Distributionally Robust Portfolio Optimization with Linearized STARR Performance Measure

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