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FRM Exam Part I · Commodity Forwards and Futures

Contango and Backwardation: Roll Yield Explained

Updated 11 October 2026 · Fact-checked

Contango means the commodity forward curve slopes upward: longer-dated futures cost more than spot. Backwardation means it slopes downward. When the curve is in contango, a long investor who rolls futures tends to lose roll yield. In backwardation, rolling tends to earn a positive roll yield. Compare the near and far prices to find the sign.

Understand Contango and Backwardation

A forward curve (or futures curve) plots futures prices against maturity for the same commodity. Its shape tells you how the market prices the future relative to today.

Contango means the curve slopes upward: F(T) > spot, and later contracts cost more than earlier ones. Backwardation means the curve slopes downward: F(T) < spot, and later contracts cost less. A flat curve is neither.

The shape comes from the cost-of-carry model with convenience yield. Storage, financing and insurance costs push the curve up. Convenience yield, the benefit of holding the physical commodity, pushes it down. When inventories are plentiful, convenience yield is low and the curve tends towards contango. When inventories are scarce, convenience yield is high and the curve tends towards backwardation. Expectations about future supply and demand also matter, and in the exam you should link shape to inventory levels.

The shape matters for investors because of roll yield. Most futures investors do not take delivery. They sell the expiring contract and buy the next one. In contango, you sell the near contract at a lower price and buy the far one at a higher price. That is a drag on returns, even if spot is unchanged. In backwardation, you sell high and buy lower, which adds to returns.

The total return on a futures position has parts: the change in the futures price (driven by spot moves and curve changes), the roll yield, and the collateral return if the position is fully collateralised. Do not confuse roll yield with the spot price change.

Key formulas to remember

Contango
F(T₂) > F(T₁) > S (upward-sloping curve)
Futures prices rise with maturity. Typical when carry costs dominate and inventories are high.
Backwardation
F(T₂) < F(T₁) < S (downward-sloping curve)
Futures prices fall with maturity. Typical when convenience yield is high and inventories are low.
Cost of carry with convenience yield
F = S × e^((r + u − y) × T)
r = risk-free rate, u = storage cost rate, y = convenience yield, all continuously compounded. Contango if r + u > y; backwardation if r + u < y.
Roll yield (per roll, long position)
Roll yield = (Price of expiring contract − Price of next contract) ÷ Price of expiring contract
Positive in backwardation, negative in contango. This is a common simple definition; some texts use the spot-futures difference, so follow the question's wording.
Futures return decomposition
Total return ≈ Spot return + Roll yield + Collateral return
For a fully collateralised long futures position. Roll yield is the part due to curve shape.

How to solve Contango and Backwardation questions

Use this method for any question on curve shape, its drivers or roll returns.

  1. 1Read the prices. Line up spot and futures prices by maturity from nearest to farthest.
  2. 2Classify the curve. Rising prices mean contango. Falling prices mean backwardation.
  3. 3Name the driver. High carry costs and ample inventory point to contango. Scarcity and high convenience yield point to backwardation.
  4. 4If the question gives r, u and y, compute r + u − y. A positive value means contango, a negative value means backwardation.
  5. 5For roll yield, identify the position (long or short) and the contracts being sold and bought.
  6. 6Compute the roll as (expiring price − new price) ÷ expiring price for a long position. Flip the sign for a short.
  7. 7Add any spot or curve change and the collateral return if asked for total return.
  8. 8Check the sign against the curve shape: contango should give a negative roll for longs.

Quickest way: Sign check in ten seconds

When to use it: Use it on multiple-choice questions that ask which curve shape or which roll sign applies, before you do any arithmetic.

  1. Compare the far price with the near price. Far higher means contango.
  2. Long investor in contango: roll yield is negative. Long in backwardation: positive.
  3. Short investor: reverse the sign.
  4. Eliminate options that pair contango with positive roll yield for a long.
  5. Only then calculate the number if the question asks for one.

Common mistakes in Contango and Backwardation

  • Saying contango always means futures prices are expected to rise

    The upward slope looks like a forecast.

    Fix: The curve reflects carry costs and convenience yield. It is not a pure forecast of spot prices. Futures converge to spot at expiry.

  • Treating roll yield as a loss in any contango market regardless of position

    Students memorise 'contango is bad'.

    Fix: It is bad for long investors who roll. Short positions gain a positive roll yield in contango.

  • Mixing up the cause of backwardation

    Convenience yield is abstract.

    Fix: Remember: scarce inventory makes holding the physical valuable, so convenience yield is high and the curve falls.

  • Confusing roll yield with the change in spot price

    Both affect futures returns.

    Fix: Roll yield comes from the price gap between contracts. Spot change is separate. Compute them separately.

  • Getting the sign of r + u − y wrong

    Convenience yield is subtracted, but students add it.

    Fix: Carry costs raise the forward price and convenience yield lowers it. Use F = S × e^((r + u − y)T).

Worked examples

Example 1

Crude oil spot is $80.00. The one-month futures price is $80.80 and the two-month futures price is $81.40. An investor is long the one-month contract and rolls it into the two-month contract at expiry, when the one-month price has converged to the spot price, assumed to be $80.80. What is the roll yield for this roll, using (expiring − new) ÷ expiring, and what is the curve shape?

Show the solution
  1. Curve shape: 80.00 < 80.80 < 81.40, so prices rise with maturity. This is contango.
  2. Expiring contract price at roll = $80.80.
  3. New contract price = $81.40.
  4. Roll yield = (80.80 − 81.40) ÷ 80.80 = −0.60 ÷ 80.80.
  5. −0.60 ÷ 80.80 = −0.00743, or about −0.74%.

Answer: Contango; roll yield ≈ −0.74% for the long investor.

Example 2

A commodity has spot price $50. The risk-free rate is 4% a year, storage costs are 2% a year and the convenience yield is 9% a year, all continuously compounded. What is the one-year forward price, and is the curve in contango or backwardation?

Show the solution
  1. Net carry = r + u − y = 0.04 + 0.02 − 0.09 = −0.03.
  2. F = 50 × e^(−0.03 × 1).
  3. e^(−0.03) ≈ 0.97045.
  4. F = 50 × 0.97045 ≈ 48.52.
  5. F (48.52) is below spot (50), so the curve slopes downward.

Answer: Forward price ≈ $48.52; the market is in backwardation because convenience yield exceeds r + u.

Exam tips

  • Questions often give prices at several maturities. Read the slope first, then decide the sign of roll yield.
  • Know both directions: curve shape to roll sign, and inventory level to curve shape.
  • When a formula uses e^((r + u − y)T), check whether rates are continuous. FRM questions usually say so.
  • Watch the position. A short futures investor earns the opposite roll yield to a long.
  • Read the roll yield definition in the question. Use it exactly as given.

Practice questions from Commodity Forwards and Futures

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.

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 upward. In backwardation, futures prices fall with maturity, so the curve slopes downward. The shapes are linked to carry costs and convenience yield.

What causes backwardation in commodity markets?

A high convenience yield, usually because inventories are scarce or users need the physical commodity now. When the convenience yield exceeds the interest and storage costs, the forward price falls below spot.

What is roll yield in commodity futures?

It is the return from rolling an expiring contract into a later one when the two have different prices. A long investor earns a positive roll yield in backwardation and a negative one in contango.

Does contango mean the price will go up?

Not necessarily. The upward slope mainly reflects the cost of carrying the commodity. Futures prices converge to spot at maturity, so a contango curve does not by itself forecast a rising spot price.