Bill Luby I November 2, 2016
When people talk about the VIX you often hear them refer to mean reversion, which refers to the tendency of the VIX to be pulled inexorably in the direction of its long-term mean. With 27 years of data from the CBOE (including some historically reconstructed data), it is possible to calculate the lifetime VIX mean, which happened to be 19.71 when calculated last November.
As an options trader, however, I am wary of giving too much weight to outliers when it comes to predicting the most likely outcome in another options expiration cycle or two. For this reason, I am more interested in knowing the lifetime VIX median, which, at the time, was only 17.84. The median is the 50th percentile while the mean just happens to be in the 60th percentile. The discrepancy is due to the fact that VIX values are not normally distributed. Instead, VIX values exhibit a positive skew (a topic for a future post), due to the fact that there are a handful of VIX historical extremes in the 50s, 60s, 70s and 80s. Meanwhile, the middle 50% of VIX values (the 25th to 75th percentiles) range from 14.04 to 23.98.
So…if the VIX median is so important, why is it that we never hear about it or about median reversion? Good question. I touched on that subject on “Drilling Down on VIX Mean Reversion” in the January 2013 issue of Expiring Monthly: The Option Traders Journal. As I see it, anyone who is focusing on means in a skewed distribution is necessarily assuming a normal distribution and statistics related to normal distributions when no such distribution or relevant statistical analysis exists.
I mention all of this because the day before I first published this blog - November 2, 2016 - was one of those periodic bursts of activity for me on Twitter. In some Twitter conversations, we discussed the median VIX vs. the mean VIX and there was a request for a chart of a five-year moving average of the median VIX. Since I have never seen such a chart – or any VIX median chart for that matter – I present below a chart of the five-year moving average of the median VIX, using data going back to 1990.
Source(s): VIX and More, CBOE
Note that at the time the current five-year median VIX was 15.07, while the five-year mean VIX was 16.63. For the full history of the VIX, going back to 1990, the lifetime median VIX was 17.84, 9.5% below the lifetime mean VIX of 19.71. What does all this mean? Mostly that one should be careful using statistics that are associated with a normal distribution when analyzing the VIX. Perhaps more importantly, VIX traders should also think at least as much about median reversion as mean reversion.
Bill Luby is an Invest In Vol Educational Partner and has been writing informative thought leadership content for more than ten years. This and other articles by Bill are available on his Blog 'VIX and More' available here.
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