Can Time‐Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?

Abstract

Why is the equity premium so high, and why are stocks so volatile? Why are stock returns in excess of government bill rates predictable? This paper proposes an answer to these questions based on a time-varying probability of a consumption disaster. In the model, aggregate consumption follows a normal distribution with low volatility most of the time, but with some probability of a consumption realization far out in the left tail. The possibility of this poor outcome substantially increases the equity premium, while time-variation in the probability of this outcome drives high stock market volatility and excess return predictability. Can time-varying risk of rare disasters explain aggregate stock market volatility? AbstractWhy is the equity premium so high, and why are stocks so volatile? Why are stock returns in excess of government bill rates predictable? This paper proposes an answer to these questions based on a time-varying probability of a consumption disaster. In the model, aggregate consumption follows a normal distribution with low volatility most of the time, but with some probability of a consumption realization far out in the left tail. The possibility of this poor outcome substantially increases the equity premium, while time-variation in the probability of this outcome drives high stock market volatility and excess return predictability.

Volatility‐Managed Portfolios

“…In fact, many equilibrium asset pricing models have largely ignored the risk-return trade-off literature, which runs regressions of future returns on volatility, because the results of that literature are ambiguous and statistically weak (see Glosten, Jagannathan, and Runkle (1993), Whitelaw (1994), Lettau and Ludvigson (2003), Lundblad (2007)). 23 We assess the statistical power of our approach by studying the predictions of four leading equilibrium asset pricing models: the habits model (Campbell and Cochrane (1999)), long-run risk model (Bansal, Kiku, and Yaron (2012)), time-varying rare disasters model (Wachter (2013)), and intermediary-based asset pricing model (He and Krishnamurthy (2013)). Specifically, we calibrate each model according to the original papers and simulate stock market return data for a sample of equal length to our historical sample.…”

“…Moments are recovered by replicating in the simulations exactly the same exercise as in the data. In the first row we show the habits model of Campbell and Cochrane (1999), in the second row the rare disaster model of Wachter (2013), in the third row the long-run risk model of Bansal and Yaron (2004), and in the last row the intermediary-based model of He and Krishnamurthy (2013). Simulations are done using the original papers' parameter calibrations.…”

Valuation Risk and Asset Pricing

“…Rare disaster models of the type proposed by Rietz (1988) and Barro (2006) also share this difficulty because all shocks, disaster or not, are to the supply side of the model. A model with a time-varying disaster probability of the type considered by Wachter (2013) and Gourio (2012) might be able to rationalize the low correlation between consumption and stock returns as a small-sample phenomenon. The reason is that changes in the probability of disasters induce movements in stock returns without corresponding movements in actual consumption growth.…”

Hidden persistent disasters and asset prices

“…As noted above, SDU's capability can be demonstrated more prominently in our model where disasters are persistent. Further, in Gabaix (2008, 2012), and Wachter (2013, the fluctuation in disaster probabilities is completely exogenous, and their model's validity remains to be tested. As Nakamura et al (2011) state, it would be difficult to obtain reliable estimators for the time-varying disaster probability process, because by definition, only rarely can economic disasters be observed.…”

“…This study is also closely related to the recent research by Gabaix (2008Gabaix ( , 2012, and Wachter (2013). By postulating the time-varying process of disaster probabilities, their models can explain many financial market puzzles.…”