Risk aversion under preference uncertainty

We show that if an agent is uncertain about the precise form of his utility function, his actual relative risk aversion may depend on wealth even if he knows his utility function lies in the class of constant relative risk aversion (CRRA) utility functions. We illustrate the consequences of this result for optimal asset allocation: poor agents that are uncertain about their risk aversion parameter invest less in risky assets than wealthy investors with identical risk aversion uncertainty.

► We derive actual risk aversion for an agent who is uncertain about the value of his risk aversion parameter. ► For power utility, relative risk aversion becomes wealth-dependent. ► A consequence is that poor agents with preference uncertainty invest less in risky assets than wealthy investors with identical risk aversion.