A novel approach to sustainable mean-variance portfolio optimization: Accounting for ESG-related uncertainty

Abstract

We develop a robust mean–variance portfolio optimization model that incorporates Environmental, Social, and Governance (ESG) risks under Knightian uncertainty. In this approach, ellipsoidal uncertainty sets constructed from ESG scores capture ambiguity in the assets’ expected returns. Unlike standard ESG portfolio models that impose direct ESG constraints or explicitly integrate the maximization of sustainability into the problem, our formulation naturally shifts the portfolio towards more sustainable assets as ESG uncertainty increases.

The resulting optimization problem separates into a classical mean–variance component and an additional ESG-specific penalty term, explicitly quantifying the trade-off between financial performance and sustainability. This trade-off is governed by a single uncertainty-aversion parameter: as it approaches zero, the solution converges to the classical Markowitz portfolio, whereas as it approaches infinity, it converges to a purely ESG-driven allocation. These results demonstrate that accounting for ESG-related Knightian uncertainty can promote sustainable investment decisions without regulatory enforcement, particularly for risk-averse investors.