Standard Stochastic Dominance

Abstract

We propose a new Stochastic Dominance (SD) criterion based on standard risk aversion, which assumes decreasing absolute risk aversion and decreasing absolute prudence. To implement the proposed criterion, we develop linear systems of optimality conditions for a given prospect relative to a discrete or polyhedral choice opportunity set in a general state-space model. An empirical application to historical stock market data shows that small-loser stocks are more appealing to standard risk averters than the existing mean-variance and higher-order SD criteria suggest, due to their upside potential. Depending on the assumed trading strategy and evaluation horizon, accounting for standardness increases the estimated abnormal returns of these stocks by about 50 to 200 basis points per annum relative to mean-variance and higher-order SD criteria. An analysis of the mean-variance tangency portfolio shows that the opportunity cost of the mean-variance approximation to direct utility maximization can be substantial.

Keywords: Decision theory, Stochastic Dominance, portfolio analysis, standard risk aversion, Linear Programming

JEL Classification: C22, C32, D81, G11, G12