  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.
