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Distributionally Robust Portfolio Optimization under Marginal and Copula Ambiguity

Author

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  • Zhengyang Fan

    (George Mason University)

  • Ran Ji

    (George Mason University)

  • Miguel A. Lejeune

    (The George Washington University)

Abstract

We investigate a new family of distributionally robust optimization problem under marginal and copula ambiguity with applications to portfolio optimization problems. The proposed model considers the ambiguity set of portfolio returns in which the marginal distributions and their copula are close—in terms of the Wasserstein distance—to their nominal counterparts. We develop a cutting-surface method to solve the proposed problem, in which the distribution separation subproblem is nonconvex and includes bilinear terms. We propose three approaches to solve the bilinear formulation, namely (1) linear relaxation via McCormick inequalities, (2) exact mixed-integer linear program reformulation via disjunctive inequalities, and (3) inner approximation method via a novel iterative procedure that exploits the structural properties of the bilinear optimization problem. We further carry out a comprehensive set of computational experiments with distributionally robust portfolios featuring Conditional Value-at-Risk (CVaR) measures. These tests aim to compare the accuracy of the proposed algorithms, analyze the impact of the radius of the Wasserstein ambiguity ball on the portfolio, and assess portfolio performance. We use a rolling-horizon approach to conduct the out-of-sample tests, which show the superior performance of the portfolios under marginal and copula ambiguity over the equally weighted and ambiguity-free Mean-CVaR benchmark portfolios.

Suggested Citation

  • Zhengyang Fan & Ran Ji & Miguel A. Lejeune, 2024. "Distributionally Robust Portfolio Optimization under Marginal and Copula Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2870-2907, December.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:3:d:10.1007_s10957-024-02550-y
    DOI: 10.1007/s10957-024-02550-y
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    References listed on IDEAS

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    1. Ran Ji & Miguel A. Lejeune, 2021. "Data-Driven Optimization of Reward-Risk Ratio Measures," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1120-1137, July.
    2. 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.
    3. Zhilin Kang & Xun Li & Zhongfei Li & Shushang Zhu, 2019. "Data-driven robust mean-CVaR portfolio selection under distribution ambiguity," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 105-121, January.
    4. Kakouris, Iakovos & Rustem, Berç, 2014. "Robust portfolio optimization with copulas," European Journal of Operational Research, Elsevier, vol. 235(1), pages 28-37.
    5. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    6. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2009. "Constructing Risk Measures from Uncertainty Sets," Operations Research, INFORMS, vol. 57(5), pages 1129-1141, October.
    7. Nagler, T. & Bumann, C. & Czado, C., 2019. "Model selection in sparse high-dimensional vine copula models with an application to portfolio risk," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 180-192.
    8. 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.
    9. David Wozabal, 2014. "Robustifying Convex Risk Measures for Linear Portfolios: A Nonparametric Approach," Operations Research, INFORMS, vol. 62(6), pages 1302-1315, December.
    10. Adam Krzemienowski & Sylwia Szymczyk, 2016. "Portfolio optimization with a copula-based extension of conditional value-at-risk," Annals of Operations Research, Springer, vol. 237(1), pages 219-236, February.
    11. Adam Krzemienowski & Sylwia Szymczyk, 2016. "Portfolio optimization with a copula-based extension of conditional value-at-risk," Annals of Operations Research, Springer, vol. 237(1), pages 219-236, February.
    12. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
    13. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    14. Ran Ji & Miguel A. Lejeune & Zhengyang Fan, 2022. "Distributionally robust portfolio optimization with linearized STARR performance measure," Quantitative Finance, Taylor & Francis Journals, vol. 22(1), pages 113-127, January.
    15. Sahamkhadam, Maziar & Stephan, Andreas & Östermark, Ralf, 2018. "Portfolio optimization based on GARCH-EVT-Copula forecasting models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 497-506.
    16. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    17. Luo, Fengqiao & Mehrotra, Sanjay, 2019. "Decomposition algorithm for distributionally robust optimization using Wasserstein metric with an application to a class of regression models," European Journal of Operational Research, Elsevier, vol. 278(1), pages 20-35.
    18. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.
    19. Tamara Teplova & Mikova Evgeniia & Qaiser Munir & Nataliya Pivnitskaya, 2023. "Black-Litterman model with copula-based views in mean-CVaR portfolio optimization framework with weight constraints," Economic Change and Restructuring, Springer, vol. 56(1), pages 515-535, February.
    20. Ran Ji & Miguel A. Lejeune & Srinivas Y. Prasad, 2017. "Properties, formulations, and algorithms for portfolio optimization using Mean-Gini criteria," Annals of Operations Research, Springer, vol. 248(1), pages 305-343, January.
    21. Xuan Vinh Doan & Xiaobo Li & Karthik Natarajan, 2015. "Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals," Operations Research, INFORMS, vol. 63(6), pages 1468-1488, December.
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