Can the Spread of the VIX Over a GARCH Model Predict Hedge Fund Returns

In the post VIX vs GARCH: Results from a New Region of Phase Space I exhibited a chart of the longitudenal relationship between the VIX index of volatility and a simple GARCH(1,1) model of the volatility of the S&P 500 index. I pointed out that, for most of the history, the VIX traded at a premium to the GARCH predicted volatility; however, during the current financial crisis this relationship had reversed.

It can be asserted that all dynamic trading strategies can be replicated by some kind of option (in much the same way that options are replicated by dynamic hedging strategies) and thus the profits accruing to traders can be mapped into the risk premium income they receive by writing "their" particular kind of options (this comment was made to me by Pete Kyle).

One could then suggest that the general price of financial risk might be related in some way to the spread between the VIX, which is the market price of market risk, and a forecast of the actual level of market risk, which we can approximate with a simple GARCH model. (Actually I would look at the spread between the squares of these quantities since "standard deviation" is a slightly artificial number from a statistical point of view -- variance is the real process that occurs.)

With this in mind I looked at the relationship between the
Barclay Trading Group's index of hedge fund returns and the lagged spread between the square of the VIX and the GARCH variance process (the Barclay data is monthly, so I looked at the variance spread on the final date of the prior month). If the assertion and inference is correct, then there should be positive correlation between these quantities.

A simple linear regression between these quantities is presented here (the notation {1} means "first lag" in the regression program I'm using). The regression indicates that this correlation exists is significant at the 3% level; although, from a physicist's point of view should be regarded on the weaker side.