What this calculator does
Optimal hedge ratio works out share of a spot position to cover with futures to minimise portfolio variance. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulah* = ρ × (σ_spot / σ_futures)
The inputs explained
| Field | What to enter |
|---|---|
| Correlation, spot vs futures returns | A number. Starts at 0.83. |
| Std. deviation of spot price changes | A number. Starts at 0.05. |
| Std. deviation of futures price changes | A number. Starts at 0.072. |
| Spot position to hedge ($) | A number, measured in your currency. Starts at 1000000. |
| Value of one futures contract ($) | A number, measured in your currency. Starts at 50000. |
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 the answer changes with correlation, spot vs futures returns
Every other input is held at the calculator’s starting values while correlation, spot vs futures returns varies. Select any row to load that scenario into the calculator.
How the answer changes with correlation, spot vs futures returns