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Minimum-Variance Hedge Ratio Calculator

Calculate the covariance-based hedge ratio from volatility and correlation.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Edit a calculated value to solve backwards, or lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

Multiply the spot-to-futures standard deviation ratio by their correlation. With spot deviation 2, futures deviation 4 and correlation 0.8, the modeled hedge ratio is 0.4.

Hedge ratio = correlation × spot-change standard deviation ÷ futures-change standard deviation

Worked example

Enter these known values and leave the other values blank.

Standard deviation of changes in spot price
2
Standard deviation of changes in future price
4
Correlation coefficient
0.8
Optimal hedge ratio
0.4

Assumptions and limitations

  • No. Contract sizing also depends on exposure size and contract units. This historical variance model assumes the volatility and correlation estimates are suitable for the hedge period; it does not guarantee future risk reduction.
  • Use consistent periods, currency and accounting definitions. The result follows the stated formula and the figures you supply.

Common questions

Does this specify how many contracts to trade?

No. Contract sizing also depends on exposure size and contract units. This historical variance model assumes the volatility and correlation estimates are suitable for the hedge period; it does not guarantee future risk reduction.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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