Optimal Hedge Ratio Calculator

Your details

Standard deviation of percentage changes in the spot price, annualised. Enter as a percentage (e.g. 25 for 25%).
%
Standard deviation of percentage changes in the futures price, annualised. Enter as a percentage (e.g. 20 for 20%).
%
Pearson correlation between spot and futures price changes. Range -1 to 1. A value near 1 means the two prices move closely together.
Total value of the position you want to hedge, in USD.
USD
Notional value of one futures contract, in USD. For example, one S&P 500 E-mini futures contract is approximately 50 x index level.
USD
Optimal hedge ratio (h*)Over-hedge
1.0625

The proportion of futures to spot position that minimises variance.

Exact contracts (N*)21.25
Rounded contracts21
Hedging effectiveness (R2)0.7%
Dollar amount hedged1,050,000USD
Hedge coverage1.1%
1.0625 h*
Negative hedge<0Under-hedge0-0.5Partial hedge0.5-0.98Perfect hedge0.98-1.02Over-hedge1.02+
Variance eliminated (R2)0.7%
Hedge coverage1.1%

Optimal hedge ratio is 1.0625 (72.2% of variance eliminated).

  • h* is 1.0625, greater than 1. You need more futures exposure than the spot position - spot volatility is higher than futures volatility relative to their correlation.
  • Hedging effectiveness (R2) is 72.2%. This hedge eliminates 72.2% of variance, leaving 27.8% as basis risk that cannot be removed by this instrument.
  • Use 21 short futures contracts to implement the hedge, covering 105.0% of the total exposure.
  • Moderate-to-high correlation means the hedge will reduce most systematic risk, but significant basis risk remains.

Next stepReview the model assumptions: this minimum-variance model assumes constant volatilities and correlation, no transaction costs, and a static hedge ratio. Rebalance periodically as market conditions change.

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