Ernie Chan recently proposed using Variance Risk Premium as a factor for future price change prediction. VRP is defined as implied volatility minus historical volatility. I've decided to check if this factor works.
There are various methods to calculate historical volatility, I tried some of them and found out that best is using average logarithm of daily range, including morning gaps. Standard deviation of daily changes works too, but, as usual, shows worst results.
Data used: SPY all available daily data from Yahoo.Finance
Correlation between VRP and future normalized daily price change: +0.051
Factor successfully pass the cross-validation of the model, which is not the usual case.
Cross-validated equity of a stategy, using only the VRP factor:
Yearly Sharpe 0.80 against 0.64 for factor-free strategy (which uses only volatility normalization).
No costs included.
Conclusion: VRP definitely works for S&P 500, correlation with future price change is positive, which means that when VIX is higher than local historical volatility, the price tends to grow. VIX tends to oscillate around local historical volatility and you can profit from it.