CFA Level II Exam · Introduction to Commodities and Commodity Derivatives
Futures Curves: Contango and Backwardation Explained
Updated 7 October 2026 · Fact-checked
A futures curve plots futures prices against maturity. In contango, longer-dated futures cost more than nearer ones, so the curve slopes up. In backwardation, longer-dated futures cost less, so it slopes down. Storage costs and interest push prices up; convenience yield pulls them down. Net of these decides the shape.
Understand Futures Curves: Contango and Backwardation
A futures curve (or forward curve) shows the futures price of the same commodity for different delivery dates. You read it from left (nearest contract) to right (furthest contract). The shape tells you how the market prices holding the physical commodity versus holding a contract.
The curve is upward sloping (contango) when later contracts are priced higher than earlier ones. It is downward sloping (backwardation) when later contracts are priced lower. A flat curve means roughly equal prices. Level II tests the definition by shape, so do not link it to whether prices are expected to rise or fall.
The cost-of-carry idea explains the shape. If you buy the physical commodity now and deliver it later, you pay the spot price, then pay interest on the money tied up and pay storage costs. These costs make a later futures price higher. Futures price ≈ spot × (1 + r) + storage costs, with storage costs treated here as a cost in currency terms or rate terms depending on the model.
The offset is convenience yield: the benefit of physically holding the commodity, such as keeping a refinery running or avoiding a stock-out. Holders of the physical get this benefit, but holders of futures do not. A high convenience yield lowers the futures price relative to spot. When it exceeds interest plus storage costs, the curve is backwardated. When it is small, costs dominate and the curve is in contango.
Convenience yield tends to be high when inventories are low or supply is tight, so scarcity often goes with backwardation. Ample inventories lead to low convenience yield and contango. Also note the link to the roll yield: in backwardation, the long sells the expiring higher-priced contract and buys the lower-priced later one, giving a positive roll yield. In contango the roll yield is negative.
Key formulas to remember
- Cost-of-carry futures price (with convenience yield)
- F₀ = S₀ × (1 + r)^T + FV(storage costs) − FV(convenience yield)
- Conceptual form. Storage and interest raise F₀. Convenience yield lowers it. Use the exact form the vignette gives.
- Contango
- Longer-dated futures price > nearer-dated futures price
- Upward-sloping curve. Defined by shape only, not by expected price direction.
- Backwardation
- Longer-dated futures price < nearer-dated futures price
- Downward-sloping curve. Usually linked to high convenience yield.
- Net cost of carry condition
- Contango if r + storage > convenience yield; backwardation if convenience yield > r + storage
- Compare the two sides on the same time basis, such as annualised rates.
- Roll yield sign
- Backwardation: roll yield > 0 for a long position; contango: roll yield < 0
- Assumes the long rolls from the near contract to the next, with the spot price unchanged.
How to solve Futures Curves: Contango and Backwardation questions
Use this sequence for any question on curve shape, its drivers or its implications.
- 1Find the futures prices in the exhibit and note each maturity, ordered from nearest to furthest.
- 2Compare adjacent prices. Rising with maturity means contango; falling means backwardation; mixed means the curve is humped or kinked.
- 3Identify the drivers given: interest rate, storage costs and convenience yield or inventory level.
- 4Check the net: interest plus storage against convenience yield. The larger side sets the slope.
- 5Link inventory to convenience yield: low inventories mean high convenience yield and backwardation; ample inventories mean low convenience yield and contango.
- 6If asked about returns, apply the sign: backwardation gives positive roll yield for a long position and contango gives negative.
- 7Re-read the question to confirm whether it asks about shape, cause or return before choosing.
Quickest way: Slope-then-sign check
When to use it: When a question gives prices or a description and asks you to classify the market or name the driver.
- Compare the far price with the near price. Higher far price is contango, lower is backwardation.
- Say the driver in one phrase: costs dominate means contango; convenience yield dominates means backwardation.
