risk
Beta-Weighted Delta
Normalizes all positions to SPY-equivalent delta. Allows comparing apples-to-apples exposure across stocks with different volatilities.
Formula
BWΔ = Position Δ × (Stock Price / SPY Price) × Beta
Variables
- BWΔ
- Beta-weighted delta (SPY-equivalent shares)
- Position Δ
- Raw delta of the position (shares)
- Stock Price
- Current price of the underlying
- SPY Price
- Current SPY price
- Beta
- Stock's beta relative to SPY
Worked Example
Inputs
- NVDA
- +100 shares @ $800, β=1.8
- JNJ
- +200 shares @ $150, β=0.6
- SPY
- $500
Calculation Steps
- 1
NVDA BWΔ = 100 × (800/500) × 1.8 = +288 SPY-equiv - 2
JNJ BWΔ = 200 × (150/500) × 0.6 = +36 SPY-equiv - 3
Total BWΔ = 288 + 36 = +324 SPY shares equiv
Result: Beta-weighted Δ = +324 SPY shares — portfolio moves like owning 324 SPY shares
Intuition
Without beta-weighting, 100 shares of NVDA ($800, β=1.8) looks similar to 100 shares of JNJ ($150, β=0.6). But in SPY terms, NVDA is 8× more exposure. Always beta-weight to understand your true market risk.