Demystifying the Volatility Risk Premium
The persistent tendency for Implied Volatility (market fear) to exceed subsequent Realized Volatility (actual market movement).
Historical Magnitude
The average VRP spread over the S&P 500 has consistently averaged 4 to 5 annualized percentage points since 1990.
High Sharpe Ratio
Strategies capturing the VRP (like put-writing) often exhibit a Sharpe Ratio of 0.6 to 0.9, indicating superior risk-adjusted returns relative to the underlying market.
Skew & Correlation Risk
The losses are asymmetric and occur when stock prices drop rapidly and correlations spike—the worst possible time for long-equity investors.
Deep Theory & Drivers
In classical finance, VRP is not a "free lunch" but fair compensation for bearing undiversifiable risk. This compensation is necessary because short-volatility strategies expose the seller to specific, unhedgeable risks.
- Jump Risk: Markets don't just move smoothly; they gap down due to unexpected news. Option sellers must be compensated for the risk of overnight gaps where delta-hedging is impossible.
- Correlation Risk: In crises, correlations go to 1. Diversification fails exactly when you need it most. Selling index volatility is implicitly shorting this correlation spike, a costly risk.
- Vega Convexity: As volatility rises, option prices rise non-linearly. Sellers are "short convexity," meaning their losses accelerate as market turmoil increases.
Math & Models
1. The Practitioner's Spread (Ex-Post)
The simplest method compares the VIX on a given day (IVt) against the subsequent realized volatility over the option's life.
Detailed Realized Volatility (RV) Calculation
RVt, t+N is the annualized standard deviation of daily log returns (ri) of the underlying index over the next N trading days.
Where 252 is the approximate number of trading days per year.
2. The Academic Variance Risk Premium (VRPₚ)
Academics use Variance over Volatility because Variance Swaps can be perfectly replicated statically (model-free), leading to the "purest" measure of the premium.
Strategies & Risks
Comparison of Harvesting Methods
Different ways to structure the trade to capture the VRP.
| Strategy | Yield Potential | Primary Risks |
|---|---|---|
| Short Put (ATM) | High | High (Equity Beta ~0.6) |
| Short Straddle | Very High | Extreme (Gamma Risk) |
| Iron Condor | Medium | Defined (Capped) |
| Variance Swaps | Purest | Convex (Vega^2) |
Deep Dive: Systematic Put-Writing
This strategy is highly correlated with VRP capture. It involves selling out-of-the-money (OTM) index puts, typically 10-20% below the current market price, and holding collateral equivalent to the potential maximum loss.
Key Exposure (Greeks)
- Short Vega: Profits when volatility falls (the definition of VRP).
- Short Gamma: The position becomes more negative delta as the market falls, forcing you to sell low (the source of negative skew).
- Long Theta: Time decay (theta) works in your favor as you collect daily premium.
Performance & Risk Profile
Historically, the Cboe PutWrite Index (PUT) has produced equity-like returns with only 50-70% of the market's beta, but its drawdowns are concentrated during sharp, downward market moves.
Case Study: "Volmageddon" (Feb 2018)
The day the short VRP trade via VIX ETPs blew up. A powerful example of negative gamma risk.
On Feb 5, 2018, the S&P 500 dropped ~4%. This triggered massive end-of-day rebalancing by leveraged VIX exchange-traded products (ETPs) that were structurally short volatility (e.g., XIV).
These ETPs were forced to buy VIX futures in a liquidity panic. This drove the VIX index from ~16 to ~34 in minutes after market close.
The outcome: The XIV fund lost ~96% of its value in one hour and was liquidated. This event demonstrated the crucial difference between the theoretical VRP edge and the immense structural risk of leveraged short-vol products.
VIX Spike - Feb 2018 (Conceptual)
Simulated representation of the VIX surge.
Literature Review
Carr & Wu (2009)
The definitive paper establishing standard methods for measuring VRP using synthetic variance swaps. Found VRP is strongly negative (investors pay to hedge variance) and surprisingly predicts future equity returns.
Bollerslev, Tauchen, Zhou (2009)
Key Finding: Linked VRP to macroeconomic uncertainty. Showed that a high VRP spread is one of the best short-term predictors of higher aggregate stock market returns (compensation for the heightened risk).
Are VRPs Always Positive?
The short answer is No, but overwhelmingly Yes over long periods.
- Positive VRP: This is the most common state (85-90% of the time) where Implied Volatility > Realized Volatility. This is the premium option sellers collect.
- Negative VRP: Occurs during major market panics or crashes (e.g., 2008, March 2020). IV spikes, but RV during the subsequent period can exceed that spike. This is when option sellers suffer large losses.
- VRP Timing: High VRP (wide spread) often signals low market complacency and often precedes a period of low realized volatility, making it a potentially attractive time to sell.