A Model-Free Tail Risk Index and Its Return Predictability

Abstract

This paper proposes a tail risk index, TIX, as the growth rate of the model-free cumulant generating function of market risk calculated from index option prices. It captures the power law decay rate of the left tail of future return distributions, and thus reflects market beliefs about the chance of a market crash. The change in these beliefs strongly predicts market returns both in and out of sample, with monthly R^2 statistics of 3.69% and 6.60%, respectively. This can generate utility gains of 9.50% per annum for a mean-variance investor. Evidence at the market and industry levels indicates informational friction between options and spot markets, with about one-third of the information content of this change in market beliefs being delayed to be incorporated into spot prices. A decomposition of VIX into its normal risk and tail risk components shows that only the change in tail risk, which accounts for on average 5% of the risks measured by VIX, has return predictability.

Keywords: Market Risk, Tail Index, VIX, SVIX, Return Predictability

JEL Classification: G12, G13, G14