Optimal Hedge Ratio Calculator
Find the futures hedge ratio that minimises the variance of a hedged portfolio: enter the correlation between spot and futures price changes and their standard deviations, plus optional portfolio size, to get h*, hedge effectiveness (R²), and the number of contracts to trade.
fraction
fraction
h* = ρ × (σ_S / σ_F) — futures units needed per unit of spot exposure
- 1
Volatility ratio (σ_S ÷ σ_F)
0.12 ÷ 0.1 = 1.2 - 2
Hedge effectiveness R²
0.85 × 0.85 × 100 = 72.25 %Fraction of spot-price variance eliminated by the optimal hedge. - 3
Optimal hedge ratio h*
ρ × (σ_S ÷ σ_F) = 0.85 × 1.2 = 1.0200
How does this calculator work?
Optimal hedge ratio h* = ρ × (σ_S / σ_F) minimises hedged-portfolio variance. Contracts needed = h* × Portfolio Value / Contract Value. Hedge effectiveness = ρ², the fraction of spot variance eliminated. Estimate ρ and σ values by regressing historical spot-price changes on futures-price changes.
Formula
How this is calculated
The optimal (minimum-variance) hedge ratio h* is the number of futures units required per unit of spot exposure to minimise the variance of the combined position. It is derived by differentiating the variance of the hedged portfolio with respect to the hedge size and setting it to zero, yielding h* = ρ × (σ_S / σ_F), where ρ is the correlation between changes in the spot price and changes in the futures price, σ_S is the standard deviation of spot price changes, and σ_F is the standard deviation of futures price changes. Both standard deviations should be measured over the same time interval as the hedging horizon.
The quality of the hedge is captured by R² = ρ², which gives the fraction of spot-price variance eliminated by the optimal futures position — if ρ = 0.9, R² = 81% of spot risk is hedged. The residual risk (basis risk) comes from imperfect correlation, which arises whenever the spot commodity and the futures contract are not identical (cross-hedging).
The number of futures contracts is N = h* × (Portfolio Value / Contract Value), where contract value equals the futures price multiplied by the contract size. N should normally be rounded to the nearest integer in practice. All inputs are estimates derived from historical regressions and may not reflect future correlation; standard deviations, correlations, and contract specifications should be verified against current market data.
Frequently asked questions
Run an ordinary least squares (OLS) regression of changes in the spot price (ΔS) on changes in the futures price (ΔF) over a historical window matched to your hedging horizon. The slope gives h* directly; the correlation ρ = Cov(ΔS, ΔF) / (σ_S × σ_F). A 3–5 year daily history is typical, but regime changes can make historical estimates unreliable.
Basis = Spot price − Futures price. Basis risk arises when the spot exposure and the futures contract are not perfectly correlated (ρ < 1). Even with the optimal hedge ratio, the hedged position retains variance proportional to (1 − ρ²). Cross-hedging — where the futures contract and the asset being hedged are different — typically results in higher basis risk.
Match the measurement period to your hedge horizon. For a 1-month hedge, estimate σ from monthly price changes; for a 3-month hedge, use quarterly changes. Daily standard deviations can be scaled by √T (e.g. √22 for a monthly horizon) if daily data is more plentiful, but this assumes i.i.d. returns which is only an approximation.
Also known as
TG we-Calculate Editorial Team. (2026). Optimal Hedge Ratio Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/optimal-hedge-ratio-calculator
TG we-Calculate Editorial Team. "Optimal Hedge Ratio Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/optimal-hedge-ratio-calculator.
TG we-Calculate Editorial Team, "Optimal Hedge Ratio Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/optimal-hedge-ratio-calculator
@misc{wecalculate_optimal_hedge_ratio_calculator, title = {Optimal Hedge Ratio Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/optimal-hedge-ratio-calculator}}, year = {2026}, note = {TG we-Calculate} }
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