Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals

Xuan Vinh Doan (), Xiaobo Li () and Karthik Natarajan ()
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Xuan Vinh Doan: DIMAP and ORMS Group, Warwick Business School, University of Warwick, Coventry, CV4 7AL, United Kingdom
Xiaobo Li: Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455
Karthik Natarajan: Engineering Systems and Design, Singapore University of Technology and Design, Singapore 487372

Operations Research, 2015, vol. 63, issue 6, 1468-1488

Abstract: In this paper, we develop a distributionally robust portfolio optimization model where the robustness is across different dependency structures among the random losses. For a Fréchet class of discrete distributions with overlapping marginals, we show that the distributionally robust portfolio optimization problem is efficiently solvable with linear programming. To guarantee the existence of a joint multivariate distribution consistent with the overlapping marginal information, we make use of a graph theoretic property known as the running intersection property. Building on this property, we develop a tight linear programming formulation to find the optimal portfolio that minimizes the worst-case conditional value-at-risk measure. Lastly, we use a data-driven approach with financial return data to identify the Fréchet class of distributions satisfying the running intersection property and then optimize the portfolio over this class of distributions. Numerical results in two different data sets show that the distributionally robust portfolio optimization model improves on the sample-based approach.

Keywords: distributionally robust optimization; portfolio optimization; overlapping marginals (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (16)

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