Curvature and the mean-variance-ESG frontier: A new measure of risk-return-ESG trade-offs

Abstract

This article develops a measure of portfolio return, variance, and ESG trade-offs, using the concept of curvature in differential geometry. This measure assesses the return reduction or risk expansion when seeking higher ESG scores for a given optimal portfolio. The application of curvature across four global markets indicates that (1) investors in the global minimum variance and the maximum Sharpe ratio portfolios can improve their ESG performance without a reduction in return or an expansion in risk; and (2) that investors with lower risk aversion have better opportunities to improve their portfolio's ESG score without considerable reductions in return compared to those with higher risk aversion.