Tail Risk and Asset Prices

TLDR: In this paper, a new measure of time-varying tail risk is proposed, which is directly estimable from the cross-section of returns and has strong predictive power for aggregate market returns: a one standard deviation increase in tail risk forecasts an increase in excess market returns of 4.5% over the following year.

Abstract: We propose a new measure of time-varying tail risk that is directly estimable from the cross section of returns. We exploit firm-level price crashes every month to identify common fluctuations in tail risk across stocks. Our tail measure is significantly correlated with tail risk measures extracted from S&P 500 index options, but is available for a longer sample since it is calculated from equity data. We show that tail risk has strong predictive power for aggregate market returns: A one standard deviation increase in tail risk forecasts an increase in excess market returns of 4.5% over the following year. Cross-sectionally, stocks with high loadings on past tail risk earn an annual three-factor alpha 5.4% higher than stocks with low tail risk loadings. These findings are consistent with asset pricing theories that relate equity risk premia to rare disasters or other forms of tail risk.