Low VIX ?

A common theme that has been much discussed is the persistent decline in the commonly referred to fear gauge in the market the VIX and whether it is too low and artificially manipulated given its relentless decline from the peak level of over 80 during the height of the crunch in 2008 to a current level of about 25. To recap, VIX is a measure of the implied volatility for a constant 30-day to maturity option chain based on the S&P500. If we accept that volatility is a mean reverting process, then the VIX level should be related to the realized volatility of the SPX plus some value of risk premium. As a fear gauge, the premium should also intuitively be higher in times of market stress. To test out this hypothesis, we shall take a look at a simple regression between the VIX premium (VIX - 1m realized SPX vol) vs. the 1m SPX realized vol and the weekly % change of the SPX level since 1990 with the following results:

The regression on these 2 variables alone explains 63% of the variation in the VIX premium, and both are statistically significant. The signs of the coefficients also corresponds to intuition. A higher level of realized volatility shrinks the premium (vol mean reverts), as does a positive return on the SPX. Applied to the current realized volatility of 21.3% and -0.1% SPX return (as of close 7/29) gives us a predicted VIX of 24.6% compared to the current spot reading of about 25%. Therefore, it looks like the VIX is fairly priced and not artificially depressed.