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Empirical Tests for Stochastic Dominance Optimality

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  • Thierry Post

Abstract

If a given risky prospect is compared with multiple choice alternatives, then a joint test for optimality is more appropriate than a series of pairwise Stochastic Dominance tests. We develop and implement a bootstrap empirical likelihood ratio test for this hypothesis. The test statistic and implied probabilities can be computed by searching over discrete distributions that obey a system of linear inequalities using quasi-Monte Carlo simulation and convex optimization methods. An extension of the Kroll–Levy simulation experiment shows favorable small-sample properties for data sets of realistic dimensions. In an application to Fama–French stock portfolios, pairwise tests classify a portfolio of small growth stocks as admissible, whereas our test classifies the portfolio as significantly non-optimal for every risk averter.

Suggested Citation

  • Thierry Post, 2017. "Empirical Tests for Stochastic Dominance Optimality," Review of Finance, European Finance Association, vol. 21(2), pages 793-810.
    • Handle: RePEc:oup:revfin:v:21:y:2017:i:2:p:793-810.
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    File URL: http://hdl.handle.net/10.1093/rof/rfw010
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    References listed on IDEAS

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    1. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    2. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
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    Cited by:

    1. Arvanitis, Stelios & Post, Thierry & Potì, Valerio & Karabati, Selcuk, 2021. "Nonparametric tests for Optimal Predictive Ability," International Journal of Forecasting, Elsevier, vol. 37(2), pages 881-898.
    2. Stelios Arvanitis & Thierry Post, 2024. "Stochastic Arbitrage Opportunities: Set Estimation and Statistical Testing," Mathematics, MDPI, vol. 12(4), pages 1-19, February.
    3. Post, Thierry & Karabatı, Selçuk & Arvanitis, Stelios, 2018. "Portfolio optimization based on stochastic dominance and empirical likelihood," Journal of Econometrics, Elsevier, vol. 206(1), pages 167-186.
    4. Gordon Anderson & Thierry Post, 2018. "Increasing discriminatory power in well-being analysis using convex stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 551-561, October.
    5. Kolokolova, Olga & Le Courtois, Olivier & Xu, Xia, 2022. "Is the index efficient? A worldwide tour with stochastic dominance," Journal of Financial Markets, Elsevier, vol. 59(PB).
    6. Liesiö, Juuso & Xu, Peng & Kuosmanen, Timo, 2020. "Portfolio diversification based on stochastic dominance under incomplete probability information," European Journal of Operational Research, Elsevier, vol. 286(2), pages 755-768.

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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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