Linear tests for decreasing absolute risk aversion stochastic dominance

Abstract

We develop and implement linear formulations of convex stochastic dominance relations based on decreasing absolute risk aversion (DARA) for discrete and polyhedral choice sets. Our approach is based on a piecewise-exponential representation of utility and a local linear approximation to the exponentiation of log marginal utility. An empirical application to historical stock market data suggests that a passive stock market portfolio is DARA stochastic dominance inefficient relative to concentrated portfolios of small-cap stocks. The mean-variance rule and Nth-order stochastic dominance rules substantially underestimate the degree of market portfolio inefficiency because they do not penalize the unfavorable skewness of diversified portfolios, in violation of DARA.