Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles

This paper incorporates a time-varying severity of disasters in the hypothesis proposed by Rietz (1988) and Barro (2006) 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, the model is tractable and all prices are exactly solved in closed form. In this paper’s “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; (viii) predictability of future bond excess returns and long term rates via the slope of the yield curve; (ix) corporate bond spread puzzle; and (x) high price of deep out-of-the-money puts. This paper provides a calibration in which those puzzles can be understood quantitatively as well. The fear of disasters can be interpreted literally, or be used to analyze how perceptions of risk affect asset prices and returns in a broad class of models