Rare Events and Long-Run Risks

Rare events (RE) and long-run risks (LRR) are complementary elements for understanding asset-pricing patterns, including the average equity premium and the volatility of equity returns. We construct a model with RE (temporary and permanent parts) and LRR (including stochastic volatility) and estimate this model with long-term data on aggregate consumption for 42 economies. RE typically associates with major historical episodes, such as the world wars and the Great Depression and analogous country- specific events. LRR reflects gradual and evolving processes that influence long-run growth rates and volatility. A match between the model and observed average rates of return requires a coefficient of relative risk aversion, γ, around 6. Most of the explanation for the equity premium derives from RE, although LRR makes a moderate contribution. We think the required γ will decline (and, thereby, become more realistic) if we allow for incomplete information about the underlying shocks, including the breakdown of RE into temporary and permanent parts. We thought that the addition of LRR to the RE framework would help to match the observed volatility of equity returns. However, the joint model still substantially understates this volatility. We think this aspect of the model will improve if we allow for stochastic evolution of the disaster probability.