Wednesday, October 28, 2015

What Exactly Does the VIX Tell Us?

Most investors know of the VIX Index, but not as many understand what information the VIX provides an investor. Here is my attempt to provide an initial outline of what it is and why the information embedded within the figure is so powerful.

VIX Defined

The CBOE has a white paper that provides a ton of detail into the VIX calculation, but the origin of the index describes what it is at a high level well enough:

In 1993, the Chicago Board Options Exchange® (CBOE®) introduced the CBOE Volatility Index® (VIX® Index), which was originally designed to measure the market’s expectation of 30-day volatility implied by at-the-money S&P 100® Index (OEX® Index) option prices. The VIX Index soon became the premier benchmark for U.S. stock market volatility.
Ten years later in 2003, CBOE together with Goldman Sachs, updated the VIX to reflect a new way to measure expected volatility, one that continues to be widely used by financial theorists, risk managers and volatility traders alike. The new VIX is based on the S&P 500® Index (SPXSM), the core index for U.S. equities, and estimates expected volatility by averaging the weighted prices of SPX puts and calls over a wide range of strike prices.
In summary... the VIX is a reflection of the market's expectation of future market volatility.

The Math Behind What the VIX Level Means

As Eddy Elfenbein of the great Crossing Wall Street blog outlined back in 2012, you can take the current market's expectation of future market volatility (i.e. the VIX), to determine the expected range of future stock market returns.
The 3.46 denominator is simply the square root of 12, which takes the VIX from an annualized figure to a monthly figure given there are 12 months in a year.

You can also vary the blue "confidence bands" in the chart above (in the chart above, the one standard deviation bands "should" capture 68% of outcomes). For example, from statistics we know that 1.96 is the z value of a 95% confidence interval. We can convert this 1.96 level to a monthly value as follows:
1.96 / (square root of 12) = 0.57
We can then take that 0.57 value and multiply it by the VIX to determine the bands that (in theory) contain that 95% percent of outcomes. For example, with a VIX of 20, the equation is:
20 x 0.57 = 11.3 or 95% of all outcomes over the next month should be within a +/- 11.3% return
In reality, the VIX typically overstates the level of market risk and understates the results within the band. As the chart shows below, the confidence bands described by the VIX understate the "capture rate" of the bands, especially at higher confidence levels. In the chart above, one standard deviation bands should capture 68% of outcomes, but instead have captured 85% of outcomes.


Neither of the following conclusions should surprise readers of the blog, but they are:
As a result, while an investor can utilize the VIX to scale equity weights to smooth out returns, an investor should rarely be buying volatility protection.