A Multiple Risk Aversions Utility. An Example on ESG Investments

Abstract

This paper introduces the concept of multivariate utility, or multiple risk aversions utility. This is a utility with the flexibility to attach different risk aversion levels to different sources of wealth (e.g. sectors, stocks, asset classes). In this context, we address the topic of environmental, social, and corporate governance (ESG) investments from the perspective of an investor with different risk aversion levels to green and brown stocks. We obtain closed-form solutions for the optimal allocations, value function, and wealth equivalent losses (WEL) from suboptimal choices. The numerical analysis demonstrates the significant increase, of up to 33%, in green investments when accounting for a differential in risk aversions levels, with up to 65% in WEL when using same risk-aversion levels.

Keywords: Multiple risk-aversion levels, Optimal control, Expected Utility Theory, multivariate utility, HJB equation