Tim Olson
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64 lines
4.3 KiB
Markdown
64 lines
4.3 KiB
Markdown
---
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description: "Volatility risk premium strategy sells S&P 500 ATM straddles when implied volatility (VIX) exceeds recent realized volatility, capturing the persistent premium that implied vol commands over realized vol in normal markets."
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tags: [volatility, risk-premium, straddle, vix, implied-volatility, realized-volatility]
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---
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# Volatility Risk Premium
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**Section**: 7.4 | **Asset Class**: Volatility | **Type**: Carry / Short Volatility
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## Overview
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Implied volatility is empirically higher than realized volatility most of the time — the volatility risk premium. This means options are, on average, overpriced relative to their Black-Scholes fair value based on realized volatility. The strategy sells options (ATM straddles on S&P 500) when the premium is positive, earning the excess implied vol over realized vol. It is profitable in sideways markets but loses money during sharp volatility spikes.
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## Construction / Mechanics
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**Volatility risk premium proxy signal**: at the start of each month, compare:
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- VIX (implied volatility of S&P 500, in %) at the beginning of the current month
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- Realized volatility of S&P 500 daily returns (in %) since the beginning of the current month
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If the spread (VIX - realized vol) is positive → **sell the ATM straddle** on S&P 500 options.
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**Position**: short 1 near-ATM straddle (1 short ATM call + 1 short ATM put) on S&P 500 index options, held for approximately 1 month.
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The straddle is ATM at inception, hence approximately Delta-neutral at entry. However, as the underlying moves, the straddle becomes Delta-nonzero.
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## Payoff / Return Profile
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- Earns the net option premium (implied vol minus realized vol differential) when the market moves less than implied by VIX.
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- Profitable in low-volatility, sideways markets.
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- Loses money when the S&P 500 moves sharply (volatility spike), which typically accompanies equity market selloffs.
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- The "short vega" position loses immediately when implied volatility rises, even before expiry.
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## Key Parameters / Signals
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- VIX at month start: measure of implied volatility
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- Realized vol of S&P 500 since month start: backward-looking volatility
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- Spread = VIX - realized vol: entry signal (sell when positive)
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- Strike selection: near-ATM (at-the-money) straddle
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- Holding period: approximately 1 month (to option expiry)
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## Variations
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### 7.4.1 Volatility Risk Premium with Gamma Hedging
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The ATM straddle is initially Delta-neutral but becomes Delta-nonzero as the S&P 500 moves. This variation adds Gamma hedging to maintain near-Delta-neutrality:
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- **Gamma (Γ = ∂²V/∂S²)**: measures the rate of change of Delta with the underlying price.
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- As the underlying moves up (down), the short straddle develops positive (negative) Delta.
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- **Gamma hedge**: buy (sell) the underlying S&P 500 to offset the Delta change; i.e., trade the underlying in the direction opposite to the move.
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Effect of Gamma hedging:
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- The strategy becomes a "Theta play": profits from Theta (Θ = ∂V/∂t) decay — the time value of the short options erodes daily.
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- The cost of Gamma hedging is the bid-ask spread and transaction costs of continuously rebalancing.
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- As the underlying moves further from the strike, Gamma hedging becomes more expensive (the underlying positions become larger) and can eventually exceed the collected option premium, at which point the strategy loses money.
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- This is also known as "Gamma scalping" (but from the short side — the hedger is short Gamma).
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**Option Greeks for reference**:
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- Θ = ∂V/∂t (Theta): time decay
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- Δ = ∂V/∂S (Delta): sensitivity to underlying price
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- Γ = ∂²V/∂S² (Gamma): sensitivity of Delta to underlying price
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- ν = ∂V/∂σ (Vega): sensitivity to implied volatility
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## Notes
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- Index options (S&P 500) are better suited than single-stock options for this strategy because index options typically have higher volatility risk premia (see Section 6.3 on dispersion trading).
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- A volatility spike (e.g., during a market selloff) causes both realized vol to rise and VIX to jump, producing large losses on both the Vega and Delta dimensions simultaneously.
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- The strategy is sometimes described as "selling tail risk" — the premium earned in normal times compensates for large, infrequent losses.
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- Gamma hedging reduces directional risk but cannot eliminate it for large moves; it also introduces transaction costs that reduce the effective premium earned.
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