Optimal Hedge Ratio Calculator
Results are estimates based on the values you enter. Recheck your inputs and assumptions before using the output for decisions.
Calculate the minimum-variance optimal hedge ratio from correlation, spot volatility, futures volatility, and exposure value.
Optimal Hedge Ratio Calculator
Free online optimal hedge ratio calculator to estimate the minimum-variance hedge ratio from correlation, spot volatility, futures volatility, and exposure value. This calculator is useful for investors, treasury teams, commodity users, risk managers, finance students, importers, exporters, and anyone trying to reduce price risk with a futures hedge. Unlike a basic hedge ratio, the optimal hedge ratio uses volatility and correlation to estimate the hedge size that best reduces risk rather than simply matching exposure value one-for-one.
This calculator uses four key inputs. Correlation coefficient means the relationship between spot price changes and futures price changes. Spot volatility means the volatility of the asset or exposure being hedged. Futures volatility means the volatility of the futures contract used for hedging. Exposure value means the value of the position you want to hedge. Once those values are entered, the calculator shows optimal hedge ratio, optimal hedge value, hedge per $100 exposure, and residual risk share. These outputs help translate the statistical hedge formula into a practical hedge amount and a simple view of how much risk may still remain.
The formula of optimal hedge ratio
Optimal hedge ratio = Correlation coefficient x (Spot volatility / Futures volatility)
Optimal hedge value = Exposure value x Optimal hedge ratio
Optimal hedge per $100 exposure = Optimal hedge ratio x 100
Residual risk share = 1 – Correlation coefficient^2
Here correlation coefficient means the degree to which spot and futures price changes move together, spot volatility means the volatility of the underlying exposure, futures volatility means the volatility of the hedge instrument, optimal hedge ratio means the hedge size that minimizes variance under the simple minimum-variance model, optimal hedge value means the dollar size of the hedge implied by that ratio, and residual risk share means the portion of risk not explained by the correlation relationship.
Solved Example
Example 1: Find the optimal hedge ratio if correlation is 0.85, spot volatility is 12%, futures volatility is 10%, and exposure value is $500,000.
Solve: Optimal hedge ratio = 0.85 x (12 / 10) = 1.0200
Optimal hedge value = 500000 x 1.02 = $510,000
Optimal hedge per $100 exposure = $102.00
Residual risk share = 1 – 0.85^2 = 27.75%
Example 2: Find the result if correlation is 0.65, spot volatility is 8%, futures volatility is 10%, and exposure value is $250,000.
Solve: Optimal hedge ratio = 0.65 x (8 / 10) = 0.5200
Optimal hedge value = 250000 x 0.52 = $130,000
Optimal hedge per $100 exposure = $52.00
Residual risk share = 1 – 0.65^2 = 57.75%
Example 3: Find the result if correlation is 0.90, spot volatility is 15%, futures volatility is 12%, and exposure value is $1,000,000.
Solve: Optimal hedge ratio = 0.90 x (15 / 12) = 1.1250
Optimal hedge value = 1000000 x 1.125 = $1,125,000
Optimal hedge per $100 exposure = $112.50
Residual risk share = 1 – 0.90^2 = 19.00%
Table of optimal hedge ratio calculator
| Correlation | Spot Volatility | Futures Volatility | Optimal Hedge Ratio | Residual Risk Share |
|---|---|---|---|---|
| 0.65 | 8% | 10% | 0.5200 | 57.75% |
| 0.85 | 12% | 10% | 1.0200 | 27.75% |
| 0.90 | 15% | 12% | 1.1250 | 19.00% |
| 0.75 | 10% | 9% | 0.8333 | 43.75% |
How to use this optimal hedge ratio calculator
Enter the correlation coefficient in the proper input field. After that, enter the spot volatility, futures volatility, and exposure value. Then click the calculate button. The calculator will show optimal hedge ratio, optimal hedge value, hedge per $100 exposure, and residual risk share in the result box.
This calculator is useful when a basic hedge ratio is too simplistic for the risk problem. If spot and futures prices do not move together perfectly or if their volatilities differ, a one-to-one hedge may not minimize risk. The optimal hedge ratio helps adjust the hedge size so it better reflects the actual statistical relationship between the exposure and the hedge instrument. That makes it especially useful in commodity hedging, currency risk management, treasury work, and futures-based portfolio protection.
When using the result, remember that the formula depends on historical or estimated correlation and volatility inputs. If those inputs change, the optimal hedge ratio can change too. Real hedging results are also affected by basis risk, contract size, maturity mismatch, and transaction costs. Even so, this calculator gives a practical first-pass estimate of the hedge size that best reduces variance under the standard minimum-variance framework. It is useful for hedge planning, classroom learning, and risk-management review.