Volatility-of-volatility and tail risk hedging returns

• We propose to consider the VVIX index as a tail risk indicator.
• The VVIX index has strong predictability for tail risk hedging returns.
• An increase in the VVIX index raises current prices of tail risk hedging options and lowers their subsequent returns.
• The predictability can be explained by time-varying crash risk or uncertainty premiums.

This paper reports that the volatility-of-volatility implied by VIX options has predictability for tail risk hedging returns. Specifically, an increase in the volatility-of-volatility as measured by the VVIX index raises current prices of tail risk hedging options, such as S&P 500 puts and VIX calls, and lowers their subsequent returns over the next three to four weeks. The results are robust to jump risk, skewness, kurtosis, option liquidity, variance risk premium, and limit of arbitrage. The predictability can be explained by either risk premiums for a time-varying crash risk factor or uncertainty premiums for a time-varying uncertain belief in volatility.