Expected VIX Option Returns

Abstract

We dissect the fine structure of volatility risks, as an important component of time-varying investment opportunities, by studying returns on VIX option portfolios. In particular, we provide model-free evidence regarding the two leading channels in modeling volatility risks: stochastic volatility-of-volatility and volatility jumps. We find that zero-delta straddles and delta-hedged portfolios of VIX options, which are neutral to changes in VIX but sensitive to volatility-of-volatility, underperform zero. In contrast, tail portfolios, which we construct by out-of-the-money and at-the-money VIX options and are only sensitive to tails risks of volatility, outperform zero. Therefore, risks in volatility-of-volatility and jump-induced volatility tails are priced, providing empirical support for both of the two leading channels. We further construct measures for volatility-of-volatility and volatility tail risks, by the whole set of out-of-the-money VIX options, to understand how they are priced relative to variance and equity risk premiums. We find that both measures predict short-horizon market returns, with the predictability from volatility-of-volatility risks subsumed by the variance premium but the volatility tail risk standing as a separate channel. Different from existing tail risk measures of merely market returns, our volatility tail index provides important information regarding how investors gauge the extreme volatility risks.