On Cost-Sensitive Distributionally Robust Log-Optimal Portfolio

TL;DR

This paper introduces a cost-sensitive, distributionally robust approach to log-optimal portfolio selection under ambiguous return distributions and convex transaction costs, using Wasserstein metrics for uncertainty quantification.

Contribution

It develops a novel framework combining distributional robustness with cost sensitivity, providing a tractable convex approximation for practical portfolio optimization.

Findings

Optimal portfolios converge to equal weights without transaction costs.

With transaction costs, portfolios shift towards risk-free assets.

The approach is validated on S ext&barv;P 500 data.

Abstract

This paper addresses a novel \emph{cost-sensitive} distributionally robust log-optimal portfolio problem, where the investor faces \emph{ambiguous} return distributions, and a general convex transaction cost model is incorporated. The uncertainty in the return distribution is quantified using the \emph{Wasserstein} metric, which captures distributional ambiguity. We establish conditions that ensure robustly survivable trades for all distributions in the Wasserstein ball under convex transaction costs. By leveraging duality theory, we approximate the infinite-dimensional distributionally robust optimization problem with a finite convex program, enabling computational tractability for mid-sized portfolios. Empirical studies using S\&P 500 data validate our theoretical framework: without transaction costs, the optimal portfolio converges to an equal-weighted allocation, while with transaction costs, the portfolio shifts slightly towards the risk-free asset, reflecting the trade-off between cost considerations and optimal allocation.