S&P Dow Jones Indices has put out a paper offering market participants without patience for “academic rigor” an accessible guide to the so-called “Fear Index,” the VIX, calculated from the prices of a specific basket of S&P options.
The contributors to the paper are: Tim Edwards, S&P Global senior director, Index Investment Strategy, and Hamish Preston, Senior associate at IIS. They say that VIX is in essence “a crowd-sourced estimate for the degree to which the market is uncertain about the future.” So if the market participants are rational, VIX will have some predictive value, predicting not the direction of prices but the amount of movement.
Take any level below 12 to be “low” and any level above 20 to be “high.” Call the territory in between “normal.” Edwards and Preston ask: has the level of VIX so understood had any predictive value regarding future volatility? One finds that the index accurately predicts what the volatility of the S&P 500 will be in the next 30 day period. A high VIX predicts high prices changes and vice versa.
But VIX levels won’t correspond directly to the volatility observed 30 days later. A VIX level of 25% does not mean that markets anticipate 25% volatility. Given the hedging value of VIX, there is typically an excess demand for the options involved (excess from the point-of-view of a pure anticipation hypothesis) and this results in a premium. VIX today slightly overstates the level of volatility that will be experienced in the month to come.
Edwards and Preston illustrate the “historical extent to which VIX has overestimated subsequent volatility” using a 252 day trading day trailing average of VIX, superimposed on the trailing average of the S&P 500 volatility over the next 30 days from 1990 through 2016. The only time when the two lines exactly corresponded was in the big run-up of volatility in 2007-08. Until then, and again after that, they had diverged. The average distance between the two lines, the overestimation, is between 4 and 5%.
Edwards and Preston offer a simply equation for expected VIX:
Expected VIX = Recent Volatility + Mean Reversion Adjustment + Volatility Premium.
They call this approach VCR, for “VIX implied Change in Realized volatility.” (Hands up if you remember when those initials had something to do with television programs.)
A Three-Year Back Test
Looking back at a three year period beginning January 2, 2014, these authors chart the Estimated Change in volatility – that is, the change that would have been estimated at each point by someone using the above arithmetic. Then they superimpose the observed changes in S&P volatility over the same period. The result is an “encouraging similarity between the two series – suggesting that market participants might have been well served by using our simple approach to interpreting VIX.”
Edwards and Preston further observe that since the CBOE first began publishing VIX levels in 1990, several institutions, including S&P and the CBOE themselves, have “applied the same VIX methodology to a wide range of equity, fixed income, and currency markets.” They apply the VCR approach to all of those as “out of sample tests for our approach.” They find encouragingly similar results.
The Scholarly Account
In a more detailed account, aimed at scholars in the field of financial economics, the same authors quote Rene Descartes, who said that his method was to “divide each difficulty into as many parts as feasible and necessary to resolve it.” Edwards and Preston believe there are in principle four parts here, only three of which are explicit in the above formula:
- The recent volatility environment;
- An anticipated (positive or negative) change in recent volatility predicted on the assu8mptyion that volatility reverts toward a long-term mean;
- An always positive volatility premium that varies in a predictable but not-quite linear fashion with recent volatility, and;
- A positive or negative component these authors call “difference to model,” adjusting for expectation regarding market-moving events.
The fourth or DTM element accounts for the fact that volatility can get things wrong, as happened around the 2016 election.
In general, though, the VCR “performs reasonably well at approximating monthly movements in realized volatility across a range of VIX indices.”