Distributionally Robust Portfolio Optimization under Marginal and Copula Ambiguity

We investigate a new family of distributionally robust optimization problem under marginal and copula ambiguity with applications to portfolio optimization problems. The proposed model considers the ambiguity set of portfolio return in which the marginal distributions and their copula are close -- in terms of the Wasserstein distance -- to their nominal counterparts. We develop a cutting-surface method to solve the proposed problem, in which the distribution separation subproblem is nonconvex and includes bilinear terms. We propose three approaches to solve the bilinear formulation, including (1) linear relaxation via McCormick inequalities, (2) exact mixed-integer linear program reformulation via disjunctive inequalities, and (3) inner approximation method via a novel iterative procedure that exploits the structural properties of the bilinear optimization problem. We further carry out a comprehensive set of computational experiments with distributionally robust Mean-CVaR portfolios to compare the solution accuracy of the proposed algorithms, analyze the impact of the radius of the Wasserstein ambiguity ball on the portfolio, and assess portfolio performance. We use a rolling-horizon approach to conduct the out-of-sample tests, which show the superior performance of the portfolios under marginal and copula ambiguity over the equally weighted and ambiguity-free Mean-CVaR benchmark portfolios