An Adjustable Robust Approach for ESG-Aware Portfolio Optimization Under Decision-Dependent Return Uncertainty

Futi Liu, Zian Zhao

Abstract

Portfolio optimization is a fundamental problem in financial decision-making, and it is concerned with balancing expected return and investment risk. With the growing emphasis on sustainable investing, environmental, social, and governance (ESG) criteria have been incorporated into portfolio optimization. In practice, ESG-aware portfolio optimization faces parameter ambiguity from market fluctuations, delayed ESG disclosure, and rating disagreement, and the exposure to return uncertainty may depend on portfolio decisions rather than being fully exogenous. Existing studies, however, generally specify uncertainty sets independently of portfolio decisions. To address this limitation, an adjustable robust approach is proposed for ESG-aware portfolio optimization under decision-dependent return uncertainty. A joint polyhedral uncertainty set is constructed to capture the ambiguity in asset returns and ESG scores, where the return bounds depend on first-stage portfolio weights through ESG-related holdings, whereas ESG score uncertainty remains decision-independent. A two-stage robust framework with recourse rebalancing and proportional transaction costs is formulated, with financial loss and ESG performance balanced in the objective and tail risk controlled by a CVaR constraint embedded in a column-and-constraint generation scheme. The resulting minimax problem is solved by a column-and-constraint generation algorithm with a Rockafellar–Uryasev linearization of CVaR over iteratively generated scenarios. Numerical experiments using real stock data are designed to evaluate downside-risk control and portfolio ESG performance relative to deterministic and classical robust benchmarks.

Source: semanticscholar · PDF

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