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.

Highlights

  • A longstanding puzzle in macroeconomics and financial economics is that consumption growth is not volatile enough to justify why the aggregate stock market earns large returns in excess of riskless bonds

  • Rietz (1988) and Barro (2006) argue that the economy is subject to rare “disasters” such as wars and depressions; in turn, the risk premium on stocks is not surprising because stocks are highly exposed to these rare events

  • This paper provides evidence of a single factor that drives the cross section of option-implied jump risk

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Summary

Introduction

A longstanding puzzle in macroeconomics and financial economics is that consumption growth is not volatile enough to justify why the aggregate stock market earns large returns in excess of riskless bonds. The core assumption of rare disaster models is that all assets in the economy are exposed to an aggregate jump-risk factor If this is the case, time-series variation in the tails of individual asset returns should be driven by this single factor, even though cross-sectionally some assets are more exposed to the tail event than others. The rare disasters paradigm makes a strong prediction for how time-series variation in the probability of disaster relates to the cross-sectional performance of stocks. In the final part of the paper, I make stronger assumptions about the mean frequency and severity of disasters, as well as preferences This allows me to quantitatively compare a calibrated version of the model to aggregate stock market movements and the cross section of equity returns. 51% of their value, though many of these stocks benefited from the unprecedented intervention of the government into U.S capital markets

Literature Review
Theoretical Motivation
A Non-Parametric Measure of Jump Risk
Mapping to a Rare Disasters Model
An Estimate of the Risk-Neutral Probability of Disaster
Construction and Data Description
Results
Disaster Risk and The Cross Section of Equity Returns
How Big Should Disaster-Ø’s Be?
Do Disaster Risky Stocks Fall Enough to Justify Their High Returns?
Conclusion
2: Time-Series of
1: Correlation
A Appendix: A Full Model of Rare Disasters
Macroeconomic Environment
Setup for Stocks
Equilibrium Stock Prices and Returns
The Risk-Neutral Disaster Intensity
A Simplified Example
Estimating Di t
Constructing Daily Dbi t for Each Firm
First Pass Filter of the Data
Building Measures of QdV and Vb
Aggregating Daily Dbi t to Monthly Dbi t
Weekly Frequency
Disaster-Ø Estimated Using Weekly Data
Disaster-Ø Estimated Using Daily Data
B.11 Monthly Returns
C Appendix
The Claim to Aggregate Consumption
Equilibrium Valuation of Any Arbitrary Stock
Equilibrium Returns
Risk-Neutral Price Dynamics
Equilibrium Short Rate Process
Girsanov’s Theorem to Change Measure
Proof of Proposition 2
Proof of Theorem 3
Proof of Proposition 1
Proof of Corollary 1
How Big Are the “Higher Order” Terms for Resilience?
Full Text
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