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Linear Tests for Decreasing Absolute Risk Aversion Stochastic Dominance

Author

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  • Thierry Post

    (Graduate School of Business, Koç University, 34450 Sariyer, Istanbul, Turkey)

  • Yi Fang

    (Center for Quantitative Economics and Business School, Jilin University, Changchun 130012, China)

  • Miloš Kopa

    (Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University Prague, 186 75 Prague 8, Czech Republic)

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 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. This paper was accepted by James Smith, decision analysis.

Suggested Citation

  • Thierry Post & Yi Fang & Miloš Kopa, 2015. "Linear Tests for Decreasing Absolute Risk Aversion Stochastic Dominance," Management Science, INFORMS, vol. 61(7), pages 1615-1629, July.
    • Handle: RePEc:inm:ormnsc:v:61:y:2015:i:7:p:1615-1629
    DOI: 10.1287/mnsc.2014.1960
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    References listed on IDEAS

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    3. Gao, Jianwei & Zhao, Feng, 2017. "Sufficient conditions of stochastic dominance for general transformations and its application in option strategy," Economics Discussion Papers 2017-40, Kiel Institute for the World Economy (IfW Kiel).
    4. Iñaki R. Longarela, 2016. "A Characterization of the SSD-Efficient Frontier of Portfolio Weights by Means of a Set of Mixed-Integer Linear Constraints," Management Science, INFORMS, vol. 62(12), pages 3549-3554, December.
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    6. Sebastiano Vitali & Vittorio Moriggia, 2021. "Pension fund management with investment certificates and stochastic dominance," Annals of Operations Research, Springer, vol. 299(1), pages 273-292, April.
    7. Courtois, Olivier Le & Xu, Xia, 2023. "Semivariance below the maximum: Assessing the performance of economic and financial prospects," Journal of Economic Behavior & Organization, Elsevier, vol. 209(C), pages 185-199.
    8. Audrius Kabašinskas & Kristina Šutienė & Miloš Kopa & Kęstutis Lukšys & Kazimieras Bagdonas, 2020. "Dominance-Based Decision Rules for Pension Fund Selection under Different Distributional Assumptions," Mathematics, MDPI, vol. 8(5), pages 1-26, May.

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