Distributionally robust mean-absolute deviation portfolio optimization using wasserstein metric.

Abstract

Data uncertainty has a great impact on portfolio selection. Based on the popular mean-absolute deviation (MAD) model, we investigate how to make robust portfolio decisions. In this paper, a novel Wasserstein metric-based data-driven distributionally robust mean-absolute deviation (DR-MAD) model is proposed. However, the proposed model is non-convex with an infinite-dimensional inner problem. To solve this model, we prove that it can be transformed into two simple finite-dimensional linear programs. Consequently, the problem can be solved as easily as solving the classic MAD model. Furthermore, the proposed DR-MAD model is compared with the 1/N, classic MAD and mean-variance model on S &P 500 constituent stocks in six different settings. The experimental results show that the portfolios constructed by DR-MAD model are superior to the benchmarks in terms of profitability and stability in most fluctuating markets. This result suggests that Wasserstein distributionally robust optimization framework is an effective approach to address data uncertainty in portfolio optimization.