Distributionally Robust Portfolio Optimization with Linearized STARR Performance Measure

28 Pages Posted: 18 Mar 2020 Last revised: 24 Sep 2021

See all articles by Ran Ji

Ran Ji

George Mason University

Miguel Lejeune

George Washington University

Zhengyang Fan

George Mason University

Date Written: July 14, 2021

Abstract

We study the distributionally robust linearized stable tail adjusted return ratio (DRLSTARR) portfolio optimization problem, in which the objective is to maximize the worst-case linearized stable tail adjusted return ratio (LSTARR) performance measure under data-driven Wasserstein ambiguity. We consider two types of imperfectly known uncertainties, named uncertain probabilities and continuum of realizations, associated with the losses of assets. We account for two typical combinatorial trading constraints, called buy-in threshold and diversification constraints, to reflect stock market restrictions. Leveraging conic duality theory to tackle the distributionally robust worst-case expectation, the proposed problems are reformulated into mixed-integer linear programming problems. We carry out a series of empirical tests to illustrate the scalability and effectiveness of the proposed solution framework, and to evaluate the performance of the DRLSTARR-constructed portfolios. The cross-validation results obtained using a rolling-horizon procedure show the superior out-of-sample performance of the DRLSTARR portfolios under the uncertain continuum of realizations.

Keywords: Distributionally Robust Optimization, STARR Performance Measure, Wasserstein Metric, Conditional Value-at-Risk

JEL Classification: C44, C61, G11

Suggested Citation

Ji, Ran and Lejeune, Miguel and Fan, Zhengyang, Distributionally Robust Portfolio Optimization with Linearized STARR Performance Measure (July 14, 2021). Available at SSRN: https://ssrn.com/abstract=3542667 or http://dx.doi.org/10.2139/ssrn.3542667

Ran Ji (Contact Author)

George Mason University ( email )

Fairfax, VA
United States

Miguel Lejeune

George Washington University ( email )

Washington, DC 20052
United States

Zhengyang Fan

George Mason University ( email )

4400 University Drive
Fairfax, VA 22030
United States

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