VIX is a widely-watched measure of market volatility and there are a variety of trading strategies that involve betting on the VIX. An anonymous letter to the SEC claims that the VIX is being gamed by traders, however. This argument is bolstered by an academic study from 2017 that suggests that such manipulation is possible (see the linked article above). The VIX is a measure of implied volatility on S&P500 options that expire within the next thirty days. The claim, as I understand it, is that traders are entering bids and offers on illiquid options which shift the market, even though the options may not trade at the biased prices. When the options prices move, the implied volatility shifts because implied volatility is determined by options prices.

Much of the discussion that I have seen ignores the well-known fact that VIX is largely determined by the trailing realized volatility of the S&P500. This is caused by the fact that the options markets tend to assume that the future will look quite a bit like the past. I thought it would be interesting to explore this relationship and see if this might shed any insight into whether the VIX is becoming less coupled to trailing realized volatility. If this is the case, it would seem more plausible that VIX is being gamed and is no longer as anchored to real life volatility. On the other hand, there are some reasons why VIX might become less correlated to realized volatility in the market. First, trading in the VIX has expanded enormously in recent years.

Trading volume of VIX future and options was minuscule in the mid 2000s but has exploded over the last decade. As more people trade the VIX, there is more opportunity for the VIX index to become less coupled to actual real-life volatility.

I have done a statistical analysis to look at the degree to which VIX tracks with realized historical volatility of the S&P500. To the extent to which VIX can be explained by actual volatility, I’d say the measure is meaningful. Because VIX is the implied volatility of near-term options, we also expect that there will be some divergence from observed volatility---the future is not just like the past. We expect to see a range of VIX around historical volatility that is well-behaved.

In my statistical model, I use a multiple regression model to try to explain VIX as a weighted combination of realized volatility over various time scales. In my little analysis, I have found that VIX is quite well-explained by a weighted combination of 3-day, 5-day, 10-day, and 20-day volatility of the S&P500, using data back to March 1993. All of these terms are highly statistically significant, and the model has an R^2 of 79.7%.

*Regression model for VIX in terms of trailing volatility of the S&P500*

This model for VIX tracks the VIX very closely.

*Model for VIX using realized volatility vs. VIX over time*

The far-right side of this chart shows the spike in VIX that occurred at the start of February 2018, and it is also evident that much of this spike can be explained by increases in actual S&P500 volatility over the days before and through February 5^{th}. This simple linear model of VIX, in which the only predictors are the observed volatility of the S&P500, suggests that VIX largely mirrors what has happened in recent days in the S&P500.

Another way to look at these model results is to chart the VIX vs. the modeled value of VIX derived from trailing volatility of the S&P500 (the model) on an X-Y chart (below). This shows the extent to which a prediction by the model will map to a range of VIX outcomes.

*Model for VIX using realized volatility vs. VIX for every trading day from March 1993-February 12, 2018*

This chart shows, for example, that on a day in which the realized volatility would tend to predict a VIX of 25 (a value of 25 on the horizontal axis), the actual observed values of VIX tend to range from about 18 to 41. On March 5^{th}, the model for VIX using trailing realized volatility suggested that VIX should be 23.2. The actual closing price of VIX was 37.3. As the chart above shows, having a predicted VIX (using realized volatility) of 23 and an actual VIX of 37 is definitely an edge case, as compared to the ranges of historical values, but there is nothing to suggest that such an outcome is an outlier.

Another way to look at this model is to examine the difference between the predicted value of VIX generated by the model (see below). I am showing this in terms of the absolute value of the error so that we can see whether there is any trend in the magnitude of the error. If there is an increasing disconnect (higher error over time), this might support the argument that VIX is being gamed—unless of course one is willing to assume that VIX has been gamed since it was introduced in 1990. In other words, I am assuming that the notion of gaming the VIX would have emerged over time. There is no evidence of an increasing error in time in the chart below.

*Percentage error of VIX model over time*

So, what does all this mean? First, there is a consistent and robust relationship between VIX and trailing realized volatility of the S&P500 that explains about 80% of the variation in VIX. This relationship is robust over the last 2+ decades. VIX is a solid measure of volatility. People looking for a different measure of volatility might just as easily look at trailing volatility rather than near-term option implied volatility (e.g. VIX). To the extent that people are conditioning the past volatility based on their expectations—and expressing this through buying and selling options—VIX is of interest. None of this suggests that VIX cannot be gamed by clever traders who have figured out a hole in the way that the VIX index is officially calculated. VIX is a derived quantity and this makes VIX susceptible to being gamed. The solution, given the unknowns, is not to bet money on the VIX directly. There are plenty of other ways to go long or short volatility without trading the VIX and that should be the takeaway from this whole controversy. If you want to go long volatility or short volatility, the sensible alternative is to trade options on SPY directly.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.