Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance *

Abstract

This paper incorporates a time-varying intensity of disasters in the Rietz-Barro hypothesis that risk premia result from the possibility of rare, large disasters. During a disaster, an asset's fundamental value falls by a time-varying amount. This in turn generates time-varying risk premia and thus volatile asset prices and return predictability. Using the recent technique of linearity-generating processes (Gabaix 2007), the model is tractable, and all prices are exactly solved in closed form. In the "variable rare disasters" framework, the following empirical regularities can be understood qualitatively: (i) equity premium puzzle (ii) risk-free rate-puzzle (iii) excess volatility puzzle (iv) predictability of aggregate stock market returns with price-dividend ratios (v) value premium (vi) often greater explanatory power of characteristics than covariances for asset returns (vii) upward sloping nominal yield curve (viiii) a steep yield curve predicts high bond excess returns and a fall in long term rates (ix) corporate bond spread puzzle (x) high price of deep out-of-the-money puts. I also provide a calibration in which those puzzles can be understood quantitatively as well. The fear of disaster can be interpreted literally, or can be viewed as a tractable way to model time-varying risk-aversion or investor sentiment.