On the Size Distribution of Macroeconomic Disasters

In the rare-disasters setting, a key determinant of the equity premium is the size distribution of macroeconomic disasters, gauged by proportionate declines in per capita consumption or GDP. The long-term national-accounts data for up to 36 countries provide a large sample of disaster events of magnitude 10% or more. For this sample, a power-law density provides a good fit to the distribution of the ratio of normal to disaster consumption or GDP. The key parameter of the size distribution is the upper-tail exponent, α, estimated to be near 5, with a 95% confidence interval between 3-1/2 and 7. The equity premium involves a race between α and the coefficient of relative risk aversion, γ. A higher α signifies a thinner tail and, therefore, a lower equity premium, whereas a higher γ implies a higher equity premium. The equity premium is finite if α 1>γ. To accord with the observed average unlevered equity premium of around 5%, we get a point estimate for γ close to 3, with a 95% confidence interval of roughly 2 to 4.