  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 trade-off, subject to all possible
perturbations of the covariate-return probability distribution in an optimal
transport ambiguity set. Despite the non-linearity of the objective function in
the probability measure, we show that the distributionally robust portfolio
allocation with 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 resulting reformulation can be further simplified to second-order or
semi-definite cone programs. Empirical studies in the US and Chinese equity
markets demonstrate the advantage of our integrative framework against other
benchmarks.
