Linear Tests for DARA Stochastic Dominance
34 Pages Posted: 30 Jun 2013 Last revised: 14 Apr 2014
Date Written: September 28, 2013
We develop and implement linear formulations of convex stochastic dominance relations based on decreasing absolute risk aversion 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 DSD inefficient relative to concentrated portfolios of small-cap stocks. The mean-variance rule and N-th 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.
Keywords: Stochastic dominance, utility theory, decreasing absolute risk aversion, linear programming, bootstrapping, market portfolio efficiency, pricing kernel, skewness
JEL Classification: C22, C32, D81, G11, G12
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