The Role of Volatility Shocks and Rare Events in Long-Run Risk Models

We generalize and extend the long-run risk model by Drechsler and Yaron (201'7 by separating the processes for the jump intensity and the stochastic conditional variance. Furthermore we replace their Ornstein-Uhlenbeck specification for the long-run mean of the conditional variance by a square-root process. Although these two modifications seem mainly technical at first sight they have major economic implications and change fundamental characteristics of the model. First they substantially improve the performance of the model in predictive regressions of future excess returns on the current price-dividend ratio and lead to an equity risk premium which is increasing not only with short-run but also with long-run uncertainty. Second, the decoupling of jump intensity and conditional variance permits a detailed analysis which of the effects first shown by Drechsler and Yaron (201'7 are due to the role of the conditional variance as a diffusive factor and which are caused by its second job, namely to control the likelihood of jumps. We find that for most effects generated by the model time-variation in the jump intensity is much more important than diffusive volatility risk