Correction to “Disasters and Recoveries”

In section III of the paper, I analyzed the implications of the disaster model for the time series predictability of returns. After stating some results which hold for CRRA utility, I considered how the results would be affected with Epstein-Zin utility if the probability of disaster is iid (the only case which can be solved analytically). The underlined part of the following paragraph needs to be suppressed:

“The natural escape route is to separate the IES and risk aversion, and to use the IES to control movements in the risk-free rate. When the disaster probability is iid, i.e. F(p_t+1|p_t)=F(p_t), and risk aversion is greater than unity, it is possible to show that the result above still applies: the P-D ratio increasing in the probability of a disaster p if and only if the elasticity of substitution is less than one, i.e. α>1, the risk premium is increasing but the equity return is decreasing in the probability of disaster. Numerical experiments suggest that relaxing the iid assumption for p does not help significantly.”

It turns out that even in the case of iid probability, this effect is ambiguous.

See my other paper “Time Series Predictability in the Disaster Model” for a proof and discussion of these statements in more detail.

This mistake has no impact on the analysis of recoveries (sections I and II).