When futures don’t move exactly with the asset you own (basis risk), hedging one-for-one is not optimal. The minimum-variance hedge ratio uses the correlation and relative volatility to minimise the variance of the hedged position.
How to use the Optimal Hedge Ratio Calculator
- Standard deviation of spot price changes
- Standard deviation of futures price changes
- Correlation coefficient
- Position size (units)
- Contract size (units)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the standard deviations of spot and futures price changes, their correlation, your position size and the contract size.
Tips
- Use the nominal annual rate and pick the compounding frequency your bank or broker states.
- Small differences in return or fees compound into large differences over decades.
- Run the calculation with a cautious, a central and an optimistic return to see the range of outcomes.
- Past returns do not guarantee future returns – nothing here is investment advice.
Common mistakes to avoid
- Comparing an APR with an APY or effective rate.
- Ignoring inflation, taxes and fees when judging a real return.
- Entering a percentage as a decimal (5 instead of 0.05 is correct here).
Inputs explained
| Field | What to enter |
|---|---|
| Standard deviation of spot price changes | In % |
| Standard deviation of futures price changes | In % |
| Correlation coefficient | A number |
| Position size (units) | A number |
| Contract size (units) | A number |
What each result means
- Optimal hedge ratio = [Correlation coefficient]×[Standard deviation of spot price changes]÷[Standard deviation of futures price changes]
- Futures contracts needed = [Optimal hedge ratio]×[Position size (units)]÷[Contract size (units)]
- Hedge effectiveness (variance reduction) = [Correlation coefficient]^2×100
Example values
How the main result changes when Standard deviation of spot price changes changes and everything else stays at the example values above:
| Standard deviation of spot price changes (%) | Optimal hedge ratio |
|---|---|
| 1.2 | 0.3943 |
| 1.8 | 0.5914 |
| 2.4 | 0.7886 |
| 3 | 0.9857 |
| 3.6 | 1.1829 |
| 4.8 | 1.5771 |
Formula
h* = ρ × σ_spot ÷ σ_futuresContracts = h* × position size ÷ contract sizeHedge effectiveness = ρ²Worked example
Inputs — Standard deviation of spot price changes: 2.4 %; Standard deviation of futures price changes: 2.8 %; Correlation coefficient: 0.92; Position size (units): 1,000,000; Contract size (units): 42,000.
Results — Optimal hedge ratio = 0.7886; Futures contracts needed = 18.8; Hedge effectiveness (variance reduction) = 84.64 %.
Frequently asked questions
What is the optimal hedge ratio?
The ratio that minimises the variance of the hedged position.
How many contracts do I need?
Optimal ratio × position size ÷ contract size, rounded.
What is hedge effectiveness?
The share of variance removed: the correlation squared.
What formula does the Optimal Hedge Ratio Calculator use?
h* = ρ × σ_spot ÷ σ_futures.