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The Variance Risk Premium (VIX vs Realized)
The Variance Risk Premium (VRP) is the gap between implied volatility (VIX) and subsequent realized volatility. It is a structural premium : option sellers have been paid for bearing the gap for decades : and it is also a forward-looking predictor of equity returns.
The hypothesis
VIX quotes implied volatility for the next 30 days. Markets systematically over-pay for optionality relative to what realizes. The gap : the Variance Risk Premium : is structural: sellers are paid for bearing it.
What the project does
- Loads VIX (CBOE) + a realized-vol estimator across 1990-2025.
- Compares implied to realized at the 30-day horizon.
- Regresses subsequent returns on the VRP with Newey-West HAC standard errors to handle the obvious autocorrelation.
The result
- 85% of 36 calendar years show implied > realized.
- The VRP is a positive forward predictor of equity returns.
- Newey-West t = +6.5 : survives heteroskedasticity-consistent inference.
What’s transferable
The pattern : model implied vs realized, regress forward returns, correct for autocorrelation : is the template for any carry signal. The Newey-West step is what makes the t-statistic interpretable; OLS t-stats in vol signals routinely overstate significance by 2-3×.