VIX® closed last night at 11.33. What, if anything, does that mean?

We recently published a research paper, together with a more digestible practitioner’s guide, that provides a method for converting a given VIX level into an expectation for S&P 500® volatility over the next 30 days. Exhibit 1 shows that these estimates have provided a reasonable, *but imperfect*, guide for what was observed.

**Exhibit 1: VIX-based Prediction Versus Actual Change in S&P 500 Volatility**

Source: “A Practitioner’s Guide to Reading VIX”. Past performance is no guarantee of future results. Chart is provided for illustrative purposes.

The first ingredient in the expected VIX is the present (or recent) volatility environment; **expectations for the future are necessarily grounded in the recent past**. Over the past month, S&P 500 volatility ran at an annualized 6.58%. The next key step is to account for the fact that **we expect volatility to mean revert. **The long-term average volatility for the S&P 500 is around 15%, and history shows that in a given month volatility tends to move about 30% of the distance between its current level and that long-term average. All else equal, this would lead to a realized volatility on January 4, 2018 of 9.10%. This mean-reverted level is called “MR volatility” in our paper.

The second ingredient is a relationship between MR volatility and the expected VIX; this essentially accounts for the fact that **VIX typically reflects a premium** that purchasers of options pay for their insurance-like characteristics. This relationship, for the S&P 500, looks like:

Substituting MR volatility = 9.10 gives expected VIX = 12.56. **Last night’s closing VIX level of 11.33 is 1.23 percentage points lower than the expected VIX. **But what does this mean? One explanation is that when VIX is less than expected VIX, market participants are more relaxed than usual about the anticipated impact of upcoming news flow on the S&P 500. However, **a slight subtlety is required before we can say that the market is predicting a decline in realized volatility.**

When VIX is different from expected, this indicates an anticipated change in realized volatility that is *different from usual*. But **mean reversion in realized volatility is usual. ** (In the current example, mean reversion is expected to cause a rise in realized volatility from 6.58% to 9.10 %). **Adding the difference between VIX and expected VIX to the MR volatility level gives the resulting “prediction”**; realized volatility is expected to rise from 6.58% to 7.87% over the next 30 days (9.10% MR volatility minus 1.23%) – a gain that is less than would be anticipated under mean reversion alone.

Of course, the observed change in realized volatility is extremely unlikely to be *exactly* 1.29%; Exhibit 1 demonstrates that it might be lower, and it could be much higher. Nevertheless, and although it is imperfect, **our approach allows for a “reading” of VIX that accounts for its major relationships, and offers a practical interpretation of what VIX is telling us. **