Why does implied risk aversion smile?

Abstract

Implied risk aversion estimates reported in the literature are strongly U-shaped. This article explores different potential explanations for these “smile” patterns: (i) preference aggregation, both with and without stochastic volatility and jumps in returns, (ii) misestimation of investors’ beliefs caused by stochastic volatility, jumps, or a Peso problem, and (iii) heterogeneous beliefs. The results reveal that preference aggregation and misestimation of investors’ beliefs caused by stochastic volatility and jumps are unlikely to be the explanation for the smile. Although a Peso problem can account for the smile, the required probability of a market crash is unrealistically large. Heterogeneous beliefs cause sizable distortions in implied risk aversion, but the degree of heterogeneity required to explain the smile is implausibly large.