Robustifying Conditional Portfolio Decisions via Optimal Transport

We propose a data-driven portfolio selection model that integrates side information, conditional estimation, and robustness using the framework of distributionally robust optimization. Conditioning on the observed side information, the portfolio manager solves an allocation problem that minimizes the worst-case conditional risk-return tradeoff, subject to all possible perturbations of the covariate-return probability distribution in an optimal transport ambiguity set. Despite the nonlinearity of the objective function in the probability measure, we show that the distributionally robust portfolio allocation with a side information problem can be reformulated as a finite-dimensional optimization problem. If portfolio decisions are made based on either the mean-variance or the mean-conditional value-at-risk criterion, the reformulation can be further simplified to second-order or semidefinite cone programs. Empirical studies in the U.S. equity market demonstrate the advantage of our integrative framework against other benchmarks.