An Axiomatic Risk-Reward Framework for Sustainable Investing

Abstract

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 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 and present an empirical analysis in which the ESG-coherent risk measures and ESG reward-risk ratios are used to rank stocks.

Figures (3)

• Figure 1: Panel A: Evolution of the daily ESG score of the constituents of the index. Panel B: Evolution of stock return. Panel C: Scatterplot of average annualized daily returns and the average annualized ESG score for each asset. Panel D: Scatterplot of the annualized daily standard deviation of returns and the annualized average ESG score.
• Figure 2: Correlations between returns and ESG of the companies in the sample.
• Figure 3: Visual representation of the ranking of the assets in the DJIA index based on $\text{ESG-}\text{AVaR}_{\lambda,\tau}$ ($\tau$ equal to 0.95 and 0.99), $\text{ESG-}\mu_\lambda$, the ESG Rachev ratio ($\tau$ equal to 0.95 and 0.99), the standard deviation, $\text{ESG-} \text{STARR}_{\alpha,\lambda}$ (the STAR ratio with p = 2), and the Sharpe ratio. Values of $\lambda$ are arranged on the X axis from 0 (only the monetary component considered, left) to 1 (only the ESG component considered, right), and companies are color-coded by sector.

Theorems & Definitions (14)

• Definition 1: ESG-coherent risk measure
• Proposition 1
• proof
• Remark
• Remark : Diversification between monetary and ESG risk
• Proposition 2
• Proposition 3
• proof
• Remark
• Proposition 4