What it means
A textbook hedge uses a contract on exactly the thing being hedged, so gains on the hedge cancel losses on the exposure almost precisely. Real markets do not offer contracts for every grade, location and delivery date, which is where cross hedging comes in.
The classic case is jet fuel. There is no deep futures market for jet fuel in most regions, so airlines hedge with crude oil or heating oil futures, which historically move closely with jet fuel prices.
The same logic applies elsewhere. A company exposed to a thinly traded currency may hedge with a closely linked major currency, and a portfolio of mid-sized shares may be hedged with an index future that only approximates the portfolio's composition.
The quality of a cross hedge depends on correlation, meaning how reliably the two prices move together. A high and stable correlation makes the hedge effective, while a correlation that breaks down in stressed markets leaves the business exposed at the worst possible moment.
Because the two prices are not identical, the hedge is usually sized using a hedge ratio rather than matching the exposure one for one. The ratio reflects both the correlation and the relative volatility of the two prices, so a more volatile exposure needs a larger hedge position.
The residual gap between the exposure and the hedge is called basis risk, and it is the price paid for using an imperfect instrument. Good practice is to measure it after the fact, comparing what the hedge actually delivered against what a perfect hedge would have delivered.
In practice
Real-world examples
Example 1
A Norwegian salmon exporter invoices in Polish zloty but finds forward pricing expensive and thin. It hedges with euro forwards instead, relying on the historically close link between the zloty and the euro, and accepts that a divergence between the two would leave a gap.
Example 2
A bakery chain exposed to butter prices hedges using dairy futures based on a broader milk-fat benchmark. The hedge covered about three quarters of a sharp price rise, which the finance director judged a better outcome than the unhedged alternative.
Example 3
An asset manager holding a concentrated portfolio of mid-cap industrial shares sells broad equity index futures ahead of an uncertain election. The index protects against the general market fall but not against the sector underperforming the index by four percentage points.
Think of it
Imagine you cannot buy an exact spare tyre for your vintage car, so you buy one for a slightly different model from the same manufacturer. It is not a 100 percent match, but it will keep you moving safely if you get a flat.
Formula
Calculation
Hedge ratio = Correlation between spot and futures price changes x (Standard deviation of spot price changes / Standard deviation of futures price changes)
Number of contracts = (Exposure in units x Hedge ratio) / Contract size
A fictional regional airline expects to buy 1,200,000 barrels of jet fuel over the next year. No jet fuel futures are available to it, so it hedges with crude oil futures of 1,000 barrels each. Historical data shows a correlation of 0.90, jet fuel price changes with a standard deviation of 12%, and crude oil price changes with a standard deviation of 10%.
Hedge ratio = 0.90 x (12% / 10%) = 0.90 x 1.2 = 1.08
Hedged position = 1,200,000 x 1.08 = 1,296,000 barrels
Number of contracts = 1,296,000 / 1,000 = 1,296 contracts
Now test it. Jet fuel rises by $8.00 per barrel over the year, so the airline's fuel bill increases by 1,200,000 x $8.00 = $9,600,000. Crude oil rises by only $6.00 per barrel, so the futures position gains 1,296,000 x $6.00 = $7,776,000.
Net uncovered cost = $9,600,000 - $7,776,000 = $1,824,000
The cross hedge absorbed $7,776,000 of a $9,600,000 shock, roughly 81% of it, and the remaining $1,824,000 is the basis risk the airline accepted by hedging with a related rather than an identical product.Case study
Seen in the real world
Skyreach Regional is an invented airline used purely as an illustrative example. It burned 1,200,000 barrels of jet fuel a year, had no access to a jet fuel futures market, and had previously left the exposure entirely unhedged on the grounds that any hedge would be imperfect.
After a year in which fuel costs rose $8.00 per barrel and wiped $9,600,000 off operating profit, the board asked the treasurer to model a crude oil cross hedge. Using a correlation of 0.90 and a volatility ratio of 1.2, the hedge ratio came out at 1.08, implying 1,296 contracts of 1,000 barrels each.
Applying that hedge to the same year would have generated $7,776,000 of futures gains, cutting the net impact to $1,824,000. In this fictional review the board accepted the residual basis risk, set a policy of hedging roughly 70% of expected volume, and required a quarterly report comparing crude and jet fuel movements so that a breakdown in the relationship would be spotted early.
Watch out
Common mistakes
- Hedging one unit of exposure with one unit of the proxy instrument. When the exposure is more volatile than the hedging instrument, a one-for-one position under-hedges the risk.
- Assuming a historical correlation will hold in a crisis. Relationships between related prices often weaken precisely when markets move sharply, which is when the hedge is most needed.
- Judging the hedge by whether it made money. A hedge that loses money while the underlying exposure becomes cheaper has done its job, and profit on the hedge alone is the wrong scorecard.
Questions
People also ask
What is basis risk?
It is the risk that the price of the hedging instrument and the price of the actual exposure do not move by the same amount, leaving a residual gain or loss after the hedge is applied.
When is a cross hedge better than no hedge?
When the correlation between the two prices is high and reasonably stable, so that most of the exposure is neutralised, and when the residual gap is small compared with the unhedged swing.
How often should the hedge ratio be recalculated?
Whenever the underlying volatilities or correlation shift materially, which for most commodity and currency programmes means at least quarterly.