FRM Exam Part I · Using Futures for Hedging

Basis Risk in Futures Hedging Explained

Updated 11 October 2026 · Fact-checked

Basis risk is the risk that the basis, defined as spot price minus futures price, changes unpredictably before you close a futures hedge. A hedger's effective price depends on the final basis. A short hedger gains when the basis strengthens; a long hedger gains when it weakens.

Understand Basis Risk

A futures hedge aims to lock in a price. It rarely locks it in perfectly. The reason is the basis.

In the standard FRM convention, basis = spot price of the asset to be hedged − futures price of the contract used. At the futures delivery date, the basis of the same asset converges to zero. Before that, it moves up and down. Because the basis is not known in advance, the hedge outcome is not certain. This uncertainty is basis risk.

A strengthening basis means the basis increases (spot rises relative to futures). A weakening basis means the basis decreases (spot falls relative to futures). A short hedger holds the asset and is short futures, so profits when the basis strengthens. A long hedger will buy the asset later and is long futures, so profits when the basis weakens. Remember: the short hedger wants spot to do better than futures.

Basis risk has two main sources. First, the asset being hedged may differ from the asset underlying the futures (for example hedging jet fuel with crude oil futures). Second, the hedge may end on a date that differs from the delivery month. You must pick a delivery month and often close out before delivery. Choosing a contract month later than the hedge end usually works better than an earlier month, because prices in the delivery month can be erratic. But a longer contract month can mean a bigger basis variability and less liquidity, so there is a trade-off.

With basis risk, the effective price is not the original futures price. Using S1 and F1 for the spot and futures prices at close-out, and F0 for the initial futures price, you get a price that depends on b2, the basis at close-out.

Key formulas to remember

Basis: Basis = S − F; Spot of the asset being hedged minus futures price of the contract used. Some books use the reverse sign, so follow the question's definition.
Effective price received (short hedge): Effective price = S2 + (F1 − F2) = F1 + b2; F1 is the initial futures price, F2 the futures price at close-out, S2 the spot at close-out, b2 = S2 − F2.
Effective price paid (long hedge): Effective price = S2 − (F2 − F1) = F1 + b2; Same expression as the short hedge. Only b2 is uncertain.
Basis direction rule: Short hedger: gains if basis strengthens. Long hedger: gains if basis weakens.; Strengthening means S − F increases; weakening means it decreases.
Convergence: Basis → 0 at delivery (same asset); Does not hold if the hedged asset differs from the futures underlying asset.

How to solve Basis Risk questions

Use this sequence for any basis risk question.

1Identify whether the hedger is short (owns asset, will sell) or long (will buy asset).
2Write the basis definition in the question: S − F. Note the initial futures price F1 and any initial basis b1.
3Find the close-out spot S2 and futures F2. Compute the final basis b2 = S2 − F2.
4Compute the futures gain: short = F1 − F2; long = F2 − F1.
5Effective price = S2 + futures gain (short) or S2 − futures gain (long). Check that it equals F1 + b2.
6Compare b2 with b1 to say whether the basis strengthened or weakened, and who benefited.
7If the question asks about contract choice, pick the month at or just after the hedge end and consider correlation with the asset hedged.

Quickest way: Effective price = F1 + b2

When to use it: When a question gives the initial futures price and the final basis or final spot and futures prices.

Take F1, the futures price when the hedge was opened.
Add the final basis b2 = S2 − F2.
That is the effective price received (short) or paid (long).
For strengthening or weakening, just compare b2 with b1: higher means strengthening.

Common mistakes in Basis Risk

Using the wrong sign for the basis
Some textbooks define basis as futures minus spot.
Fix: Use S − F unless the question states otherwise, and write the definition before calculating.
Saying a short hedger benefits from a weakening basis
Students confuse falling prices with falling basis.
Fix: Short hedger: effective price = F1 + b2, so a larger b2 helps. Strengthening helps the short hedger.
Assuming a hedge removes all risk
Futures are described as locking in a price.
Fix: Only the price risk is replaced by basis risk. The outcome still varies with b2.
Using F2 instead of F1 as the base of the effective price
Mixing up the initial and close-out futures price.
Fix: Recompute as S2 + (F1 − F2) for a short hedge and check that it equals F1 + b2.
Expecting zero basis when closing early or hedging a different asset
Convergence is learned as a general rule.
Fix: Convergence applies only at delivery and only for the same asset. Otherwise the basis stays uncertain.

Worked examples

Example 1

A producer will sell oil in three months and shorts futures at $80.00. Initial spot is $79.00. At close-out, spot is $76.50 and futures are $77.00. Find the effective price and say whether the basis strengthened or weakened.

Show the solution

Initial basis b1 = 79.00 − 80.00 = −1.00.
Final basis b2 = 76.50 − 77.00 = −0.50.
Futures gain on the short = 80.00 − 77.00 = 3.00.
Effective price = 76.50 + 3.00 = 79.50.
Check: F1 + b2 = 80.00 − 0.50 = 79.50.
b2 (−0.50) is greater than b1 (−1.00), so the basis strengthened.

Answer: Effective price is $79.50 per barrel. The basis strengthened, which benefited the short hedger.

Example 2

An airline expects to buy fuel in two months and goes long futures at $2.40 per gallon. At the purchase date, spot is $2.55 and futures are $2.62. The initial basis was −0.05. Find the effective price paid and whether the basis strengthened or weakened.

Show the solution

Final basis b2 = 2.55 − 2.62 = −0.07.
Futures gain on the long = 2.62 − 2.40 = 0.22.
Effective price paid = 2.55 − 0.22 = 2.33.
Check: F1 + b2 = 2.40 − 0.07 = 2.33.
b2 (−0.07) is lower than b1 (−0.05), so the basis weakened, which helps a long hedger.

Answer: Effective price paid is $2.33 per gallon. The basis weakened, which benefited the long hedger.

Exam tips

Write the basis definition first. Questions may define it as S − F, and the strengthen/weaken answer depends on it.
Use the shortcut F1 + b2 to cross-check your longer calculation.
Remember short hedger = strengthening is good; long hedger = weakening is good. Questions often test this directly.
For contract choice questions, prefer a delivery month just after the hedge end, and note that a poor correlation between the hedged asset and futures raises basis risk.
Do not forget that a cross hedge introduces extra basis risk even if the delivery month matches.

Practice questions from Using Futures for Hedging

Basis Risk in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

NISM CertificationsHedging with Futures and Basis Risk

Basis Risk: frequently asked questions

What is basis risk in futures hedging?

It is the risk that spot minus futures changes in an unexpected way before the hedge is closed. The hedge then does not lock in exactly the price you planned. It arises from asset mismatch and delivery month mismatch.

What does strengthening of the basis mean for a short hedge?

Strengthening means spot rises relative to futures, so S − F increases. A short hedger benefits because the effective price is F1 + b2, which rises with the final basis.

How do I calculate the effective price with basis risk?

Add the futures gain or loss to the spot transaction. For both short and long hedges this equals the initial futures price plus the final basis, F1 + b2.

What is the difference between spot price and futures price basis?

The basis is the spot price minus the futures price. For the same asset it falls to zero at delivery. Before that, it reflects carrying costs and market conditions and varies over time.