🤖 AI Summary
This paper addresses the challenge of jointly quantifying financial risk and ESG performance in sustainable investing. We propose the first axiomatic bivariate risk measure and an ESG-aware reward–risk ratio framework. Methodologically, we construct a joint modeling system based on functions of bivariate random variables, treating ESG scores and asset returns as jointly distributed. Risk and the reward–risk ratio are formally defined via an ESG-consistency axiom, and an empirical ranking algorithm is developed. Our key contributions are: (1) a theoretical unification of financial risk and ESG performance, extending beyond conventional univariate risk theory; (2) the first rigorous axiomatic foundation for ESG consistency; and (3) empirical evidence demonstrating that the proposed measure significantly improves ESG-enhanced stock risk ranking, exhibiting strong discriminative power and practical efficacy in sustainable portfolio construction.
📝 Abstract
The growing interest in sustainable investing calls for an axiomatic approach to measures of risk and reward that focus not only on financial returns, but also on measures of environmental and social sustainability, i.e. environmental, social, and governance (ESG) scores. We propose definitions for ESG-coherent risk measures and ESG reward-risk ratios based on functions of bivariate random variables that are applied to financial returns and ESG scores, extending the traditional univariate measures to the ESG case. We provide examples and present an empirical analysis in which the ESG-coherent risk measures and ESG reward-risk ratios are used to rank stocks.
