Linear Tests for DARA Stochastic Dominance

34 Pages Posted: 30 Jun 2013 Last revised: 14 Apr 2014

See all articles by Thierry Post

Thierry Post

Graduate School of Business of Nazarbayev University

Yi Fang

Jilin University (JLU) - Center for Quantitative Economics

Milos Kopa

Charles University in Prague - Faculty of Mathematics and Physics

Date Written: September 28, 2013

Abstract

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

Suggested Citation

Post, Thierry and Fang, Yi and Kopa, Milos, Linear Tests for DARA Stochastic Dominance (September 28, 2013). Available at SSRN: https://ssrn.com/abstract=2287269 or http://dx.doi.org/10.2139/ssrn.2287269

Thierry Post (Contact Author)

Graduate School of Business of Nazarbayev University ( email )

53 Kabanbay Batyra Avenue
Astana, 010000
Kazakhstan

Yi Fang

Jilin University (JLU) - Center for Quantitative Economics ( email )

Changchun, Jilin 130012
China

Milos Kopa

Charles University in Prague - Faculty of Mathematics and Physics ( email )

Czech Republic

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