- Attach the roll yield sign: contango negative, backwardation positive for longs.
- Eliminate options that tie shape to expected spot direction.
Common mistakes in Futures Curves: Contango and Backwardation
Saying contango means prices are expected to rise.
Students read an upward curve as a forecast.
Fix: Contango is only a shape. Theory says it reflects carry costs, and the curve does not predict spot prices by itself.
Adding convenience yield to the futures price.
It sounds like a cost or a return that adds value.
Fix: Convenience yield is a benefit to holders of the physical, so it lowers the futures price relative to spot.
Mixing up the roll yield sign.
Students remember the names but not the mechanics.
Fix: Backwardation: you sell the expiring contract high and buy the next one lower, so roll yield is positive. Contango is the reverse.
Applying storage costs to financial futures or assuming every commodity has one.
Students memorise cost-of-carry as universal.
Fix: Storage and convenience yield matter for physical commodities. Costs and perishability vary by commodity, so use the vignette's data.
Comparing rates and currency amounts directly.
Interest is a percentage and storage may be a cost per unit.
Fix: Convert everything to the same basis, such as percent of spot per year, before comparing.
Worked examples
Example 1
Vignette: A copper futures curve shows the 1-month contract at $9,000 per tonne, the 3-month at $9,090 and the 6-month at $9,200. Inventories are high. Q1: What is the shape of the curve? Q2: Is the convenience yield likely high or low? Q3: What is the sign of the roll yield for a long investor?
Show the solution
- Q1: Prices rise with maturity: 9,000 < 9,090 < 9,200. This is contango.
- Q2: High inventories mean little benefit from holding extra physical, so convenience yield is low.
- Q3: In contango, the long sells a cheaper expiring contract and buys a dearer later one, so roll yield is negative, assuming spot is unchanged.
Answer: Contango; convenience yield is low; roll yield is negative.
Example 2
Vignette: A crude oil market has spot at $80. Over one year, interest costs are 4% of spot, storage costs are 3% of spot and convenience yield is 10% of spot. Using the simple approximation F₀ = S₀ × (1 + interest + storage − convenience yield), Q1: What is the one-year futures price? Q2: What is the curve shape? Q3: What does it imply about inventories?
Show the solution
- Q1: Net carry = 4% + 3% − 10% = −3%. F₀ = 80 × (1 − 0.03) = 80 × 0.97 = $77.60.
- Q2: The one-year futures price of 77.60 is below spot of 80, so the curve slopes down: backwardation.
- Q3: Convenience yield above interest plus storage typically signals tight inventories.
Answer: $77.60; backwardation; inventories are likely tight.
Exam tips
- Define the shape strictly by price comparison across maturities. Do not rely on market stories.
- Memorise the driver pairing: storage and interest favour contango; convenience yield favours backwardation.
- Check whether the vignette gives rates on a common basis before comparing them.
- Expect the roll yield sign to be tested here and in related return-component questions.
- Each item set has 4 questions answered from the vignette, so use the exhibit's prices and drivers, and eliminate any option that says convenience yield raises the futures price.
Futures Curves: Contango and Backwardation in other exams
The same ground in other exams, if you are preparing for more than one or want another angle on it.
Futures Curves: Contango and Backwardation: frequently asked questions
What is the difference between contango and backwardation?
In contango, futures prices rise with maturity, so the curve slopes up. In backwardation, futures prices fall with maturity, so the curve slopes down. The definition depends only on the shape of the curve.
How do storage costs affect the futures curve?
Higher storage costs raise the cost of carrying the physical commodity. That pushes longer-dated futures prices up and favours contango. They matter most for commodities that are costly to store.
What is convenience yield?
It is the benefit of holding the physical commodity instead of a futures contract, such as keeping production running. It tends to be high when inventories are low. A high convenience yield lowers futures prices relative to spot and favours backwardation.
Does contango mean the price will go up?
No. Contango describes the shape of the curve. It reflects carry costs, not a reliable forecast of future spot prices.