases average out-of-sample return by almost seven percentage points per annum without incurring more downside risk, using quarterly rebalancing and without short selling.