Calculate the optimal hedge ratio that minimises variance in a hedged portfolio using the minimum-variance method.
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Risk Management
The optimal hedge ratio minimises the variance of a hedged portfolio by determining the ideal proportion of a spot position to offset with futures contracts, based on the correlation and relative volatility of spot and futures prices.
A hedge ratio of 1.0 means hedging the full position dollar-for-dollar. But if spot and futures prices do not move in perfect lockstep, a 1:1 hedge is suboptimal. The minimum-variance hedge ratio adjusts for the actual correlation and relative volatility.
Hedge effectiveness (R²) tells you what proportion of the spot position’s variance is eliminated by the optimal hedge.
Derived from regression of spot price changes on futures price changes.
h* = ρ × (σ_s / σ_f)
ρ = correlation between spot and futures price changes, σ_s = std dev of spot price changes, σ_f = std dev of futures price changes.
Spot std dev 0.025, futures std dev 0.030, correlation 0.85. h* = 0.85 × (0.025 / 0.030) = 0.708. Hedge effectiveness = 0.85² = 72.25%.
Assumes linear relationship between spot and futures. Based on historical data which may not persist. Does not account for basis risk changes, margin costs, or contract size constraints.
Frequently asked questions
You should hedge less than 100% of your spot position. This occurs when futures are more volatile than the spot asset, or when correlation is imperfect — over-hedging would actually increase portfolio variance.
R² (correlation squared) measures the proportion of spot price variance eliminated by the optimal hedge. An R² of 72% means the hedge removes about three-quarters of the price risk.
Calculate from historical daily or weekly price changes over a representative period (6–24 months). Use log returns for better statistical properties. Ensure the sample period reflects current market conditions.
Yes — cross-hedging (hedging with a related but different contract) is exactly where the optimal ratio matters most, because correlation will be less than 1.0 and volatilities will differ.
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