Rare Disasters and Risk Sharing with Heterogeneous Beliefs

Abstract

Although the threat of rare economic disasters can have large effect on asset prices, difficulty in inference regarding both their likelihood and severity provides the potential for disagreements among investors. Such disagreements lead investors to insure each other against the types of disasters each one fears the most. Due to the highly nonlinear relationship between consumption losses in a disaster and the risk premium, a small amount of risk sharing can significantly attenuate the effect that disaster risk has on the equity premium. We characterize the sensitivity of risk premium to wealth distribution analytically. Our model shows that time variation in the wealth distribution and the amount of disagreement across agents can both lead to significant variation in disaster risk premium. It also highlights the conditions under which disaster risk premium will be large, namely when disagreement across agents is small or when the wealth distribution is highly concentrated in agents fearful of disasters. Finally, the model predicts an inverse U-shaped relationship between the equity premium and the size of the disaster insurance market.

Crash Sensitivity and the Cross Section of Expected Stock Returns

“…Furthermore, we document that the risk premium for LTD is higher following large stock market declines. This result is consistent with the theoretical predictions of Chen, Joslin, and Tran (2012). They show that disaster risk premia can increase substantially when the risk-sharing capacity of the "optimists" in their model is reduced, and they argue that this is likely to be the case in the aftermath of a crisis.…”

“…In the option pricing literature, it is sometimes argued that investors became crash-o-phobic after the experience of the 1987 crash (Rubinstein (1994), Bates (2000)). 26 Furthermore, Chen et al (2012) argue that the risk premium for disaster risk is typically small, but it increases substantially after a disaster (because then the wealth share of pessimists rises). In a similar vein, Gennaioli et al (2015) propose a theoretical model where investors overstate the fear of a future market crash when they can remember the occurrence of a black swan event.…”

Heterogeneity in Beliefs and Volatility Tail Behavior

“…Although we have a discrete-time model, there is some progress in modeling heterogeneity in beliefs in continuous time, as in Dieckmann (2011) and Chen, Joslin, and Tran (2012). The recent works of Song and Xiu (2013) and Amengual and Xiu (2013) highlight the possible role of jumps in generating realistic pricing kernels of the volatility market.…”

Stock market response to potash mine disasters

“…As investors are not always fully rational, we could expect them to react irrationally to news on a potash mining disaster (Chen, Joslin, and Tran, 2012). We expect that investor behavior will strongly depend on the extent of the coverage of the mining accident in the mass media (News) and social media (Twitter).…”