Over the past decade, demand for investment strategies incorporating environmental, social, and governance (ESG) criteria has surged. Investors increasingly expect portfolios to align with sustainability goals, not just financial returns. Market practices are heterogeneous: some strategies simply screen out “bad” firms, others factor in ESG scores in a pre-selection step, and still others attempt to jointly optimize sustainability and financial performance.

Joint optimization over sustainability and financial performance is typically done by either integrating the ESG scores of the assets in the objective function or introducing constraints to the optimization. The variability overtime of the ESG scores is often disregarded, due to difficulties in forecasting future evolutions of such variables, and due to the lack of high frequency data (ESG scores are typically issued with annual frequency).

The ESG scores are thus used alongside the financial returns but are not integrated in the measurement of risk and reward, limiting the power of existing frameworks to account for the tradeoffs between returns and ESG performance. We argue for a bivariate principled, axiomatic extension of classical risk / reward measures to an ESG-aware setting. The problem is becoming increasingly relevant in light of the appearance of high frequency ESG data, such as the Factset Truvalue Scores, that are updated daily.

Key gap: how to measure ESG-inclusive risk and reward

• Traditional risk measures (e.g. Value at Risk, expected shortfall) focus solely on financial returns, ignoring sustainability fluctuations or ESG score volatility.
• ESG scores are often treated deterministically or exogenously (i.e. fixed), rather than as stochastic processes evolving over time.
• Investors with strong ESG preferences (beyond pure financial optimization) require risk/reward metrics that internalize ESG considerations, rather than treating them as side constraints.

Thus, the central question: Can we define coherent, axiomatic risk and reward measures that integrate both monetary returns and ESG outcomes, in a way that respects investor preferences (tradeoffs)?

We point out that the main goal of this work is not to use ESG analysis to improve financial performance, but we aim instead to develop a framework that integrates investors’ preferences towards sustainable investment per se, for ethical reasons or to satisfy some specific institutional mandate.