# Volatility of Volatility as an Edge

My new book has a section on specific trading edges. Vol of vol gives one such edge. I’ll summarize the effect and give references and a suggested strategy to monetize the edge. The “confidence factor” is 1 to 3. 3 is something that I have high confidence in. Confidence is based on the amount of empirical evidence and the plausibility of a reason for the effects existence.

### Volatility of Volatility as an Edge

Options on products with high volatility of volatility tend to be overpriced. This is true both in the cross section: options on stocks with high volatility of volatility are over-priced relative to options on stocks with low volatility of volatility, and in the time series: the VIX tends to decline (rise) after very high (low) values of the VVIX index.

The first empirical study of this effect was done by Ruan (2017). Using data on US equity options from 1996 to 2016, he found that ranking stocks by the volatility of their implied ATM volatility showed that there was a strong and consistent negative relationship between delta neutral long option positions and volatility of volatility.

A similar study independently carried out by Cao et al (2018) also studied US equity options. Again, using data from 1996 to 2016, they found that the delta-hedged returns of long option positions decreased in uncertainty of volatility. This was true whether they used implied volatility, time series volatility from daily returns (specifically EGARCH), or high frequency volatility. Their results were robust with respect to idiosyncratic volatility, jumps, term structure, the implied-realized spread, liquidity, analyst coverage, and the Fama-French factors. They also showed that the effect was largely driven by volatility of positive volatility moves, and that volatility of negative volatility moves had a negligible effect.

These studies leave little room to interpret this effect as anything other than a separate volatility of volatility premium.

Ruan just states, “Investors indeed dislike uncertainty about volatility of individual stocks, so that they are willing to pay a high premium to hold options with high VOV (sic)”, with no supporting argument. Cao et al. speculated that market makers were charging a higher premium for options with high uncertainty of volatility because those are more difficult to hedge. This might be a partial reason, but it doesn’t take into account the time-series result that shows high volatility of volatility predicts a fall in subsequent implied volatility. This effect is independent of hedging issues.

The relationship between high VVIX (the model free implied volatility derived from VIX options) and subsequent lower VIX levels is very strong. Using VVIX data from 2007 through 2018, I calculated the rolling one year 90th percentile of VVIX. Going forward, if the VVIX crossed above this level, I “sold” the VIX and “held” until VVIX reached its rolling one-year median. This produced 31 trades. The total “profit” was 108 points. 27 trades were winner. “Buying” the 10th percentile was also “profitable”, making 62 points over 35 trades, 26 of which were winners. Clearly this particular idea cannot be implemented, as the VIX is not a traded product. I’ve included it to show that VVIX is a strong predictor of the VIX (though if we traded VIX futures, the idea is still profitable). No optimization was attempted. This was my first try. The idea also works if we use different look back periods or moving averages instead of medians.

This effect has been studied (far more rigorously) by others. Huang et al. (2018) showed that volatility of volatility significantly and negatively predicts delta-hedged long option payoffs. Park (2015) showed that high levels of VVIX raised the prices of S&P 500 puts and VIX calls and lowered their subsequent returns over the next three to four weeks (a similar time period to the average holding period in my simple test). He speculates that the effect is caused by either “risk premiums for a time-varying crash risk factor or uncertainty premiums for a time-varying uncertain belief in volatility”. Both of these are plausible but at this point, there is no independent evidence for these causes.

Confidence Level: 2

### Trading Strategy

When VVIX reaches extremely high (low) levels, either sell (buy) VIX futures or sell (buy), and dynamically hedge, S&P 500 straddles.

### References

Cao, J., Vasquez, A., Xiao, X. and X. Zhan, 2018, “Volatility Uncertainty and the Cross Section of Option Returns”, SSRN: 3178263.

Huang, D., Schlag, C., Shaliastovich, I. and J. Thime, “Volatility of Volatility Risk”, Journal of Financial and Quantitative Analysis, 1-63.

Park, Y., 2015, “Volatility-of-volatility and tail risk hedging returns “, Journal of Financial Markets, 26, 38-63.

Ruan, X., 2017, “Cross Section of Option Returns and Volatility-of-Volatility”, SSRN: 3055982.