Guest post submitted by onlyvix.blogspot.com
VIX / VVIX Divergence
Last week Matt at Distressed Volatility posted a chart showing recent divergence between VIX and VVIX index (volatility index based on VIX options). It looks from the chart that for VIX and VVIX followed similar trajectory but in the recent 3 weeks have gone in starkly different directions - with VIX declining while its implied volatility rising. Looking at the chart the spread seems significant.
However looking at longer history of VIX and VVIX different picture emerges: the levels of indexes are not really related. Here is the same plot for the past 6 years - there is some similarity (timing of the peaks) but the levels are not really related. I also fitted a more complicated model to quantify relationship between levels of VIX and levels of VVIX but without success.
Scatterplot also does not show a simple relationship.
However a simple relationship exists between changes in VIX (daily difference) vs changes in VVIX, and returns in VIX vs returns in VVIX - on daily, weekly, and even monthly time scales. The chart on the side is the scatterplot of daily returns on two indexes, a consistent relationship with correlation over 0.6. This is not much different from SPX & VIX - little correlation in levels but high correlation in returns.
Using weekly data I estimate that VVIX returns are ~ 0.41 * VIX returns sigma=0.066, which makes last weeks move (VIX lost 10% VVIX gained 11%) to be significant. However this is not to conclude that indexes will mean-revert; rather they will continue their paths from these new levels.