This internet appendix provides information on summary statistics, the estimation technique, as well as on the simulation study that are not contained in the paper.Section 1 comprises a table with summary statistics of the data used in the paper.Section 2 describes how we estimate the model parameters and conduct tests with GMM. In Section 3, we briefly review the long-run risks model and its solution.We then discuss the conditional expected value, a key feature of the smooth ambiguity model. Afterwards, we extensively discuss the finite sample properties of our estimation technique based on simulated data.

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This article estimates and tests the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji based on stock market data. We introduce a novel methodology to estimate the conditional expectation, which characterizes the impact of a decision maker's ambiguity attitude on asset prices. Our point estimates of the ambiguity parameter are between 25 and 60, whereas our risk aversion estimates are considerably lower. The substantial difference indicates that market participants are ambiguity averse. Furthermore, we evaluate if ambiguity aversion helps explaining the cross-section of expected returns. Compared with Epstein and Zin preferences, we find that incorporating ambiguity into the decision model improves the fit to the data while keeping relative risk aversion at more reasonable levels. Supplementary materials for this article are available online.

This article investigates the informational content implied in the risk‐neutral distribution of the VIX, a leading barometer of economic uncertainty. We extract the risk‐neutral distribution from VIX option prices over the sample period from 2006 to 2011 using a non‐parametric approach. We analyze the time‐series behavior of the option‐implied moments and assess whether the information implied in the risk‐neutral distribution has predictive power. The risk‐neutral distribution considerably changed shape during the financial crisis. Furthermore, risk‐neutral moments contain useful information with respect to the likelihood of upward jumps in volatility. Consistent with investors disliking high levels of economic uncertainty, we find that the overall shape of the estimated volatility pricing kernel is increasing. For certain periods, there is a puzzling U‐shape. The behavior of the volatility pricing kernel over time reveals that the financial crisis has affected investors’ attitudes towards risk. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:597–624, 2015