Cross Hedging: Using a Related Instrument
An airline wants to hedge jet fuel, but there's no good jet fuel futures contract. It has to borrow the closest-priced instrument instead.
Risk warning: forex, CFDs, options, futures and crypto assets usually involve leverage or high volatility, and you can lose more than you put in. This lesson only teaches the concepts; all numbers are for illustration and are not investment advice.
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Text version · Hedging Strategies, lesson 7: “Cross Hedging: Using a Related Instrument”
An airline wants to hedge jet fuel, but there's no good jet fuel futures contract. It has to borrow the closest-priced instrument instead.
No matching futures? Find the closest match
Jet fuel has no good futures, so use heating oil (diesel) futures, whose price is closest, instead. That's a cross hedge. The higher the correlation between the products, the smaller the leftover basis risk.
Contracts = ratio × exposure ÷ contract size
First use the minimum-variance hedge ratio to decide how much to hedge, then convert the exposure into a number of contracts. The airline is the side that has to "buy fuel," so it buys futures to hedge.
Correlations change, so check the ratio
Hedge ratios are estimated from historical data. When supply and demand shift (refinery maintenance, a change of season), the correlation between jet fuel and heating oil can drop from 0.9 to 0.6, and the old ratio is no longer optimal. In practice you re-estimate with fresh data regularly and check how well the hedge works.
Key takeaways
- When there's no directly matching futures contract, using a highly correlated instrument instead is called a cross hedge.
- The lower the correlation, the more basis risk is left after hedging. Choose the instrument by correlation first, then liquidity.
- Number of contracts = hedge ratio × exposure ÷ quantity per contract.
- Correlations change over time, so review the hedge ratio regularly with fresh data.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Click "Example: heating oil": how many contracts do you need to buy? After hedging, how much does the 90% range of the fuel bill narrow?
- Switch to WTI crude: what are the optimal ratio and the narrowing now? Why is it worse than heating oil?
- Switch to natural gas at the optimal ratio: the cyan distribution is almost as wide as the red one. What does that tell you?
- With heating oil, push the hedge ratio to 1.2: does the distribution get narrower or wider?
Quiz and explanations
- 1. An airline wants to hedge jet fuel prices. Which futures contract is usually most suitable?
- Answer: Heating oil (diesel) futures.Heating oil and jet fuel are both middle distillates, with the highest price correlation.
- 2. You need to hedge 10 million gallons of jet fuel with a hedge ratio of 0.9, and each contract is 42,000 gallons. Roughly how many contracts do you need?
- Answer: 214.0.9 × 10,000,000 ÷ 42,000 ≈ 214 contracts.
- 3. Jet fuel volatility is 2.5%, heating oil futures volatility 2% and the correlation 0.8. What's the minimum-variance hedge ratio?
- Answer: 1.0.0.8 × 2.5% ÷ 2% = 1.0. The ratio depends on correlation and the ratio of the two volatilities; it isn't necessarily 1:1 or the correlation itself.
Terms in this lesson
- basis risk (Basis Risk): The risk left after hedging because the asset and the hedging instrument don't move perfectly together.
- correlation (Correlation): How much two prices move together, from −1 to 1; the closer to 1, the more in sync.
- cross hedge (Cross Hedge): Hedging with a related but not identical product, such as using heating oil futures to hedge jet fuel.
- hedge ratio (Hedge Ratio): The size of the hedge relative to the original exposure; 1 means a full hedge, 0.5 means hedging half.
- minimum-variance hedge ratio (Minimum-Variance Hedge Ratio): The ratio that makes the hedged portfolio swing the least = correlation × spot volatility ÷ futures volatility.