A hedge ratio converts an exposure into a practical position size. This guide explains the main hedge ratio formulas, shows how to apply them to futures, forwards, and options, and provides a repeatable worksheet for updating the hedge as exposure, volatility, and market relationships change.
Overview
The hedge ratio is the proportion of a risk exposure that is offset by a hedging instrument. It helps answer a basic treasury or portfolio question: how much of the hedge should be bought or sold?
There is no single hedge ratio formula for every situation. The appropriate calculation depends on the instrument, the exposure being protected, the objective of the hedge, and the relationship between the exposure and the hedge. A company hedging a known foreign-currency invoice may use a straightforward notional ratio. A portfolio manager using equity futures may estimate a beta-adjusted ratio. A risk team seeking to reduce volatility may use a minimum variance hedge ratio.
For a simple futures hedge, the starting formula is:
Number of contracts = Exposure amount ÷ Notional value per contract
When the exposure and futures contract are not perfectly matched, the calculation can include a hedge ratio adjustment:
Number of contracts = (Exposure amount ÷ Contract size) × Hedge ratio
The hedge ratio is normally below, equal to, or above 1.00 depending on the relationship between the exposure and the instrument. A ratio of 0.75 means the calculated hedge covers 75% of the unadjusted position. A ratio above 1.00 may be appropriate when the chosen hedge tends to move less than the exposure.
A hedge is not automatically successful because its notional value matches the exposure. Maturity, currency, grade, location, duration, liquidity, and price behavior can all differ. These mismatches create basis risk: the possibility that the exposure and the hedge do not move together as expected.
How to estimate
1. Define the exposure
Start with the quantity and direction of the risk. Record whether you are exposed to rising or falling prices, rates, or exchange rates. For example, an importer expecting to pay euros in 90 days is exposed to a rising euro against its reporting currency. A producer planning to sell a commodity is exposed to falling commodity prices.
Use the exposure at the relevant hedge date, not an informal estimate of annual sales. Separate committed transactions from forecast transactions where possible.
2. Identify the hedge instrument
List the contract size, currency, settlement date, expiration date, price quotation, and whether the instrument is linear or option-based. Futures and forward contracts generally provide a direct notional offset. Options provide conditional protection, so their delta and strike must also be considered.
3. Calculate the basic notional ratio
For a futures hedge, divide the exposure by the amount represented by one contract. Round the result to a tradable number of contracts, then document the rounding effect. If the exposure is 250,000 units and each futures contract represents 5,000 units, the unadjusted hedge is 50 contracts.
4. Adjust for the relationship between the exposure and hedge
A commonly used minimum variance hedge ratio is:
h* = Covariance of exposure returns and hedge returns ÷ Variance of hedge returns
In practical terms, this estimates the hedge size that would have minimized historical variance over a selected observation period. The result is often expressed as the slope coefficient from a regression of exposure changes on hedge changes. It is an estimate, not a permanent rule.
For an equity portfolio hedged with an index future, a simplified beta approach is:
Number of contracts = (Portfolio value × Portfolio beta) ÷ Futures contract value
For options, a first estimate can use delta:
Option contracts = Exposure to offset ÷ (Option contract size × absolute delta)
Because delta changes as the underlying price, time to expiration, and implied volatility change, an options hedge may require more frequent monitoring than a notional futures hedge. A detailed explanation of this process is available in our Delta Hedging Explained guide.
Inputs and assumptions
A useful hedge ratio worksheet should contain more than the final number. Include these fields:
- Exposure: quantity, currency, market value, timing, and risk direction.
- Instrument: contract size, underlying, maturity, strike if applicable, and quotation convention.
- Coverage target: the percentage of the exposure the policy permits or requires you to hedge.
- Relationship adjustment: historical hedge ratio, beta, duration ratio, or option delta.
- Rounding: the number of whole contracts and the residual unhedged exposure.
- Costs: bid-ask spreads, commissions, financing, margin requirements, option premium, and collateral effects.
