Conditional Value-at-Risk Constraint and Loss Aversion Utility Functions

TL;DR

This paper interprets risk constraints in expected return optimization as a form of generalized utility maximization, revealing a loss aversion factor when using Conditional Value-at-Risk as the risk measure.

Contribution

It provides an economic interpretation of risk constraints, especially CVaR, as a form of generalized expected utility maximization involving ambiguity and loss aversion.

Findings

Risk constraints induce a maxmin expected utility behavior.

Conditional Value-at-Risk introduces a loss aversion factor.

The framework links risk measures to economic decision-making models.

Abstract

We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random return under constraint that the risk measure is bounded above, he then behaves as a ``generalized expected utility maximizer'' in the following sense. The DM exhibits ambiguity with respect to a family of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called ``Maxmin under risk'' and studied by Maccheroni (2002). This economic interpretation allows us to exhibit a loss aversion factor when the risk measure is the Conditional Value-at-Risk.