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Portfolio Choice Based on Third-Degree Stochastic Dominance

Author

Listed:
  • Thierry Post

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

  • Miloš Kopa

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

Abstract

We develop an optimization method for constructing investment portfolios that dominate a given benchmark portfolio in terms of third-degree stochastic dominance. Our approach relies on the properties of the semivariance function, a refinement of an existing “superconvex” dominance condition, and quadratic constrained programming. We apply our method to historical stock market data using an industry momentum strategy. Our enhanced portfolio generates important performance improvements compared with alternatives based on mean-variance dominance and second-degree stochastic dominance. Relative to the Center for Research in Security Prices all-share index, our portfolio increases average out-of-sample return by almost seven percentage points per annum without incurring more downside risk, using quarterly rebalancing and without short selling.

Suggested Citation

  • Thierry Post & Miloš Kopa, 2017. "Portfolio Choice Based on Third-Degree Stochastic Dominance," Management Science, INFORMS, vol. 63(10), pages 3381-3392, October.
    • Handle: RePEc:inm:ormnsc:v:63:y:2017:i:10:p:3381-3392
    DOI: 10.1287/mnsc.2016.2506
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    2. Luigi-Ionut Catana & Anisoara Raducan, 2020. "Stochastic Order for a Multivariate Uniform Distributions Family," Mathematics, MDPI, vol. 8(9), pages 1-10, August.
    3. Raymond H. Chan & Ephraim Clark & Xu Guo & Wing-Keung Wong, 2020. "New development on the third-order stochastic dominance for risk-averse and risk-seeking investors with application in risk management," Risk Management, Palgrave Macmillan, vol. 22(2), pages 108-132, June.
    4. Chenglu Jin & Thomas Conlon & John Cotter, 2023. "Co-Skewness across Return Horizons," Journal of Financial Econometrics, Oxford University Press, vol. 21(5), pages 1483-1518.
    5. Kouaissah, Noureddine, 2023. "Robust reward-risk performance measures with weakly second-order stochastic dominance constraints," The Quarterly Review of Economics and Finance, Elsevier, vol. 88(C), pages 53-62.
    6. Kouaissah, Noureddine, 2021. "Using multivariate stochastic dominance to enhance portfolio selection and warn of financial crises," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 480-493.
    7. Jerry Anunrojwong & Krishnamurthy Iyer & David Lingenbrink, 2024. "Persuading Risk-Conscious Agents: A Geometric Approach," Operations Research, INFORMS, vol. 72(1), pages 151-166, January.
    8. Chi, Yichun, 2018. "Insurance choice under third degree stochastic dominance," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 198-205.
    9. Josef Jablonský & Michal Černý & Juraj Pekár, 2022. "The last dozen of years of OR research in Czechia and Slovakia," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 435-447, June.
    10. Patrizia Beraldi & Maria Elena Bruni, 2022. "Enhanced indexation via chance constraints," Operational Research, Springer, vol. 22(2), pages 1553-1573, April.
    11. 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.
    12. Chan, Raymond H. & Chow, Sheung-Chi & Guo, Xu & Wong, Wing-Keung, 2022. "Central moments, stochastic dominance, moment rule, and diversification with an application," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    13. Barbora Petrová, 2019. "Multistage portfolio optimization with multivariate dominance constraints," Computational Management Science, Springer, vol. 16(1), pages 17-46, February.
    14. 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.
    15. Fang, Yi & Post, Thierry, 2022. "Optimal portfolio choice for higher-order risk averters," Journal of Banking & Finance, Elsevier, vol. 137(C).
    16. Conlon, Thomas & Cotter, John & Kovalenko, Illia & Post, Thierry, 2023. "A financial modeling approach to industry exchange-traded funds selection," Journal of Empirical Finance, Elsevier, vol. 74(C).
    17. Francesco Cesarone & Justo Puerto, 2024. "New approximate stochastic dominance approaches for Enhanced Indexation models," Papers 2401.12669, arXiv.org.
    18. Kolokolova, Olga & Xu, Xia, 2024. "Enhancing betting against beta with stochastic dominance," Journal of Empirical Finance, Elsevier, vol. 76(C).
    19. 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.
    20. 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).
    21. 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.
    22. 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.
    23. Liesiö, Juuso & Kallio, Markku & Argyris, Nikolaos, 2023. "Incomplete risk-preference information in portfolio decision analysis," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1084-1098.

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