The CBOE Volatility Index (VIX) was created to measure the market’s expectation of near-term volatility. It is a calculation that is derived from the

pricing of options on the Standard and Poor’s S&P 500 Index (SPX.)

The relationship between the VIX and the SPX is well known. The two tend to move in the opposite directions. This is especially true when the market

crashes. During these periods of upheaval, the VIX tends to spike upwards.

The gist is that investors will pay more for options when their expectation for price movement increases. The increase in options pricing is a result of an

increase in the implied volatility. (There is a bit of “chicken or the egg” thing when it comes to changes in option pricing and implied volatility. But,

that’s another topic altogether.)

A change in the VIX is not necessarily bullish or bearish. It just represents relative increase in option pricing. However, fear of a downward move tends

to send people into protective options – put contracts – more than a move to the upside would send them into bullish call contracts. Thus, the VIX tends to

spike in response to the bearish sentiment. That is why the VIX why it is sometimes called the “Fear Index.”

The VIX was specifically developed to represent the implied volatility of a theoretical, at-the-money option on the SPX that expires in 30 days.

Implied volatility is the volatility that is expected to occur over the life of an option. Essentially, what this means is that the VIX attempts to predict

the historic volatility that will be realized, 30-days in the future.

Historic volatility is a measure of the volatility that happens in the stock movement. It has nothing to do with options or options pricing. There are

differ methods to calculate historic volatility, the most common convention is to take the standard deviation of the logarithmic change in price over the

past 30 days.

The following graph compares the SPX Historic Volatility (black) and the VIX (blue.)

From this, you can see that the VIX and the SPX historic volatility appear to be related. The VIX and SPX historic volatility tend to spike together. One

can also observe that the VIX tends to fall more quickly than the historic volatility. This is because of the nature of the historic volatility

calculation, which is a rolling 30-day calculation. Just a few significant day-to-day price changes will cause the historic volatility to rise

dramatically. But, it will take 31 days for those significant changes to roll out of the calculation. That explains why the historic volatility falls more

slowly than the VIX falls.

How good is the VIX at doing what it was designed to do?

It was designed to estimate the SPX historic volatility 30 days in the future. So, we can compare a scatter plot of the VIX to the Historic Volatility that

is realized in 30 days. If there is a correlation, a distinct pattern should emerge.

One can see that there is a cluster pattern in this plot. However, it seems to fall apart at extreme values. The R^{2} measure gives an objective

measurement of the correlation between the VIX and historic volatility. An R^{2} of 1 would be a perfect fit. If the R^{2} was 1, the dots

would fall perfectly in a line. The VIX has an R^{2} correlation of 0.2519 when compared SPX historic volatility that is realized 30 days later.

A keen observer may notice that the “30 days” in this plot is actually 30 trading days. Which is much farther in time than 30 calendar days. In 30 calendar

days, there are about 21 trading days. Following is the scatter plot for the historic volatility of the SPX that emerges 21 days later.

Considering this shorter and more realistic time frame, we can see that the R^{2} correlation improves to 0.4213. This is a significant

improvement.

A curious investigator may ask if the timeframe was even shorter, would the R^{2} improve even more?

Below is a plot of the various R^{2} correlations for different time periods of the realized historic volatility. What you can see from this chart

is that the R^{2} correlation is pretty good in the beginning and then trails off as you go out further in time.

The highest R^{2} correlation occurs in just 3 days and is 0.7361. Following in a scatter plot of the VIX vs the historic volatility of the SPX

that is realized 3 days later.

If you asked a statistician, they would say that this is a pretty good correlation.

What does this all mean? It means that the VIX does a pretty good job at predicting what the historic volatility of the SPX will be in next 3 to 7 days.

But, it does a poor job of predicting what the volatility will be in 30 days, which is what it is purported to do.

A hypothesis which explains this relationship is that volatility in the SPX actually causes the VIX to rise. That is the opposite of what it is intended to

occur.

This is not a difficult hypothesis to imagine when one considers the human nature of traders. Many things cause traders to seek protection through the

purchase of options. However, it is movement of the SPX itself that most often causes traders to seek protection. The increased demand in SPX options would

cause the price, and thus the implied volatility, of those options to increase. That affects an increase in the VIX.

A separate investigation using Granger Bivariate Causal Analysis showed that the SPX does likely cause changes in the VIX. That also supports the reverse

notion of the VIX.

One can debate this interpretation of the VIX and SPX and which is actually causing the other. However, what is very clear is that the VIX does a poor job

telling us about the historic volatility that occurs in 30 days. It may be good at telling us what is happening now and in the next few days. However, why

do we need a complicated index to tell us what is readily apparent in the market?

The author of this blog believes that all that we really know from the VIX is the relative price of options: are they expensive or cheap?

This news will take the wind out of the sails of someone who hoped to learn something about the VIX and use it to their advantage. You may take some solace

in that if you didn’t already understand the VIX, you were not missing much.

This is not to imply that implied volatility indices (VIX type calculations) are worthless. With some equities, implied volatility indices do provide

significant insight to their future.

One example of these implied volatility indices is the CBOE Equity VIX® on Apple (VXAPL.) This is a relatively new index, recently made available by the

CBOE. I will leave the reader with following chart of the R^{2} correlations of the VXAPL vs different periods of time.

From this chart, one can see a significantly different result than what the SPX and the VIX showed. From VXAPL and the historic volatility on Apple, we

find there is a very distinct correlation with the historic volatility that is realized in 21 days. That is powerful and insightful information.

Unfortunately, this is the end of this blog post. I will just have to whet the appetite of the reader and leave the discussion of this enlightenment to a

future posting.

Eric Hale

OptionsANIMAL Instructor

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