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Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

Author

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  • Jose Blanchet

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Lin Chen

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Xun Yu Zhou

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models.

Suggested Citation

  • Jose Blanchet & Lin Chen & Xun Yu Zhou, 2022. "Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances," Management Science, INFORMS, vol. 68(9), pages 6382-6410, September.
    • Handle: RePEc:inm:ormnsc:v:68:y:2022:i:9:p:6382-6410
    DOI: 10.1287/mnsc.2021.4155
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    References listed on IDEAS

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    1. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    2. Costa, O. L. V. & Paiva, A. C., 2002. "Robust portfolio selection using linear-matrix inequalities," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 889-909, June.
    3. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    4. Jun-ya Gotoh & Akiko Takeda, 2011. "On the role of norm constraints in portfolio selection," Computational Management Science, Springer, vol. 8(4), pages 323-353, November.
    5. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    6. David Wozabal, 2012. "A framework for optimization under ambiguity," Annals of Operations Research, Springer, vol. 193(1), pages 21-47, March.
    7. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    8. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    9. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    10. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    11. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    12. B.V. Halldórsson & R.H. Tütüncü, 2003. "An Interior-Point Method for a Class of Saddle-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 559-590, March.
    13. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    14. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
    15. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
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    Cited by:

    1. Castro-Iragorri, Carlos & Gómez, Fabio & Quiceno, Nancy, 2024. "Worst-case higher moment risk measure: Addressing distributional shifts and procyclicality," Finance Research Letters, Elsevier, vol. 65(C).
    2. Tim J. Boonen & Yuyu Chen & Xia Han & Qiuqi Wang, 2024. "Optimal insurance design with Lambda-Value-at-Risk," Papers 2408.09799, arXiv.org.
    3. Castro-Iragorri, Carlos & Gómez, Fabio & Quiceno, Nancy, 2024. "Worst-Case Higher Moment Risk Measure: Addressing Distributional Shifts and Procyclicality," Documentos de Trabajo 21048, Universidad del Rosario.
    4. Qingliang Fan & Ruike Wu & Yanrong Yang, 2024. "Shocks-adaptive Robust Minimum Variance Portfolio for a Large Universe of Assets," Papers 2410.01826, arXiv.org.
    5. Marcelo Righi, 2024. "Robust convex risk measures," Papers 2406.12999, arXiv.org, revised Oct 2024.
    6. Chung-Han Hsieh & Jie-Ling Lu, 2024. "On Accelerating Large-Scale Robust Portfolio Optimization," Papers 2408.07879, arXiv.org.
    7. Wang, Xianhe & Ouyang, Yuliang & Li, You & Liu, Shu & Teng, Long & Wang, Bo, 2023. "Multi-objective portfolio selection considering expected and total utility," Finance Research Letters, Elsevier, vol. 58(PD).
    8. Yanwei Jia, 2024. "Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty," Papers 2404.12598, arXiv.org.

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