Calculate the minimum variance (optimal) hedge ratio, number of futures contracts, hedge effectiveness, and basis risk for commodity, FX, and financial hedging.
The hedge ratio determines how much of a spot position should be covered by an offsetting futures position to minimize portfolio risk. The minimum variance hedge ratio — ρ × (σ_spot / σ_futures) — is the gold standard in risk management for commodities, currencies, and financial instruments. The point is not to remove every price move, but to reduce the variance of the combined position as efficiently as possible.
A naive 1:1 hedge assumes perfect correlation and equal volatility, but real-world spot and futures prices rarely move in perfect lockstep. The optimal hedge ratio accounts for differences in volatility and the degree of correlation between the two instruments, giving you the precise number of futures contracts to minimize the overall portfolio variance. That is especially important for cross-hedges where the hedge instrument is only an approximation of the exposure you are trying to protect.
This calculator computes the optimal ratio, the number of contracts needed, hedge effectiveness (R²), variance reduction, and residual volatility. The scenario table shows how different correlation levels impact hedge performance, helping you plan for imperfect cross-hedges. It keeps the relationship between spot size, futures size, and hedge quality visible so the result can be reviewed before any trade is placed.
Use this calculator to estimate an optimal futures hedge size and see how much variance reduction you might realistically expect from the chosen contract. It is the practical way to translate a risk exposure into a contract count while accounting for imperfect correlation and different volatilities. That makes it useful for commodity producers, exporters, and portfolio managers who need a hedge size they can actually execute rather than a theoretical perfect match.
Optimal Hedge Ratio (h*) = ρ × (σ_spot / σ_futures) Number of Contracts = h* × Spot Qty / Contract Size Hedge Effectiveness = ρ² Variance Reduction = ρ² × 100% Basis = Futures Price − Spot Price
Result: Optimal HR = 0.8364, 17 contracts
With 92% correlation and spot/futures vol of 20%/22%, the optimal ratio is 0.836. For 100,000 units with 5,000-unit contracts, you need 17 futures contracts. Hedge effectiveness is 84.6%.
The minimum-variance hedge ratio is designed to reduce return variance, not to guarantee a perfect price lock. That distinction matters because many hedgers are dealing with basis risk, maturity mismatch, and correlations that drift over time.
A one-to-one hedge only makes sense when the spot and futures exposures move almost identically and with similar volatility. In many practical cross-hedges, the optimal ratio is lower or higher because the hedge instrument is only an approximation of the exposure being protected.
Historical volatility and correlation are estimates, not constants. Re-estimate the ratio periodically and remember that contract granularity means the implemented hedge will often be an approximation rather than the exact continuous optimum.
It's the hedge ratio that minimizes the variance of the combined spot + futures position. It equals correlation × (spot vol / futures vol), so both correlation and relative volatility matter.
A 1:1 hedge only works when correlation is 1 and volatilities are equal. In practice, optimal ratios are typically less than 1, meaning you hedge less than 100% of the spot position.
Basis risk is the risk that spot and futures prices don't converge as expected. It arises from imperfect correlation, maturity mismatch, or cross-hedging with a different commodity, so it is the reason hedges are never perfect.
Use historical return data — typically 30-90 days of daily returns. Calculate standard deviations and the Pearson correlation coefficient, then update the inputs when market behavior shifts.
Low correlation means the hedge is less effective. Below 0.7, consider whether the futures contract is appropriate for hedging your specific risk exposure before committing capital.
Yes — you must trade whole contracts. Rounding introduces a small deviation from the optimal ratio, which is unavoidable for discrete contract sizes, so the result should be treated as a practical implementation.