ESG Risk: Lessons Learned from Utility Theory

TL;DR

The paper addresses how to integrate ESG risk into monetary risk measurement by replacing the traditional loss with a multi-attribute utility $u(x,s)$, yielding $\rho[X,S] = \inf\{m: \mathbb{E}[u(X+m,S)] \ge 0\}$ and preserving the axioms of monetary risk. It develops a rigorous framework under mutual utility independence, deriving properties such as translation invariance, monotonicity, and convexity, and introduces ESG risk premia and indifference positions. The authors instantiate the framework with entropic utilities, discuss canonical constructions, and apply it to S&P 500 data using Sustainalytics ratings to compute single-asset ESG risk and to construct minimum-risk ESG-aware portfolios. The empirical results show that ESG risk measures differentiate assets with similar financial performance, and ESG-aware portfolios achieve notable ESG improvements with only modest differences in financial performance, highlighting practical implications for ESG-conscious investing.

Abstract

We propose a new class of monetary risk measures for assessing financial and ESG risk. The construction is based on classical shortfall risk measures with loss function replaced by a multi-attribute utility function. We present an extensive theoretical analysis of these risk measures, showing specifically how properties of the utility function translate into properties of the associated risk measure. We furthermore discuss how these multi-attribute risk measures can be used to compute minimum risk portfolios and show in a numerical study that accounting for ESG risk in optimal portfolio choice has a significant influence on the composition of portfolios.

Figures (7)

• Figure 1: Correlation analysis between historical stock price returns and changes in normalized ESG ratings This figure shows Pearson correlation coefficients between monthly stock price log returns and monthly log changes in normalized ESG ratings. Each dot represents one company.
• Figure 2: Entropic risk and the entropic ESG risk for S&P 500 companies Left: Classical entropic risk (x-axis) against entropic ESG risk (y-axis). Right: Cumulative stock price returns and normalized ESG ratings for CLX, HAS, and MMM.
• Figure 3: Impact of shifts in the normalized ESG rating Entropic ESG risk (top) and marginal entropic ESG risk (bottom) as functions of rating shifts for $c=0.1$ (left) and $c=0.05$ (right). The plots for the marginal entropic ESG risk are restricted to the range on which the entropic ESG risk is not flat.
• Figure 4: Entropic risk (left) and entropic ESG risk (right) plotted against the expected return of S&P 500 companies The plot highlights the risk assessment of the three representative companies HAS, CLX, and MMM relative to their expected returns.
• Figure 5: Cumulative returns and normalized ESG ratings for the basket of S&P 500 stocks, and optimal portfolio weights of the minimum risk strategies Cumulative returns and normalized ESG ratings (left) and optimal portfolio weights (right) for the eleven-stock basket. Portfolio optimization starts in June 2023 (dashed line); weights are shown for classical entropic risk (top) and entropic ESG risk (bottom).

Theorems & Definitions (18)

• definition 2.1
• Theorem 2.1: Translation Invariance
• proof
• example 2.1: Penalty and Threshold ESG Risk Measures
• remark 2.1
• Theorem 2.2: Monotonicity
• proof
• Proposition 2.1: Monotonicity of $u$
• proof
• remark 2.2