How likely is it that a severe economic disaster will occur in the next 100 years? With a relatively short sample of historical data, it is difficult to accurately estimate the likelihood of disasters or the size of their impact. For example, one cannot reject the hypothesis of a constant disaster intensity of 3% per year at the 5% significance level even after observing a 100 year sample without a disaster. This suggests that there is likely to be significant heterogeneity in the beliefs of market participants about disasters. In this paper, we show that such disagreements can generate strong risk sharing motives among investors and significantly affect asset prices.
We study an exchange economy with two types of agents. Markets are complete, so that the agents can trade contingent claims and achieve optimal risk sharing. Using the affine heterogeneous beliefs framework developed in Chen, Joslin, and Tran (2010), our model can capture very general forms of disagreements among the agents while maintaining tractability. For example, the agents can disagree about the intensity of disasters or the severity of disasters, and the amount of disagreements can fluctuate over time.
We find that having a second group of agents with different beliefs about disasters can cause the equity premium to drop substantially, even when the new agents only have a small amount of wealth. This result holds whether the disagreement is about the intensity or impact of disasters. In fact, the result can still be true even when the new agents are generally more pessimistic about disasters. We analytically characterize the sensitivity of risk premiums to the wealth distribution and derive its limit as the amount of disagreement increases.
When we calibrate the beliefs of one agent using international macro data (from Barro (2006)) and the other using only consumption data from the US (where disasters have been relatively mild), raising the fraction of total wealth for the second agent from 0 to 10% lowers the equity premium from 4.4% to 2.0%. The decline in the equity premium becomes faster when the disagreement is larger, or when the new agents also have lower risk aversion.
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Rare Disasters and Risk Sharing with Heterogeneous Beliefs
