A Flight-to-Safety Principle for Cost-Sensitive Distributionally Robust Log-Optimal Portfolio

Abstract

This letter investigates how distributional ambiguity interacts with transaction costs in a log-optimal portfolio control formulation. Return ambiguity is modeled by a 1-Wasserstein ball centered at the empirical distribution, and trading frictions are incorporated via a convex, positively homogeneous transaction cost function applied at each rebalance. We establish a flight-to-safety principle: as trading frictions rise, the critical ambiguity radius—the smallest radius beyond which the optimizer retreats entirely to the risk-free asset—weakly decreases. Rolling-window experiments on S&P 500 constituents illustrate this mechanism, showing that higher transaction costs systematically shift the robust allocation toward the risk-free asset.