The VIX as a market predictor?

There was an interesting article in www.seekingalpha.com a few days ago, here:

http://seekingalpha.com/article/252838-4-reasons-the-stock-market-has-doubled?source=tracking_email#comment-1481460. Although the main theme was on why the market's been on such a tear lately, there was an interesting digression in the comments about the VIX and whether or not it has any predictive powers as far as the market is concerned.

Now many people, myself included, do use the VIX to try to get a handle on future market moves. And I've found it to be quite useful, but I thought it was time to put the issue to the test,

Mythbusters-style. So I decided to crank up Matlab and do a little math.

The ExperimentI started by collecting closing daily values of the Dow, the S&P, and the VIX, going back to 12/11/09. That's 300 sessions. I chose that number because that was all I could get eSignal to cough up. There's no obvious way I can see to tell it I want more data.

In any case, I thought that doing a cross-covariance of the VIX with the Dow or S&P might prove revealing. Let's start off with the raw data. Here's the S&P (in blue) and the Dow (in red) from 12/11/09 to 2/18/11. I divided the Dow numbers by 10 so both plots would display nicely on the same graph. (Click on the image for a larger version)

They look pretty similar, right? Basically what you'd expect.

Now let's do a simple cross-covariance on these two datasets just to get a feel of what the xcov function looks like. Recall that the cross-covariance is just the cross-correlation function of two sequences with their means removed. Imagine having both graphs printed on transparencies and sliding one past the other looking for points where they either line up or don't. That's what the x-axis shows here - how far away from their starting position the two graphs are.

Pretty much what you'd expect, right? There's maximum correlation between the Dow and the S&P right in the middle, which represents the zero-lag point. As you slide one past the other in either direction, the correlation decreases, and it does it symmetrically. So - nothing to see here. The Dow cannot predict the S&P, and vice-versa.

Right about here, I'm having nightmares about some savant working for Goldman Sachs in a big room surrounded by racks of massively parallel supercomputers laughing at my puny efforts, but bear with me. It's new to me, at least.

Now let's take a look at the VIX for the same period:

Kind of looks like an inverse of the markets, right? Which it should. When the VIX is up, the market is down and vice-versa.

The $64,000 question is, how often, if ever, does the VIX go up the day before the market goes down? So let's do the cross-covariance of the VIX with the market.Here's the result using the S&P:

Hmmm, very interesting. First of all, as expected, the zero lag spot (the middle of the x axis), has a big spike downward, illustrating how the VIX is highly negatively correlated with the market (VIX up, market down & vice versa). But now, focus both left and right of the center line. Notice how, unlike the xcor of the Dow with the S&P, here the left and right halves to the graph are decidedly asymmetrical.

There is predictive power here.

To make this a bit more clear, let's try an example with two really simple data sets. a is just [1 2 3 4 5 6 7 8 9 10 9 8 7 6 5 4 3 2 1]. b is [2 3 4 5 6 7 8 9 10 9 8 7 6 5 4 3 2 1 2]. Ie. b is the same thing as a, but it peaks one position sooner (one day if you will). This means that b can be used as a predictor for a. When b peaks, you know a will peak the next day. Here they are in a graph.

Now let's plot the cross-covariance of a and b.

If a and b were identical, ie. completely correlated, they would have no predictive power and the graph would be symmetrical about the center of the y-axis. Not so here. Note that a and b are identical except that b peaks one day earlier. From day 9 to 10, b is falling while a is still rising. In every other spot, both a and b rise and fall together. This one discrepancy can be seen as the asymmetry in the curve. This is exactly what we see in the VIX cross-correlation. Let's zoom in on it.

Note that the slope of every day to the right of the center of the graph (point 300) is lower than that on the left.

This represents places where the VIX has changed direction before the S&P.Let's check this on the actual data. Here's the last 11 days of the S&P, with the corresponding VIX overlaid in red. The y-axis numbers are S&P prices. The VIX values have been scaled to look nice.

Here we see that the VIX rose from the 4th to the 8th where it peaked. Meanwhile the S&P was also rising, but it peaked on the 8th, then declined on the 9th. The VIX peaked one day before the S&P!

Then the VIX bottomed on the 11th and started rising. Meanwhile the S&P peaked on the 14th, one day later! It certainly appears that there's something to this.

Which brings us to the dreaded right-hand edge of the chart. We see that the VIX peaked on last Wednesday, the 16th. It fell Thursday and Friday. Meanwhile the S&P has been rising since the 15th. Watch for the next VIX bottom. Let's see what the S&P does the next day.

ConclusionOf course, this is just a tiny sample, but it sure looks promising. So what's the bottom line? It definitely appears that the VIX can be used to predict the short-term movement of the market. This leaves the questions of how much, how well, and what other outside influences might exist, but this post is long enough. That will have to wait for Part Two.