What this calculator does
Hedging with futures rarely means matching the exposure one for one. The futures contract does not move exactly with the asset being hedged, and the ratio that minimises variance accounts for both the correlation between them and their relative volatility.
Both factors pull in the same direction here. A correlation of 0.83 with futures more volatile than the spot gives a ratio of 0.576, so a $1,000,000 exposure is best hedged with about $576,389 of futures, not the full amount.
The formula
The ratio is the correlation between spot and futures returns multiplied by the ratio of their standard deviations. Applying it to the exposure gives the value to hedge, which divided by the contract size gives the number of contracts.
| Term | Meaning |
|---|---|
| Hedge ratio | The proportion of the exposure to cover with futures. |
| Basis risk | The residual risk left because futures and spot do not move identically. |
| Cross hedge | Hedging with a futures contract on a related but different asset, where the ratio matters most. |
The inputs explained
| Field | What to enter |
|---|---|
| Correlation, spot vs futures returns | Correlation between spot and futures price changes, between −1 and 1. |
| Std. deviation of spot price changes | Standard deviation of spot price changes. |
| Std. deviation of futures price changes | Standard deviation of futures price changes. |
| Spot position to hedge ($) | The value of the spot position being hedged. |
| Value of one futures contract ($) | The value of one futures contract. |
When to use it
Hedging a commodity exposure
Where no exact contract exists, a related one hedged at the optimal ratio is the usual approach.
Hedging an equity portfolio
Index futures hedge a portfolio imperfectly, and the ratio accounts for the mismatch.
Sizing a futures position
The contract count follows directly once the ratio and contract value are known.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does correlation change the hedge?
The same exposure at three correlation levels.
| Correlation | Optimal hedge ratio | Value to hedge with futures |
|---|---|---|
| 0.5 | 0.347 | $347,222.22 |
| 0.83 | 0.576 | $576,388.89 |
| 1 | 0.694 | $694,444.44 |
Questions
Why not hedge the full exposure?
Because a one-for-one hedge only minimises variance when the futures move identically to the spot. Where the futures are more volatile, hedging the full amount overshoots and introduces risk of its own.
What is basis risk?
The risk remaining after hedging, caused by futures and spot prices not moving together. It is what the correlation term captures, and it is why a hedge reduces rather than eliminates risk.
Can the ratio exceed 1?
Yes, when the spot is more volatile than the futures. In that case more than the full exposure in futures is needed to offset the same dollar movement.
How are the inputs estimated?
From historical price changes over a period matching the hedge horizon. The estimates are backward-looking, so the ratio should be reviewed as market relationships shift.
For pricing the futures contract, see the futures fair value calculator. For measuring the risk being hedged, see the maximum drawdown calculator.