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. Funding: The material in this paper is based on work supported by the Air Force Office of Scientific Research [Award FA9550-20-1-0397]. Additional support is gratefully acknowledged from the National Science Foundation [Grants 1915967, 1820942, and 1838676], the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2016-05208], and the China Merchant Bank. V. A. Nguyen gratefully acknowledges the generous support from the Chinese University of Hong Kong [Improvement on Competitiveness in Hiring New Faculties Funding Scheme] and the Chinese University of Hong Kong [Direct Grant 4055191]. S. Wang is partially supported by the National Natural Science Foundation of China [Grant 72371022]. Finally, this research was enabled in part by support provided by Compute Canada. Supplemental Material: The computer code and data that support the findings of this study and the online appendix are available within this article’s supplemental material at https://doi.org/10.1287/opre.2021.0243 .