Variance Risk Premium

The VRP is mathematically defined as the difference between risk-neutral expected variance (implied by options) and physical expected variance (realized historically).

• Implied Variance: Extracted from the square of VIX or at-the-money option strips.
• Realized Variance: Calculated from the sum of squared high-frequency log returns.
• Excess Return: VRP = IV² - RV². A positive premium implies sellers of volatility are compensated over time.

This spread exists because dealers require compensation for absorbing asymmetric crash risk.

The VRP functions as a systemic risk premium. Investors pay a recurring premium (via overpriced options) to protect against sudden drawdowns.

• Supply Side: Market makers and volatility sellers provide liquidity but face gap risk.
• Demand Side: Asset managers buy downside puts to hedge tail risk, accepting negative carry.
• Equilibrium: The premium spikes during crises and decays during complacency.

This is structurally similar to how insurance premiums exceed expected actuarial losses.

The VRP is tightly coupled with the leverage effect—the negative correlation between asset returns and volatility.

• Mechanism: As stock prices fall, leverage ratios mechanically increase, raising equity risk and future realized volatility.
• Skew Impact: This asymmetry causes out-of-the-money puts to carry significantly higher implied volatility than calls.
• Volatility Feedback: The anticipation of this dynamic causes implied volatility to structurally overestimate realized volatility in normal regimes.

The premium is essentially the price of negative skewness.

A variance swap is the purest instrument for isolating the VRP. It pays the difference between realized variance and a pre-agreed strike.

• Replication: The fair strike is calculated via a static portfolio of out-of-the-money options weighted by the inverse of the strike squared.
• P&L Attribution: Profit = Notional × (Realized Vol² - Strike²).
• Convexity: Variance swaps offer linear exposure to variance, unlike VIX futures which have non-linear convexity.

This instrument allows direct harvesting of the premium without delta risk.

The VRP is not earned smoothly; it exhibits sharp negative skewness in its return distribution.

• Quiet Regimes: The premium is collected steadily as small positive daily returns (theta decay).
• Crisis Regimes: Massive negative jumps occur when realized volatility spikes above implied levels.
• Peso Problem: Backtests may overstate the Sharpe ratio if the sample excludes rare catastrophic events.

A short volatility strategy effectively sells tail risk to harvest this premium.

The VRP varies across the term structure of variance. Short-dated variance typically carries a higher premium per unit of time.

• Slope: The variance term structure is usually in contango (upward sloping) during calm markets.
• Roll Yield: Selling short-dated variance and rolling positions captures the steepest part of the curve.
• Inversion: During panics, the curve inverts (backwardation), and the premium becomes negative for front-month contracts.

This temporal dimension requires active management of roll-down strategies.

The purest instrument for isolating the variance risk premium. A forward contract on future realized variance where the buyer pays a fixed strike variance and receives the difference between realized variance and that strike at expiry.

• No delta exposure—pure volatility play
• P&L is linear in variance, not volatility
• Market convention quotes strikes in vega notional terms
• The spread between the swap strike and expected realized variance is the VRP in its most direct form

The contango shape of the VIX futures curve is the primary mechanism by which the variance risk premium is harvested systematically. When the curve slopes upward, rolling futures positions incurs a negative roll yield.

• Contango: Longer-dated futures trade above spot VIX
• Backwardation: Rare inverted state during panic events
• The VRP is embedded in the slope—the market consistently overprices future volatility relative to what materializes
• Short VIX futures strategies capture this structural premium but face severe gap risk during volatility events

The variance risk premium is the empirical observation that implied volatility systematically exceeds realized volatility over time. This spread exists because:

• Risk transfer demand: Equity holders pay a premium to offload downside tail risk to options sellers
• Crash-o-phobia: Investors overpay for disaster insurance following market trauma
• Leverage constraints: Dealers charge a premium for warehousing short-gamma exposure
• The spread widens during uncertainty and compresses during calm regimes

Systematic approaches that harvest the variance risk premium by structurally shorting volatility:

• Short straddles/strangles: Collect theta decay but carry unlimited tail risk
• Put underwriting: Selling out-of-the-money puts to capture the elevated skew premium
• Iron condors: Defined-risk premium collection bounded by wings
• Variance swap receiving: Directly receiving the fixed variance leg
• All strategies exhibit negative skew—steady small gains punctuated by rare large losses

The structural short-gamma position of options market makers creates a mechanical feedback loop that influences the variance risk premium:

• Dealers sell options to meet institutional demand for protection
• To hedge, they buy high and sell low in the underlying—amplifying realized volatility
• This hedging flow creates a volatility supply that dealers must be compensated for
• The VRP partially reflects this intermediation cost passed through to end-users
• Gamma positioning data (GEX) reveals where dealer hedging may accelerate or dampen moves

While related, these are distinct compensation streams:

• Variance Risk Premium: Compensation for bearing uncertainty about realized variance across the entire distribution—captured through variance swaps or delta-hedged options
• Tail Risk Premium: Specific compensation for bearing extreme left-tail events—captured through deep out-of-the-money puts
• The tail component is typically more expensive due to higher demand for crash protection and lower capacity from sellers
• The put skew in implied volatility surfaces reflects this additional tail premium embedded within the broader VRP