βοΈ Hedge Ratio Calculator
Futures per unit of spot exposure.
Minimum-variance hedge ratio
Estimates for planning only, not financial advice.
The minimum-variance hedge ratio tells you how much futures to short against a spot position: correlation times the ratio of spot volatility to futures volatility. With correlation of 0.90, spot volatility of 20%, and futures volatility of 25%, the hedge ratio is 0.9 x (20/25) = 0.720. Short 0.72 futures per unit of spot to minimize the variance of the combined position.
How to Use This Calculator
Enter the correlation between spot and futures price changes and the volatilities of each over the hedge horizon. The calculator returns the hedge ratio and its plain meaning.
Enter the correlation of spot and futures returns, between -1 and 1.
Enter annualized volatilities for the spot position and the futures contract.
Read the ratio. For the interest-rate math behind futures pricing, see our forward rate calculator.
The Hedge Ratio Formula
This is the slope of the regression of spot changes on futures changes: the position in futures that minimizes the variance of the hedged portfolio. Perfect correlation with equal volatilities gives h = 1, a one-for-one hedge. Lower correlation or relatively jumpier futures shrink the ratio, because each futures contract carries more risk per unit. The number of contracts is h times the spot exposure divided by the futures contract size, rounded to what the exchange allows.
Worked Example
Correlation 0.90, spot vol 20%, futures vol 25%: h = 0.720. Hedging $10M of spot exposure with $1M-notional futures contracts needs 0.72 x 10 = 7.2 contracts, so 7 contracts in practice. Hedge effectiveness is rho squared: 0.81, meaning the hedge removes about 81% of the variance. Contrast a cross-hedge with correlation 0.6 and equal vols: h = 0.6 and effectiveness is only 36%, leaving most of the risk in place. That gap is why hedgers prefer the most correlated contract available.
When the Textbook Hedge Fails
Three real-world frictions. First, basis risk: spot and futures never move in lockstep, and the hedge leaves the basis unhedged. Second, the ratio drifts: correlations estimated on calm data break in crises, exactly when the hedge matters most. Third, margin calls: futures are marked to market daily, so a hedge can demand cash at the worst moment even if it converges by expiry. Re-estimating h as conditions change keeps the hedge honest, at the cost of constant trading.
My advice: treat the computed ratio as a starting point and stress it. If effectiveness below 70% (correlation under ~0.84), question whether the hedge is worth its cost and margin risk. An imperfect hedge that bleeds cash in a crisis can be worse than the honest choice of carrying less exposure.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is a hedge ratio?
The size of the hedging position relative to the exposure: how much futures to hold per unit of spot risk. The minimum-variance ratio, correlation times relative volatility, minimizes the hedged portfolio's variance.
How many futures contracts do I need?
Multiply the hedge ratio by your spot exposure and divide by the futures contract size: N = h x (spot value / futures notional). Round to whole contracts; the rounding error is usually trivial.
What is hedge effectiveness?
Rho squared: the fraction of spot variance the hedge removes. A 0.9 correlation gives 81% effectiveness. Below 50% effectiveness, most practitioners question whether the hedge earns its keep.
What is basis risk?
The risk that spot and futures prices do not move together, leaving the difference (the basis) unhedged. It is the main reason real hedges underperform the textbook ratio.
Should I hedge 1-for-1?
Only if correlation is near 1 and volatilities match. Otherwise the naive one-for-one hedge is over- or under-hedged. Compute the ratio; the naive hedge is a special case, not the default.
What is a cross hedge?
Hedging with futures on a different but correlated asset, like hedging jet fuel with crude futures. Correlation is lower, so the ratio and the effectiveness both fall, and basis risk rises.
Do hedge ratios change over time?
Yes. Correlations and volatilities drift, especially in stress. Active rebalancing re-estimates the ratio periodically; static hedging sets it once. Most corporate hedgers review quarterly.
Can hedging lose money?
The hedge itself can show losses while the underlying gains, which is the point, but margin calls on futures demand cash before the offset arrives. Poorly managed hedges have bankrupted firms that were right about direction.
What is a perfect hedge?
Correlation of exactly 1 with matching volatility, giving h = 1 and 100% effectiveness. It exists mostly in textbooks; real hedges live with basis risk and ratios below one.
How often should hedge ratios be updated?
Quarterly for most corporate programs, more often in volatile markets. Each update trades accuracy against transaction costs, so set a calendar and stick to it rather than chasing every wiggle.
What data should I use to estimate the hedge ratio?
Price changes over your hedge horizon: daily data for short hedges, weekly or monthly for longer ones. Match the estimation window to how long you will hold the hedge, and refresh it as markets evolve.