Risk Premia and the Conditional Tails of Stock Returns∗

Theory suggests that the risk of infrequent yet extreme events has a large impact on asset prices. Testing models of this hypothesis remains a challenge due to the difficulty of measuring tail risk fluctuations over time. I propose a new measure of time-varying tail risk that is motivated by asset pricing theory and is directly estimable from the cross section of returns. My procedure applies Hill’s (1975) tail risk estimator to the cross section of extreme events each day. It then optimally averages recent cross-sectional Hill estimates to provide conditional tail risk forecasts. Empirically, my measure has strong predictive power for aggregate market returns, outperforming all commonly studied predictor variables. I find that a one standard deviation increase in tail risk forecasts an increase in excess market returns of 4.4% over the following year. Crosssectionally, stocks that highly positively covary with my tail risk measure earn average annual returns 6.0% lower than stocks with low tail risk covariation. I show that these results are consistent with predictions from two structural models: i) a long run risks economy with heavy-tailed consumption and dividend growth shocks, and ii) a time-varying rare disaster framework. ∗I thank my thesis committee, Robert Engle (chair), Xavier Gabaix, Alexander Ljungqvist and Stijn Van Nieuwerburgh for many valuable discussions. I also thank Mikhail Chernov, Itamar Drechsler, Marcin Kacperczyk, Anthony Lynch and Seth Pruitt for insightful comments. †Department of Finance, Stern School of Business, NYU, 44 West Fourth Street, Suite 9-197, New York, NY 10012-1126. Office Phone: 212-998-0368. Cell Phone: 646-469-4466. E-mail: [email protected]. Homepage: http://pages.stern.nyu.edu/∼bkelly.