How this calculator works
The minimum-variance hedge combines the correlation of price changes with their relative standard deviations. Use matching observation intervals and compatible price units. A positive ratio describes the size of a short futures offset against a long spot exposure; a negative correlation can imply a negative ratio. Contract counts require additional exposure and contract-size inputs.
Formula
h* = rho × sigma_spot/sigma_futures. Residual variance divided by unhedged variance = 1 - rho², when spot variance is positive.
Worked example
With spot deviation 2, futures deviation 4 and correlation 0.8, the ratio is 0.4 and modelled variance falls by 64%. Equal deviations with correlation -0.5 give a ratio of -0.5.
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Frequently asked questions
Can the ratio be negative?
Yes. Negative correlation reverses the hedge direction under this sign convention.
Can I mix price levels and returns?
Use a consistent definition for both series. A ratio based on dollar price changes differs from a ratio based on percentage returns.
What does optimal mean here?
It minimizes variance within this linear model. It does not optimize profit or account for margin, liquidity or transaction costs.