A New Data-Driven Distributionally Robust Portfolio Optimization Method Based on Wasserstein Ambiguity Set

Abstract

Since optimal portfolio strategy depends heavily on the distribution of uncertain returns, this article proposes a new method for the portfolio optimization problem with respect to distribution uncertainty. When the distributional information of the uncertain return rate is only observable through a finite sample dataset, we model the portfolio selection problem with a robust optimization method from the data-driven perspective. We first develop an ambiguous mean-CVaR portfolio optimization model, where the ambiguous distribution set employed in the distributionally robust model is a Wasserstein ball centered within the empirical distribution. In addition, the computationally tractable equivalent model of the worst-case expectation under the uncertainty set of a cone is derived, and some theoretical conclusions of the box, budget and ellipsoid uncertainty set are obtained. Finally, to demonstrate the effectiveness of our mean-CVaR portfolio optimization method, two practical examples concerning the Chinese stock market and United States stock market are considered. Furthermore, some numerical experiments are carried out under different uncertainty sets. The proposed data-driven distributionally robust portfolio optimization method offers some advantages over the ambiguity-free stochastic optimization method. The numerical experiments illustrate that the new method is effective.