Hedge Ratio Explained: Definition, Calculation, and Examples

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The hedge ratio is the size of a hedging position divided by the size of the exposure it protects. A ratio of 0.5 means half the exposure is offset. A ratio of 1.0 means the full position is offset, and a ratio of 0 means it is unhedged. In futures markets the ratio usually compares the value of futures contracts bought or sold with the value of the cash commodity or asset being hedged. In options it describes how many units of the underlying offset one option.

How the basic hedge ratio works

Suppose you hold $10,000 of foreign stocks. Their value in dollars moves with the exchange rate, so you carry currency risk on top of equity risk. If you take an offsetting currency position worth $5,000, for example by selling the foreign currency forward, your currency hedge ratio is:

$5,000 ÷ $10,000 = 0.5

Half of the position’s currency exposure is protected. The other half still gains or loses as the exchange rate moves. Fund managers use the same arithmetic when they describe a portfolio as 50% or 100% currency-hedged. Some call this figure the hedge coverage ratio, since it states how much of the exposure is covered.

This version of the ratio measures coverage only. It says nothing about whether the hedge instrument will actually track the exposure, which is what the minimum variance hedge ratio addresses.

Minimum variance hedge ratio

When the hedge instrument is not the same asset as the exposure, a one-for-one hedge can over- or under-protect. This is called cross-hedging: hedging jet fuel with crude oil futures, or a regional currency with a more liquid one. The minimum variance hedge ratio picks the hedge size that makes the combined position’s value fluctuate as little as possible.

Formula:

h* = ρ × (σS ÷ σF)

where ρ is the correlation between changes in the spot price and changes in the futures price, σS is the standard deviation of spot price changes, and σF is the standard deviation of futures price changes. An equivalent form is h* = Cov(S, F) ÷ Var(F), which is the slope from regressing spot price changes on futures price changes.

Number of contracts:

N* = (h* × units of exposure) ÷ units per contract

Hedge effectiveness

The square of the correlation (ρ²) shows the share of spot price variance that the optimal hedge removes. Even a well-sized cross-hedge leaves some residual risk, known as basis risk.

Example: an airline hedging jet fuel

Hypothetical example for illustration. An airline expects to buy 15 million gallons of jet fuel over the next year and worries that prices will rise. Jet fuel futures are less liquid, so it hedges with NYMEX WTI crude oil futures, a contract that covers 1,000 barrels, or 42,000 gallons.

Assumptions:

• Correlation between jet fuel spot price changes and oil futures price changes: 0.95
• Standard deviation of jet fuel spot price changes: 3%
• Standard deviation of oil futures price changes: 6%

Hedge ratio: 0.95 × (3% ÷ 6%) = 0.475

Contracts: (0.475 × 15,000,000) ÷ 42,000 ≈ 169.6, rounded to 170 long contracts.

Hedging the full 15 million gallons one for one would need about 357 contracts. Because oil futures in this example swing twice as much as jet fuel, that larger hedge would add volatility instead of removing it. Under these assumptions, ρ² ≈ 0.90, so the hedge removes about 90% of the price variance and leaves roughly 10% as basis risk.

Hedge ratio for options

In option pricing, the hedge ratio is the number of shares of the underlying needed to offset one option, which is the option’s delta. In a one-period binomial model:

h = (option value if up − option value if down) ÷ (stock price if up − stock price if down)

Hypothetical example: a stock at $50 will be either $60 or $40 at expiry. A call struck at $50 is worth $10 or $0, so h = (10 − 0) ÷ (60 − 40) = 0.5. Buying 0.5 shares for each call written gives a portfolio worth $20 in both outcomes (30 − 10 or 20 − 0). The position is riskless, which is how the model prices the option.

For a put option with the same strike, the payoffs are $0 or $10, so h = (0 − 10) ÷ 20 = −0.5. Put deltas are negative, so a long put is hedged by buying shares. Owning 0.5 shares with each long put gives $30 in either case (30 + 0 or 20 + 10).

Because delta changes as the stock price and time to expiry change, an options hedge must be rebalanced to stay riskless.

Limitations

• Estimates, not constants. Correlation and volatility come from historical data and shift over time. A hedge ratio calculated from last year’s data may be wrong next quarter.
• Basis risk remains. The relationship behind a cross-hedge can weaken in stressed markets.
• Rounding and contract size. Futures trade in whole contracts, so the actual ratio rarely equals the optimal one exactly.
• Rebalancing costs. Keeping a dynamic ratio in line, especially for options, means repeated trading and transaction costs.
• Margin and cash flow. A futures hedge can require variation margin while it is losing, even when the underlying exposure is gaining. A large adverse move can trigger a margin call on the hedge leg.

Common confusions

Hedge ratio vs. correlation. Correlation measures how closely two prices move together. The minimum variance hedge ratio also scales by relative volatility, so a 0.95 correlation can produce a 0.475 ratio.

Hedge ratio of 1 vs. optimal hedge. A ratio of 1.0 means full notional coverage, not minimum risk. It is optimal only when the hedge and the exposure have equal volatility and perfect correlation. Choosing a ratio between 0 and the optimal level trades less protection for keeping some upside.

FAQs

The Bottom Line

The hedge ratio matters to investors, fund managers and companies offsetting currency, commodity or option exposure. A ratio of 1.0 gives full coverage but minimizes risk only when the hedge and exposure have equal volatility and perfect correlation, so cross-hedges are better sized with the minimum variance formula. Correlation and volatility shift over time, and futures hedges can still bring basis risk, rounding gaps and margin calls.