We develop and implement linear formulations of convex stochastic dominance (SD) relations based on decreasing absolute risk aversion (DARA) for discrete and polyhedral choice sets. Our approach is based on a piece wise-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 SD inefficient relative to concentrated portfolios of small-cap stocks. The mean-variance rule and N-th order stochastic dominance rules substantially under estimate the degree of market portfolio inefficiency, because they do not penalize the unfavorable skewness of diversified portfolios, inviolation of DARA.

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