High frequency tail risk

Abstract

This paper proposes an alternative way to measure high-frequency Tail Risk ex-tracted from market returns: A risk-neutral mean-adjusted expected shortfall. We rely on a non-parametric estimator for the state price density based on Hellinger's distance to risk-neutralize returns. The measure is easy to interpret and does not depend on option prices, being straightforward to apply to different markets and asset classes. Despite not making use of option data, our tail risk factor has around 90% correlation with the VIX index, reassuring the 'fear nature' of the volatility index. Empirically, we document a persistent negative relation between tail risk and one-day ahead returns, for different assets. Consistent with the crash-insurance property of put options, tail risk predicts positive one-day ahead returns for portfolios long out-of-the-money short in-the-money put options. The same analysis for stock portfolios formed on the level of exposure to tail risk indicates a premium for bearing such a risk, even when controlling for known and established factors related to cross-section variability. Our analysis is robust to the inclusion of volatility measures, macroeconomic condition measures, and uncertainty indexes.