Calculator inputs
Use the form below. Results appear above this form after calculation.
Example data table
These examples show how different methods can change the recommended hedge size.
| Scenario | Method | Exposure ($) | Key assumptions | Estimated ratio | Approx. contracts* |
|---|---|---|---|---|---|
| Equity portfolio | Beta-adjusted | 1,000,000 | Beta 1.10, target 100%, price 4,300, multiplier 50 | 1.1000 | 5 |
| Commodity hedge | Minimum variance | 500,000 | ρ 0.80, spot vol 20%, futures vol 16% | 1.0000 | 2 |
| Partial protection | Direct | 750,000 | Target hedge 60%, price 200, multiplier 1,000 | 0.6000 | 2 |
*Contracts are rounded for execution and depend on actual contract notional.
Formula used
1) Direct hedge ratio
Hedge Ratio = Target Hedge % ÷ 100
This method is best when you already know the portion of exposure you want to hedge.
2) Minimum variance hedge ratio
h* = ρ × (σs ÷ σf) × Target Factor
Where ρ is correlation, σs is spot volatility, and σf is futures volatility.
3) Beta-adjusted hedge ratio
Hedge Ratio = Portfolio Beta × Target Factor
This method is common when hedging equity portfolios with index futures.
Contracts required
Contracts = (Exposure × Hedge Ratio) ÷ (Futures Price × Contract Multiplier)
Scenario loss after hedge
Net Loss = Unhedged Loss - Hedge Offset + Transaction Cost
This gives a simple stress-test estimate under the adverse move you entered.
How to use this calculator
- Choose a method based on your hedging approach.
- Enter the total exposure value you want to protect.
- Set the target hedge percentage for full or partial coverage.
- For statistical hedging, enter beta, volatility, and correlation inputs.
- Add futures price and contract size to estimate actual contracts.
- Include basis and transaction cost values for a more realistic result.
- Enter an adverse price move to run a simple scenario analysis.
- Submit the form and review the summary, graph, and downloads above the form.
Frequently asked questions
1) What does a hedge ratio mean?
A hedge ratio shows how much of an exposure is offset by a hedge instrument. A ratio of 1.00 means the hedge notional matches the exposure. Lower values mean partial hedging, while values above 1.00 can indicate over-hedging.
2) When should I use the minimum variance method?
Use it when the hedge instrument does not perfectly match the asset being hedged. It combines correlation and relative volatility to estimate the hedge size that may reduce portfolio variance more effectively than a simple one-to-one hedge.
3) Why does beta matter in portfolio hedging?
Beta measures how sensitive a portfolio is to market movements. If a portfolio beta is above 1, it tends to move more than the market. Beta-adjusted hedging scales the hedge so it reflects that market sensitivity.
4) What is basis risk?
Basis risk is the risk that the spot position and hedge instrument do not move together perfectly. Even with a strong hedge ratio, changing basis can leave gains or losses that make the hedge less precise.
5) Why are exact and rounded contracts both shown?
Exact contracts show the mathematically precise hedge size. Rounded contracts are the tradable amount because you usually cannot trade fractional futures contracts. Comparing both helps you understand execution slippage from rounding.
6) Can a hedge ratio be greater than 1?
Yes. A ratio above 1 can appear when beta is high, volatility differences are large, or the portfolio needs more aggressive protection. It may also indicate an over-hedged position, so review the result carefully.
7) Does this calculator replace professional risk management?
No. It is a planning and estimation tool. Real hedging decisions should also consider liquidity, margin rules, contract specifications, rolling costs, taxes, correlation breakdowns, and the operational limits of your trading process.
8) What inputs most affect the result?
Exposure value, target hedge percentage, volatility estimates, correlation, beta, and contract notional all matter. Small changes in these assumptions can produce noticeably different contract counts and hedge effectiveness estimates.