An Axiomatic Risk-Reward Framework for Sustainable Investing

Paper: arXiv 2309.05866

Authors: Gabriele Torri, Rosella Giacometti, Darinka Dentcheva, Svetlozar T. Rachev, W. Brent Lindquist

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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 5.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a formal, axiomatic mathematical extension of coherent risk measures to bivariate random variables incorporating financial returns and ESG metrics. It includes both theoretical formulations and a practical empirical stock-ranking application to demonstrate its utility.

Research Flowchart

  flowchart TD
    A[Goal: Axiomatic Risk-Reward Framework for ESG Investing] --> B[Inputs: Financial Returns & Real-Time ESG Scores]
    B --> C[Method: Extend Univariate Measures to Bivariate Random Variables]
    C --> D[Define ESG-Coherent Risk Measures & ESG Reward-Risk Ratios]
    D --> E[Empirical Analysis: Rank Equities using New Ratios]
    E --> F[Outcome: ESG-Adjusted Stock Rankings & Sustainable Selection Framework]