How the Optimal Hedge Ratio Calculator works
When you hedge a spot position with a futures contract, a one-to-one hedge is rarely the position that minimizes risk. The spot and futures prices do not move in perfect lockstep — they are correlated but not identical — so the hedge that minimizes the variance of the combined position is usually something other than a 1:1 ratio. This calculator applies the standard minimum-variance hedge ratio from futures hedging theory to tell you how large that hedge should be, in both ratio and contract-count terms.
The formula
The optimal (minimum-variance) hedge ratio is:
h* = ρ × (σS / σF)
where ρ is the correlation coefficient between changes in the spot price and changes in the futures price, σS is the standard deviation of spot price changes over the hedging horizon, and σF is the standard deviation of futures price changes over the same horizon. This is the same value you would get as the slope coefficient from an ordinary least-squares regression of spot price changes on futures price changes — h* is the slope that best explains spot moves using futures moves.
To turn the ratio into a tradable position, multiply by the ratio of the exposure size to the contract size:
N* = h* × (QA / QF)
where QA is the size of the position being hedged and QF is the size of one futures contract, both in the same units. Since futures trade in whole contracts, N* is rounded to the nearest integer before execution.
Worked example
A jet-fuel buyer wants to hedge 2,000,000 gallons of exposure using heating oil futures, which trade in contracts of 42,000 gallons. Historical monthly price changes show a correlation of ρ = 0.928, with a standard deviation of σS = 0.0263 for spot jet fuel and σF = 0.0313 for the futures. The hedge ratio is h* = 0.928 × (0.0263 / 0.0313) ≈ 0.7798. The contract count is N* = 0.7798 × (2,000,000 / 42,000) ≈ 37.1, rounded to 37 contracts. That hedge is expected to remove about ρ² ≈ 86.1% of the price variance, leaving roughly 13.9% as residual basis risk.
Hedge effectiveness and basis risk
The proportion of variance the optimal hedge removes equals ρ² (the R² of the regression). A correlation of 0.928 gives R² ≈ 0.861, meaning the hedge eliminates about 86% of the variance in the value of the unhedged position — the remaining variance is basis risk, the risk that spot and futures prices do not move together exactly as history suggests. The lower the correlation, the less effective any hedge ratio can be, and the more residual risk remains regardless of position size.
Assumptions and limits
- The formula assumes ρ, σS, and σF are stable and estimated from a representative sample of historical price changes over a horizon similar to your hedge period.
- It minimizes variance, not expected cost — it does not account for margin requirements, transaction costs, or the possibility that futures and spot prices diverge structurally (e.g., quality or location mismatches) beyond what the correlation already captures.
- Rounding N* to a whole number of contracts means the realized hedge ratio will differ slightly from h* — the "Hedged exposure" result shows the gap.
- This is a computational tool only. It is not investment, trading, or risk-management advice; futures hedging carries margin and liquidity risk that a hedge ratio alone does not capture.