Distributionally robust sparse portfolio selection

Abstract

In this paper, we construct a distributionally robust sparse portfolio selection model by combining semi-absolute deviation (SAD) risk function with Wasserstein distance. First, we assume the actual distribution of risky assets' return is contained in a Wasserstein ball. The objective function is to minimize the worst-case excepted loss and risk measures of the portfolio. Since the proposed model is an infinite dimensional programming, we transform it into a mixed-integer programming problem through some principles. Second, a Lagrangian relaxation method is designed to solve the resulting problems. In the end, we use three data sets to evaluate the performance of the proposed model and algorithm. The results show that adding sparsity constraint can lead to better investment strategies and the designed algorithm can effectively solve the sparse portfolio selection model.