**Background**

The events of the past month, most notably the implosion of XIV, has focused public interest on volatility as an asset class. They’ve also illustrated that short vol as a strategy might be a little more risky than advertised (gasp!).

The VIX is supposed to serve as a gauge of how much uncertainty exists in the market. For the long-form, math-heavy definition of this, the CBOE lays it out here. The short version is that the VIX is the market’s prediction of annualized volatility in the S&P 500 for the next 30 (calendar) days, implied from SPX option prices.

However, all uncertainty is not created equally. Investors tend not to fret about whether their holdings will increase by 10% or 12% in the coming year. The stock market has a tendency to “take the escalator up , and the elevator down”, falling more rapidly than it rises. For this reason, VIX and SPY daily returns are strongly negatively correlated, as seen in the correlation matrix below. A (far too simple) explanation for this goes like: prices drop, investors get uneasy, they buy options as insurance, thereby driving up their prices and increasing the VIX.

**Implied Vol vs Realized Vol**

So we know that the VIX is supposed to forecast volatility. But how does what’s implied match reality? To answer this, I calculated the rolling 21-day annualized volatility for SPY using daily adjusted closing price returns. Using all data since the ETF’s inception, I compared the volatility implied by the VIX to the actual forward 21-day volatility. Also included is the historical volatility from the previous 21 days.

From the table/figure below, we can see that these three values are highly correlated with one another. This is largely to be expected. One interesting note, however is that the VIX is more highly correlated with future volatility than historical vol. This seems to indicate that although prior volatility can be used by itself as a decent predictor or forward volatility, there may be additional information contained in the volatility index.

The strongest correlation of the three values is between the VIX (implied volatility) and the historical volatility. With no additional information, just using the past 21 days’ volatility is probably a pretty good guess for the next 21 days. In fact, if we fit a linear regression model to these two variables, we find that historical volatility explains nearly 80% of the variance in implied volatility.

**Excess Volatility**

The most interesting information offered by the VIX then, is most likely contained in what is not explained by historical vol. To try and extract this information, we’ll look at the residuals of the model. We do so by subtracting the value predicted by the linear model from the true value. We’ll also scale the values to the range [-1, 1] to simplify things.

We’ll call this Excess VIX; that is, the amount of volatility predicted by VIX in excess of what would be predicted by the historical volatility of SPY. To see what impact the level of Excess VIX has on forward SPY returns, we’ll bucket Excess VIX into deciles, and examine the mean return by level. The returns used are percent changes in price from the market open after the signal to the following open.

Even though the returns don’t increase monotonically with Excess VIX, we can see a slight trend. It appears that returns were most positive when Excess VIX was highest. The takeaway here would be that when implied volatility is much higher than would be expected given the current level of historical volatility, there may be a good buying opportunity. To illustrate this, we’ll compare some summary statistics about the S&P over time as compared to during periods of high excess volatility.

As compared the broad history of the S&P, returns during periods of high excess volatility have a higher expected value, higher win rate, and higher avg win/ avg loss ratio. This comes at the expense of having significantly (nearly 2x) more volatile returns. I’ll refrain from showing an equity curve, since this couldn’t be traded directly as a strategy. Since we can only determine a threshold with percentiles by using all of the data, it would introduce data-snooping bias into the analysis. However, it may serve as a solid foundation for further strategy development.

**Conclusions**

Even though the VIX functions to predict future volatility, we’ve shown that the majority of its signal is derived from volatility in the past. If we remove the influence that this past volatility has, there may be useful signal left over. This “excess volatility” incorporates the rest of the analysis that traders are using to value options, and may signal when volatility could rise or fall. We’ve examined one use of this signal, but there are likely many more! Leave a comment below if you found this interesting.

It should go without saying that nothing in this article represents either financial advice or an offer to buy/sell securities.

Jupyter notebook with source code here