- Basis assumptions: expected correlation, maturity alignment, and any differences in location, grade, or settlement.
For interest rate hedging, match the sensitivity of the exposure rather than relying only on principal. A duration-based estimate compares the market value multiplied by duration for the liability or asset with the equivalent sensitivity of the futures or swap. For currency hedging, distinguish the foreign-currency amount from its home-currency value and confirm which side of the forward contract offsets the exposure.
Historical data can help estimate a minimum variance hedge ratio, but the chosen lookback period matters. A short period may reflect unusual market conditions; a long period may include relationships that no longer apply. Test several reasonable windows and compare the resulting ratios rather than treating one output as precise.
Worked examples
Commodity futures hedge
Assume a manufacturer expects to purchase 120,000 units of a commodity in four months. A futures contract represents 10,000 units. The basic ratio is:
120,000 ÷ 10,000 = 12 contracts
Suppose analysis indicates that the futures price has historically moved about 0.85% for each 1% move in the company’s relevant physical price. Applying a 0.85 hedge ratio gives:
12 × 0.85 = 10.2 contracts
The company must choose between 10 and 11 contracts. Ten contracts leave a larger residual exposure; 11 contracts provide greater protection but may over-hedge if the relationship changes. The decision should follow the documented risk limit and coverage policy, not just the rounded mathematical result. The difference between the physical price and futures price is the basis, and changes in that difference should be included in the risk review.
Foreign-currency forward hedge
An exporter expects to receive 500,000 units of a foreign currency in 60 days and wants to reduce the risk of the currency falling. If the approved policy calls for 80% coverage, the forward notional is:
500,000 × 0.80 = 400,000 currency units
The exporter would typically sell 400,000 foreign-currency units forward, subject to the contract terms and counterparty process. If the expected receipt later changes to 450,000, the original hedge covers about 89% of the revised exposure. That may be acceptable, but it should be recorded and reviewed rather than assumed to remain aligned. Businesses with several currency exposures can first map transaction, translation, and economic exposure using the FX Exposure Mapping Guide.
Protective put estimate
An investor holds 1,000 shares and buys put options covering 100 shares each. If each option currently has a delta of 0.50, the option-equivalent protection is approximately:
10 contracts × 100 shares × 0.50 = 500 delta-adjusted shares
This is not the same as guaranteeing protection for 500 shares. Delta changes, and the put only provides contractual protection according to its strike and expiration. Premium, liquidity, time decay, and the desired floor should be assessed alongside the ratio. A portfolio comparison of puts, collars, inverse funds, and futures is available in our Portfolio Downside Protection Strategies Compared guide.
When to recalculate
Recalculate the hedge ratio whenever the exposure, instrument, or market relationship changes materially. Practical triggers include a revised sales or purchase forecast, an invoice or loan being delayed, a futures contract approaching expiration, a change in portfolio composition, or a major shift in volatility and correlation.
Set a scheduled review as well as event-based triggers. A monthly or quarterly review may be appropriate for stable corporate exposures, while options books and actively managed portfolios may require daily monitoring. At each review, compare the current exposure with the hedge notional, estimate the residual basis risk, and calculate the effect of rounding.
Use a simple update routine:
- Refresh the exposure amount, timing, price, and currency.
- Confirm contract size, maturity, delta, duration, or other sensitivity inputs.
- Recalculate the basic notional ratio and any statistical adjustment.
- Run adverse scenarios for price, rate, currency, basis, and volatility changes.
- Decide whether to add, reduce, roll, or leave the hedge unchanged.
- Record the assumptions, approval, residual exposure, and next review date.
A hedge ratio is a decision aid, not a promise that losses are eliminated. Keep the worksheet with the trade documentation, test the result under stressed conditions, and revisit the inputs whenever the underlying risk changes. For a broader review of scenario design, see Stress Testing a Hedge; for extending or closing positions, see Rolling a Hedge.
