Extracting Tail Risk from High-Frequency S&P 500 Returns

This paper proposes to extract tail risk from a risk-neutral mean-adjusted expected shortfall of high-frequency stock returns. Risk adjustment is based on a nonparametric estimator of the state price density that does not use option prices and relies solely on a stock index returns. This makes the measure methodology applicable to many financial markets with illiquid or nonexistent options. Empirically, the tail risk factor extracted from S\&P 500 returns has a 90% correlation with the options-based VIX index and predicts well realized jumps in the stock market index at various frequencies. We document a persistent negative relation between tail risk and one-day ahead returns of several assets classes. 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. An analysis of equity portfolios sorted on exposure to tail risk reveals a premium for bearing such a risk, even after controlling for known and established factors related to cross-sectional variability. This cross-sectional analysis is robust to the inclusion of uncertainty indexes, as well as macroeconomic and volatility measures