Investigating the VIX-S&P 500 Correlation

Recently, with the VIX getting higher and the broader market driving lower, the possibility of an inverse correlation relationship between the VIX and SPX has been brought up several times. How true is this relationship and how accurate is it? The charts and data below try to get a little closer to answering that question. As usual, I got ahead of myself and started with real data and started looking for correlations between the VIX and S&P 500. However, I used only the data from September 2003 since the calculation method of the VIX changed at that point and the set ends on January 3rd, 2008. So here's what is found in terms of correlations:

The correlation of the VIX to the S&P 500 is 0.078. This isn't all that great over the long term as many have already pointed out. But others have also rightly noted that there are clearly areas of inversely related behaviour. This is observed in the drops in the S&P being reflected in an increase in the VIX. So what is the VIX? The lay-man, throwaway definition is that it's the "fear gauge" of the market, which isn't a very satisfying answer. The other answer heard is that it is a measure of volatility, which makes a lot more sense. It's actually implied volatility which is why the "fear gauge" comment is somewhat accurate. To many people, volatility is a measure of deviation from an expected line, curve or other pattern. This led to analysis of the various ranges of the S&P 500, which yielded some more interesting results. The first thing that checked was a simple correlation of the VIX (left axis) to the S&P 500 daily range (right axis). Here's the chart:

The blue line is the VIX, the yellow line is the S&P daily range and the black line is a 5 period moving average of the range that was inserted purely to make the chart more readable but turned out to be interesting as noted below. The correlation here is 0.577 which is far more significant than 0.078 noted above. (The S&P 500 range as a percent of the opening value was also considered. The correlation there was 0.567 – essentially the same.) The S&P 500 range is a very noisy value as seen in the chart. The 5 period moving average was intriguing since it smoothed out some of the noise and looked like it mapped well onto the VIX line. The next potential correlation examined was a 5-day range of the S&P 500. This was calculated using the maximum and minimum values in a 5 day period and then comparing this to the VIX. Here's the chart:

The correlation here is better and calculates to 0.699. This is a pretty decent value for most data sets. It's also incrementally better than the correlation using a 3 day range which came out to 0.648. Something still didn't seem quite right though since there clearly are short periods where the VIX and S&P are inversely related. The next step was taking into account the direction of the move as well as the magnitude. For this, the S&P 500 percentage change from close to close was used and compared to the VIX change from close-to-close.

The chart is unfortunately, very hard to read because of the volume of data. However, the correlation is -0.813! This makes sense for a couple of reasons. First, it corresponds with the observed behaviour of the VIX rising when the S&P 500 drops. But it also takes into account the day range noise that is volatility by another name. In the last 5 years the direction of the S&P has been primarily up. So any deviation downward will cause more nervousness (implied volatility) than a deviation upward (trend acceleration). The latter still causes volatility though and thus will somewhat inflate the VIX. After arriving at this correlation level, a bit more research on the VIX – what it is, how it's calculated, what it implies, etc. – was done There's an interesting note in Wikipedia that says this:

The VIX is quoted in terms of percentage points and translates, roughly, to the expected movement in the S&P 500 index over the next 30-day period, on an annualized basis. For example, if the VIX is at 15, this represents an expected annual change of 15%; thus one can infer that the index option markets expect the S&P 500 to move up or down.
That is, if, for example, the S&P 500 is currently at 100, index options are priced with the assumption of a 68% likelihood (one standard deviation) that the 30- day change in the S&P 500 will be within 4.3 points up or down.

This is very noteworthy and lends itself to testing historic VIX values and their implied S&P 500 values against the actual S&P performance to see how often the VIX prediction was wrong. The chart with the implied upper and lower bands, actual 30 days ahead, along with the VIX is below:

So the bands are mostly accurate, not unlike typical Bollinger bands. One note is that 30 trading days ahead were used, instead of 30 calendar days because it's far easier than referencing calendar days in Excel. It turns out that the S&P 500 gets outside of its predicted band about 21% of the time – less than would be expected from the Wikipedia definition.

If the number of trading days is changed to 20 to approximate the calendar days, the prediction is wrong about 10% of the time. (A potential short strangle strategy is implied here.)

This research helps to better understand the VIX and how it reflects the current market but can it predict near term movement? Typical indicators would be the RSI, Slow Stochastic and MACD. For the examples below only data from 2006 to the January 3rd, 2008 was reviewed. The discussion also has an underlying assumption that the VIX tends to revert to an average and that any moves to the range extremes will snap back to this average. RSI: The VIX data mentioned above was used and RSI was calculated on a daily basis. The RSI breaks above 60 or below 40 on 20% of the trading days looked at. There are a few times when the VIX RSI seems useful – mainly at confirming temporary bottoms – and with extreme moves where the RSI gets to >65. RSI can be useful when a stock reaches a 2nd high level but RSI does not also make a new high, portending a reversal or at least a leveling out. As noted already, there is some short-term correlation between the VIX and S&P 500. So we can look at areas where the S&P drops, the VIX RSI spikes up and when the S&P moves lower again the VIX RSI fails to move past its initial spike and then back below 60. This is a place to consider starting a long position while watching for other confirmation signals. For example:

Unfortunately, the VIX RSI doesn't appear to be very good at predicting large drops. MACD: The VIX MACD would have been providing fairly weak signals for much of the period looked at because of the low movement of the VIX and complacency in the market. However, when volatility returns to the market and looking at only strong crossovers, there is some utility as seen in the table below:

In the positive-to-negative crossover table, 3/12/2007 and 3/19/2007 are 5 trading days apart and 3/19 was a confirmation of the move on 3/12. Slow Stochastic: The slow stochastic suffers from a similar lack of strong signals because of the nature of the VIX. The performance is not as good as the MACD signal and there are fewer of them – at least using the tighter constraints.

Overall then, it looks like there is some value to watching the VIX and MACD indicators as additional signals on the standards one would use on the S&P 500. As independent signals they are infrequent and not always accurate but this is true of most other signals and technical analysis systems. VIX Options – The first and most important thing to know about VIX options are that they are "European" style. This means that they can only be executed on their expiration date and not before as is true for "American" style options. This has the practical effect of causing option prices to be "sticky," for the following reason. If the options have a couple of weeks until expiration, a large spike on the VIX index will most likely not show up as a spike in price, contrary to what would be expected if these were American options. This is because there is a high probability that two weeks on at expiration, the index will have relaxed and the options will be out of the money. This is the same mean reversion as noted before. With this in mind, buying VIX options anytime until about a week before expiration seems more risky than necessary.

Disclosure: None

Comments

[Metzenbaum ...:]

Brilliant--- attn Bespoke--- THIS is number crunching. Useful number crunching.

2008 Mar 12 03:07 PM

[Option Dragon:]

Thanks non!

2008 Mar 12 10:18 PM

[granger:]

Good stuff, thank you. Actually great.

2008 Mar 13 08:59 AM

[Nidhi Kadalbal:]

Good work!

2008 Mar 14 09:21 PM

[Nidhi Kadalbal:]

Good work!

2008 Mar 14 09:22 PM