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We propose a data-driven portfolio selection model that integrates sideinformation, conditional estimation and robustness using the framework ofdistributionally robust optimization. Conditioning on the observed sideinformation, the portfolio manager solves an allocation problem that minimizesthe worst-case conditional risk-return trade-off, subject to all possibleperturbations of the covariate-return probability distribution in an optimaltransport ambiguity set. Despite the non-linearity of the objective function inthe probability measure, we show that the distributionally robust portfolioallocation with side information problem can be reformulated as afinite-dimensional optimization problem. If portfolio decisions are made basedon either the mean-variance or the mean-Conditional Value-at-Risk criterion,the resulting reformulation can be further simplified to second-order orsemi-definite cone programs. Empirical studies in the US equity marketdemonstrate the advantage of our integrative framework against otherbenchmarks.

Robustifying Conditional Portfolio Decisions via Optimal Transport