The Probability of Rare Disasters: Estimation and Implications

Abstract

I analyze a rare disasters economy that yields a measure of the risk neutral probability of a macroeconomic disaster, p § t . A large panel of options data provides strong evidence that p § t is the single factor driving option-implied jump risk measures in the cross section of firms. This is a core assumption of the rare disasters paradigm. A number of empirical patterns further support the interpretation of p § t as the risk-neutral likelihood of a disaster. First, standard forecasting regressions reveal that increases in p § t lead to economic downturns. Second, disaster risk is priced in the cross section of U.S. equity returns. A zero-cost equity portfolio with exposure to disasters earns risk-adjusted returns of 7.6% per year. Finally, a calibrated version of the model reasonably matches the: (i) sensitivity of the aggregate stock market to changes in the likelihood of a disaster and (ii) loss rates of disaster risky stocks during the 2008 financial crisis.

Tail risk premia and return predictability

“…The recent cross-sectional-based tail index estimates reported in Chollete and Lu (2011), Kelly and Jiang (2014), and Ruenzi and Weigert (2011) also point to strong dynamic dependencies. All of these studies, however, pertain to the actual return distributions and the shape of the tails under P. Recent studies that have estimated somewhat simpler dynamic dependencies in the tails under Q include Almeida, Vicente, and Guillen (2013), Du and Kapadia (2012), Hamidieh (2011), Siriwardane (2013, and Vilkov and Xiao (2013). 29 We also experimented with other choices for this "tail" cutoff, resulting in qualitatively very similar dynamic features and predictability regressions to the ones reported below.…”

What does the tail of the distribution of current stock prices tell us about future economic activity?

“…They show that the tail risk factor has significant explanatory power of stock returns. Siriwardane (2015) relies on options prices to estimate the probability of macroeconomic disaster. He finds that this probability is priced in the cross-section of US equity returns.…”

“…However, although using the same metric, we differ from Kelly and Jiang since we evaluate the relationship of this measure with economic activity instead of identifying it as a risk factor of stock returns. 2 As pointed out by Siriwardane (2015), options are a natural source of information to solve the problem of estimating tail risk because they are forward-looking instruments. However, we do not use options in this article because the Brazilian option market has poor liquidity.…”

Changes in Natural Disaster Risk: Macroeconomic Responses in Selected Latin American Countries

“…Isoré and Szczerbowicz (2017) further showed how to extend this approach to a New Keynesian environment, and found that disaster risk shocksn-again, absent of actual disaster realization-, generate procyclical responses of consumption, investment, labor, wage, and inflation, simultaneously to the recession and rise in equity premium. Further empirical evidence by Siriwardane (2015) and Marfè and Penasse (2017) support the relationship between changes in the probability of a disaster and macroeconomic variables.…”