Breaking Down Volatility of the VIX

I had never heard of the VVIX index (the volatility of the stock market's volatility "volatility of VIX") until a week back when Bill Luby from the always insightful 'VIX and More Blog' posted about the recent gap seen between the historical volatility "HV" of the VIX (i.e. the trailing volatility of the VIX index) and the implied volatility "IV" (i.e. what was currently priced in as the forward expected volatility of the VIX index).

To Bill:

Much to my surprise the current 20-day HV is 144, while the current IV is only 98. In other words, the markets expect the VIX to be considerably less volatile in the month ahead than it has been over the course of the last month.

But as we'll see, based on the historical relationship between the VIX and VVIX, the pricing wasn't all that unexpected. Over the previous month, the VIX index had fluctuated between roughly 17 and 26, so (ignoring any opinion of the market for a moment) the reading of 98 was actually right in the heart of where one would expect it based on historical data since the VVIX index 2007 inception.

And this is where things get interesting.

The historical chart shown above makes the assumption that the volatility of the VIX index is lower when the VIX index is lower, which would have been my first guess had I not really thought about it. When I did think about it, that actually makes no sense whatsoever.

Why?

• Volatility is a measure of change in percent terms
• A change from a low starting value is a much higher percentage change than an equivalent unit change from a high starting value (i.e. a 2 point change from 10 is a 20% move... a 2 point change from 80 is a 2.5% move)

With that understanding, the chart below showing the realized one month change from various VIX starting points shouldn't be too surprising because a 15 point move higher in the VIX from a starting value of 15 is much more likely than a 40 point move higher in the VIX from a starting point of 40.

The interesting thing is that this conflicts with how the VVIX (vol of VIX) has been priced. At low levels of VIX, the VIX is MORE likely to have wide outcomes (in percentage movement) while at high levels the mean reverting characteristic of the VIX has made a move down from high levels much more likely.

A chart attempting to summarize the first two charts is shown below. It shows the realized one-month forward volatility of VIX resulting from various starting VIX and VVIX index values. Interestingly enough, it shows that realized volatility of VIX spikes when the VIX index is low, but only when the market isn't pricing it in.

Potential thoughts from the above to consider further...

• When the VIX and the implied volatility of the VIX are low, buy options on the VIX (i.e. calls / puts)
• When the VIX is high and implied vol on the VIX is high, sell calls on the VIX

Source: CBOE