# VIX Mean Reversion After a Volatility Spike

In a previous post, we showed that the spot volatility index, VIX, has a strong mean reverting tendency. In this follow-up installment we’re going to further investigate the mean reverting properties of the VIX. Our primary goal is to use this study in order to aid options traders in positioning and/or hedging their portfolios.

To do so, we first calculate the returns of the VIX index. We then determine the quantiles of the return distribution. The table below summarizes the results.

 Quantile 50% 75% 85% 95% Volatility spike -0.31% 3.23% 5.68% 10.83%

We next calculate the returns of the VIX after a significant volatility spike. We choose round-number spikes of 3% and 6%, which roughly correspond to the 75% and 85% quantiles, respectively. Finally, we count the numbers of occurrences of negative VIX returns, i.e. instances where it decreases to below its initial value before the spike.

Tables below present the numbers of occurrences 1, 5, 10 and 20 days out. As in a previous study, we divide the volatility environment into 2 regimes: low (VIX<=20) and high (VIX>20). We used data from January 1990 to December 2017.

 VIX spike > 3% Days out All cases VIX<=20 VIX>20 1 56.1% 54.9% 58.1% 5 59.7% 58.4% 61.8% 10 60.3% 57.0% 65.8% 20 61.6% 57.0% 69.5%

 VIX spike > 6% Days out All cases VIX<=20 VIX>20 1 58.2% 56.9% 60.3% 5 62.5% 62.0% 63.3% 10 64.0% 61.7% 67.6% 20 65.9% 61.4% 73.2%

We observe the followings,

• The greater the spike, the stronger the mean reversion. For example, for all volatility regimes (“all cases”), 10 days after the initial spike of 3%, the VIX decreases 60% of the time, while after a 6% volatility spike it decreases 64% of the time,
• The mean reversion is stronger in the high volatility regime. For example, after a volatility spike of 3%, if the VIX was initially low (<20), then after 10 days it reverts 57% of the time, while if it was high (>20) it reverts 66% of the time,
• The longer the time frame (days out), the stronger the mean reversion.

The implication of this study is that

• After a volatility spike, the risk of a long volatility position, especially if VIX options are involved, increases. We would better off reducing our vega exposure or consider taking profits, at least partially,
• If we don’t have a position prior to a spike, we then can take advantage of its quick mean reversion by using bounded-risk options positions.