Implied Volatility vs. Next Year's S&P Return

You can download the VIX index, daily, from 1986. I took all these datapoints, and grouped them into deciles. I then looked at the average 12 month ahead returns within those deciles. The results are in the graph above, and show that there is no clear relationship between volatility and future index returns, at least over the past 20 years.

It's standard in theory to assume that higher anticipated systematic volatility increases the expected return. Many researchers have documented this is not so (eg, Glosten, Nelson), but Christian Lundblad took the innovative approach of going back to 1836 and showing that under certain assumptions, you could not reject the hypothesis that return is positively related to volatility. Clearly, he tortured the data into talking. If the effect is this subtle, it is meaningless for driving behavior. I reminds William Sharpe's interview, where he notes that they were incredibly naive to think returns would be the same as expected returns, as if the failure of beta is due to a small sample variation in the CRSP data--an anomalous 80 year draw.