How this instrument works
The optimal hedge ratio, h*, is the size of a futures position — expressed as a fraction of the spot position — that leaves the combined spot-plus-futures portfolio with the least possible variance. It comes from Ederington's 1979 minimum-variance framework: multiply the correlation between spot and futures price changes by the ratio of their volatilities. When spot and futures move in lockstep and are equally volatile, h* equals 1 — a full, one-for-one hedge. Whenever they diverge even slightly, the minimizing ratio drops below 1, because over-hedging with an imperfectly correlated instrument adds variance rather than removing it.
Commodity desks reach for this figure when the futures contract available doesn't exactly match the spot position — an airline hedging jet-fuel purchases with crude-oil futures, a copper fabricator covering a physical order book with an exchange contract priced on a slightly different grade, or a portfolio manager offsetting a factor exposure with a stock-index future that only partially tracks it. In each case the question isn't whether to hedge but how much futures notional to carry per unit of spot exposure, and h* answers that by weighing how tightly the two prices actually co-move against how much more the futures price swings.
The formula treats correlation and volatility as fixed, known numbers, but both are estimated from a historical price window and can shift once the position is live — a hedge sized on last year's correlation can under- or over-cover this year's exposure. It also says nothing about transaction costs, margin calls on the futures leg, or the rollover risk of using a near-dated contract to cover a longer exposure; h* answers a variance question, not a cash-flow or liquidity question.
- Enter Correlation between spot and futures, ρ — the historical correlation coefficient between spot and futures price changes, from -1 to 1.
- Enter Spot price volatility, σₛ — the standard deviation of spot price changes over your chosen estimation window.
- Enter Futures price volatility, σf — the standard deviation of futures price changes over that same window.
- Read Optimal hedge ratio, h* — the futures position size, as a fraction of the spot position, that minimizes combined variance.
- Recompute whenever you re-estimate correlation or volatility from fresh price data; h* moves with both.
Worked example — ρ = 0.85, volatility 20% and 25%
Set correlation to 0.85, spot volatility to 0.20, and futures volatility to 0.25 — a spot position 20% as volatile as its own price history, hedged with a futures contract that swings 25% as much. Multiplying the correlation by the volatility ratio, 0.85 times (0.20 divided by 0.25), gives h* = 0.68.
A trader holding this spot position should short futures covering 68% of it, not 100%, because spot and futures don't move in perfect lockstep here — chasing a full one-for-one hedge would add variance from the 15% of movement the two prices don't share. Ederington's 1979 result is exactly this: the ratio that minimizes the combined position's variance, given the correlation and volatilities on hand.
Questions
Why is the optimal hedge ratio usually below 1.0?
Because h* multiplies correlation by the volatility ratio, and correlation between spot and futures is almost never exactly 1. A ratio of 0.68, as in this page's example, means the two prices share about 85% of their movement — full correlation would require identical or near-identical instruments, which most hedgers don't have. Hedging the full notional amount when correlation is imperfect adds variance instead of removing it, which is why the minimum-variance math pulls the ratio down.
How is this different from a 1:1 or notional hedge ratio?
A notional hedge ratio simply matches position sizes — futures units against exposure units — and assumes the two prices move together dollar for dollar. The optimal hedge ratio instead weighs how closely they actually co-move, using correlation and volatility, and lands below 1:1 whenever that co-movement is imperfect. The two agree only in the special case where the futures contract is priced identically to the spot exposure.
Where do the correlation and volatility inputs come from?
Typically from historical price data — daily or weekly returns on the spot asset and the futures contract over some estimation window, such as the trailing 60 or 250 trading days. Correlation is the Pearson correlation of the two return series; volatility is each series' standard deviation. Longer windows smooth out noise but react slower to a structural shift in how the two prices relate.
Does a higher h* mean a safer hedge?
Not by itself — h* only tells you the size of the minimizing futures position, not how much risk remains after hedging at that size. The share of variance actually removed is closer to ρ², correlation squared; a 0.85 correlation removes roughly 72% of variance even at the optimal ratio, leaving the rest as basis risk the formula cannot eliminate.
What happens if correlation or volatility shifts after the hedge is set?
The position sized at that h* stops being optimal, since h* was computed from a snapshot of past correlation and volatility. Instruments that normally track each other closely can decouple during stress — a supply shock, a delivery-month squeeze — leaving a hedge sized for calmer conditions either over- or under-covering the exposure. Re-estimating h* on fresher data and adjusting the futures position is the usual response.
Can the optimal hedge ratio exceed 1.0?
Yes, whenever ρ times (σₛ divided by σf) works out above 1 — which happens when futures volatility is low relative to spot volatility and correlation stays high. That calls for a futures position larger than the spot exposure itself, the mirror image of the more common under-1.0 case, and it still minimizes variance for the pair of instruments on hand.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.