An axiomatic risk-reward framework for sustainable investing

Continued 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 axiomatic 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 real-time ESG scores, extending the traditional univariate measures to the ESG case. We provide examples, discuss the dual representation, and present an empirical analysis in which the ESG-coherent risk measures and ESG reward-risk ratios are used to rank stocks.