Rare Events and Long-Run Risks for Asset Prices: Empirical Identification and Evaluation

Rare events and long-run risks are two types of risks that significantly affect asset markets. A vast amount of literature investigates them separately. Here I identify them simultaneously from a rich data set and evaluate their contributions to asset pricing in a unified framework. Using the annual national-accounts data for 42 economies over 160 years (the Barro-Ursua macroeconomic data set), I estimate the proposed model of rare events and long-run risks with a Bayesian Markov-chain Monte-Carlo method incorporating conditional prior beliefs about the model's parameters. Empirical estimates disentangle (1) discrete jumps in the levels of consumption and output and (2) persistent smooth fluctuations in growth rates. Compared with previous rare-event models, the estimates for the disaster process--including disaster probability, size, and duration--are closer to the data. Utilizing parameter values that match the risk-free rate and the market return, I calculate asset pricing statistics for the models of (a) rare events and long-run risks, (b) rare events, and (c) long-run risks. Major evaluation results include: (1) for the unleveraged annual equity premium, the predicted values are 4.8%, 4.2%, and 1.0%, respectively; (2) for the Sharpe ratio, the values are 0.72, 0.66, and 0.15, respectively.