### The VIX isn’t Magical

24Jul08

I am about 72% in agreement with a recent post from Mark Hulbert and follow up posts from (among others) the Daily Options Report and VIX and More.  The VIX isn’t as magical as it might look at first glance.  The reason is that so much of the VIX is comprised of information we already know.

If you are unfamiliar with the VIX, I would suggest reading this very good VIX primer.

Last year, I put a couple of weeks of intense analysis into the idea of deconstructing the VIX into its constituent parts to understand how it could be used as a timing indicator. For the life of me, I can’t seem to find that data, but the general idea went something like this…

For the most part, the absolute VIX level is a function of recent market volatility (not necessarily future volatility).  As depicted in the graph above, there is an 84% correlation between the previous 20-day standard deviation (volatility) of S&P 500 returns and the absolute level of the VIX.  Linear reg. equation for the chart above: Estimated Absolute Value (EAV) = 1244.0x + 7.7

To a lesser degree, day-to-day changes on the VIX are a function of day-to-day changes on the S&P 500.  As depicted in the second graph, there is a -69% correlation between (lognormal) changes in the two. Linear reg. equation for the chart above: Estimated Price Change % (EPC) = -4.0x

Putting these two factors into a very SWAG’ish formula for predicting the VIX we get something like Estimated VIX = EAV + (EAV * EPC).

A graph of these estimated versus actual VIX values looks very tight:

That’s an 85% correlation (r-squared = 72%, hence why I’m 72% in agreement).  By comparison, that’s about the same level of predictive ability the S&P 500 has in determining the value of the Nasdaq 100 (and that’s pretty darn high).

A more rigorous analysis could definitely do a better job at coming up with a formula for predicting the VIX, but I just want to prove a point: the vast majority of what the VIX is telling us, we already know (changes in price and volatility).

But as I mentioned in the opening to this post, I disagree a slight bit with some previous posters.  In the past, no matter how much I have tried to decompose the VIX into its building blocks, there was always an element of trader-driven unpredictability.  I haven’t figured out how just yet, but I think that if we can isolate what that smaller subset of information is telling us, we might have something useful and unique.

ms

#### 2 Responses to “The VIX isn’t Magical”

1. 1 tranquil trader

hi, just found your site recently. Some great analysis!!
I have been doing some work on the VIX too as a predictor of short run S&P returns.
Your analysis on VIX movement vs S&P movement is very much in agreement with what i have found, although the edge is too thin to trade on.

Just to clarify, was it the actual reported VIX that you are using in your analysis? or was it the futures data?

As i have found out, thee is a BIG diference between the two. actual VIX has a definite mean reversion properties to it and does depend heavily on recent market volatility. whereas the futures data (seems to be less dependent on it)

Keep posting!

2. 2 marketsci

I’m using the index data, not the futures data.

I couldn’t agree more with your last paragraph. The underlying index is very predictable. I’ll get a post on that shortly (a golden oldie that use to live on the MarketSci.com site). Even though it can’t be traded directly, it can be used as a good input for trading the market (because it is so predictable).

You hit the nail on the head though, that also as a result of that predictability, the futures contract trades wildly differently. Heck, if it didn’t we could just print money trading it. I haven’t done very much work on trading the futures directly…possibly a topic for a future post?

Thanks for the comment and for visiting!

ms