Distributionally robust optimization with Wasserstein metric for multi-period portfolio selection under uncertainty

Abstract

The mean-variance model formulated by Markowitz for a single period serves as a fundamental method of modern portfolio selection. In this study, we consider a multi-period case with uncertainty that better matches the reality of the financial market. Using the Wasserstein metric to characterize the uncertainty of returns in each period, a new distributionally robust mean-variance model is proposed to solve multi-period portfolio selection problem. We further transform the developed model into a tractable convex problem using duality theory. We also apply a nonparametric bootstrap method and provide a specific algorithm to estimate the radius of the Wasserstein ball. The effects of the parameters on the corresponding strategy and evaluation criteria of portfolios are analyzed using in-sample data. The analysis indicate that the return and risk of our portfolio selections are relatively immune to parameter values. Finally, a series of out-of-sample experiments demonstrate that the proposed model is superior to some other models in terms of final wealth, standard deviation, and Sharpe ratio.