Monday, February 21, 2011

Can the VIX Really Predict the Market?

The VIX as a market predictor?

There was an interesting article in a few days ago, here: 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 Experiment

I 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.


Of 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.


  1. I would think you would want to filter it down. More along the lines of testing to see If vix higher on days market higher then next day market down. Otherwise you may just be testing the likelihood of a down day leading to a down day since vix higher can be essentially substituted with down day due to its high correlation. Now if VIX was higher on an up day and yet following day was a down price day, that would be interesting.

    Truth is it is just telling you what price people are willing to hold options for based on a daily cost of carry. People refuse to accept this.

    Best of Luck!

  2. I think the real interesting question is does the VIX have a good predictive power in its extremes. If the VIX is under 16 is it a good idea to stay in cash, and if the VIX is above 40 is it, in fact, a very good time to invest. My very simplistic excel spreadsheets indicate that VIX levels above 35 or 40 presented excellent entering points to equities. Would be extremely interested in hearing your view.

  3. Interesting observation. I think it depends on your trading style and time horizon. For example, the VIX went above 40 on 9/29/08. On that day the Dow closed at 10,365. It then proceeded to move mostly lower until bottoming on 3/5/09 just south of 6600 and did not recover 10,365 until 11/16/09.

    The other problem is that it is exceedingly difficult to choose good entry points when the VIX is i outer space. The Dow can be up 400 one day and down 400 the next. Just off-hand, my guess would be that it would be better to wait until the VIX drops back *below* 40 before investing.

    For short-term trading, a VIX above 40 guarantees some wild swings, but then that's not "investing".

    On the other end, I wouldn't be in cash when the VIX is low. That characterizes strongly trending markets, and as we know, the trend is your friend - if you get on the bus early enough.

    My personal style is to stop trading entirely when the VIX goes above 30. Then the lower it goes, the more I trade.

    I'd be curious how you arrived at your conclusions.

  4. 2008 was an exception because at that year the VIX reached 90. But in most market bottoms the VIX reaches a max point of between 35 and 45. I investigated all of the market (S&P 500) significant low points since year 2000 (e.g. Sep 17, 2001, July 29, 2002, Sep 30, 2002....all the way to Sep 26, 2011). I checked the VIX level at these points (10 such points in total), as well as 30 days before and after. My hypothesis was: it is a good long term entry point if the VIX is above 40. My conclusion was that indeed it was, however, it was an even better (and safer) entry point if the market registered a new low but VIX, while high, was showing a positive divergence (i.e. a lower VIX). If you'd like to discuss further I can be reached at :


Due to some people who just won't honor my request not to post spam on my blog, I have had to re-enable comment moderation. Comments may take up to 24 hour to appear, depending on when they're made. Sorry about that.