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.

[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 misestima 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.]

When information is costly, a seller may wish to prevent prospective buyers from acquiring information, for the cost of information acquisition ultimately is borne by the seller. A seller can achieve the desired prevention through posted-price selling, by offering prospective buyers a discount. No such prevention is possible in the case of an auction. We establish the result that the seller prefers posted-price selling when the cost of information acquisition is high and auctions when it is low. We view corporate bonds as an instance of the former case, and government bonds as an instance of the latter.