Mean-Covariance Robust Risk Measurement

TL;DR

This paper proposes a universal framework for robust risk measurement and portfolio optimization using Gelbrich distance, connecting to optimal transport theory, and simplifies to a regularized Markowitz model with efficient solutions.

Contribution

It introduces a novel mean-covariance robust risk measurement framework based on Gelbrich distance, unifying various risk measures and enabling efficient optimization.

Findings

Framework exhibits superior statistical properties.

Risk optimization reduces to regularized Markowitz model.

Applicable to value-at-risk and conditional value-at-risk.

Abstract

We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. We find that, for a large class of risk measures, mean-covariance robust portfolio optimization boils down to the Markowitz model, subject to a regularization term given in closed form. This includes the finance standards, value-at-risk and conditional value-at-risk, and can be solved highly efficiently.