Commodities · M2 · 8 min
The futures curve: contango and backwardation
Work out a fair futures price from today’s price, and say what it means when later months cost more or less.
In the news: “The oil curve has flipped into contango” is the market saying stocks are building. This lesson shows why.
The essentials
- Spot and futures prices
- Spot is the price for delivery now; a futures price is agreed today for delivery later. Lined up by delivery month, futures prices form the futures curve.
- Cost of carry
- Interest on the money tied up in the commodity, plus storage and insurance. With spot at $100, interest at 5% and $3 of storage, oil for delivery in a year should cost about $108.
- Convenience yield
- The benefit of having the commodity on hand, such as keeping a refinery running. It is highest when stocks are scarce, and it comes off the futures price.
- Contango and backwardation
- In later months cost more than nearer ones, a sign of ample stocks. In the costs most, because stocks are scarce and buyers pay up to have the commodity now.
- Storage limits
- Buying spot, storing it and selling forward (cash and carry) caps contango only while there is space. When storage at Cushing ran short in April 2020, the expiring May contract settled at −$37.63 a barrel.
Cost of carry
F ≈ S × (1 + (r + u − y) × t)
- F
- futures price for delivery in t years
- S
- spot price
- r
- interest rate, % a year
- u
- storage cost, % of spot a year
- y
- convenience yield, % a year
- t
- time to delivery, in years
How it works
1. Buy now, or agree a price for later
Oil costs $100 a barrel today; that is the spot price. You need a barrel in a year. You can buy it now and keep it, or agree a price today to buy it in a year: a futures price. Buying now ties up $100 for a year, and you need somewhere to keep the oil.
2. Interest plus storage
With interest rates at 5%, the $100 costs you $5 of lost interest over a year. Say storing and insuring the barrel costs $3. Then oil delivered in a year should cost about $100 + $5 + $3 = $108. Those holding costs are the .
3. Why the price can’t stray far
Suppose the one-year future traded at $112 instead. You could buy oil at $100, pay $8 to carry it for a year, and sell it forward at $112: $4 a barrel with no price risk. This trade is cash and carry. Traders doing it push spot up and the future down until the profit disappears.
4. Having oil now is worth something
Sometimes the future trades below spot, which interest and storage can’t explain. A refinery that runs out of crude has to shut, so in a shortage having oil in the tank is worth paying for. That benefit is the , and it comes off the futures price.
5. The formula
Put the pieces together as yearly rates: F ≈ S × (1 + (r + u − y) × t). S is spot, r the interest rate, u storage as a share of the price, y the convenience yield and t the years to delivery. Spot $80, r 4%, u 6%, no y, six months: $80 × (1 + 10% × 0.5) = $84.
6. Contango: later costs more
Line up the futures prices for each delivery month and you get the futures curve. When each month costs more than the one before, the curve is in . It happens when stocks are plentiful: nobody pays extra for oil now, so later prices just add the cost of carry.
7. Backwardation: now costs more
When the nearest contract, the , costs more than later ones, the curve is in . Stocks are scarce, the convenience yield beats the cost of carry, and buyers pay up for oil now. A widening backwardation says stocks are being drawn down; a widening contango says they are filling up.
8. When storage runs out
Cash and carry limits contango only while there is space to store. In April 2020, as lockdowns cut demand, the tanks at , where futures are delivered, filled fast. Holders of the expiring May contract with nowhere to put the oil paid others to take it: on 20 April it settled at −$37.63 a barrel, while June settled at $20.43.
Try it
Move the sliders and watch the curve. Above the dashed spot line is contango; below it is backwardation.
Contango
Net carry r + u − y +8.00% a year
| Delivery | Price |
|---|---|
| Spot | $75.00 |
| 1 month | $75.50 |
| 2 months | $76.00 |
| 3 months | $76.50 |
| 4 months | $77.00 |
| 5 months | $77.50 |
| 6 months | $78.00 |
| 7 months | $78.50 |
| 8 months | $79.00 |
| 9 months | $79.50 |
| 10 months | $80.00 |
| 11 months | $80.50 |
| 12 months | $81.00 |
- 12-month future
- $81.00 (+8.0%)
- Roll, front to second
- −0.66% a month
- Roll, annualised
- −7.9%
- Roll plus interest on cash
- −3.9%
Worked example
Brent spot is $80.00 a barrel. Interest rates are 4% a year, storage costs $0.40 a barrel a month and there is no convenience yield. The six-month future trades at $84.50.
- Interest for six months: $80.00 × 4% × 6/12 = $1.60.
- Storage for six months: $0.40 × 6 = $2.40.
- Fair future: $80.00 + $1.60 + $2.40 = $84.00.
- The future at $84.50 is $0.50 above fair value.
- Buy spot, store it and sell the future: that locks in $0.50 a barrel.
Fair value is $84.00; at $84.50, cash and carry earns about $0.50 a barrel.
Check yourself
8 quick questions on the explanation above.
Practice
New numbers every set. Misses and guesses go into your review deck.
In the interview
Answer out loud in under a minute, then compare.
What does a backwardated oil curve tell you?
How did WTI go negative in 2020?
What’s convenience yield?
Remember
F ≈ S × (1 + (r + u − y) × t)
Contango says stocks are ample and storage is being paid for; backwardation says the market will pay to have the commodity now.
Sources
- Commodity Futures Trading Commission — CFTC Staff Publishes Interim Report on NYMEX WTI Crude Contract Trading on and around April 20, 2020
- US Energy Information Administration — Crude oil prices briefly traded below $0 in spring 2020 but have since been mostly flat
Definitions and maths are standard textbook material; dated facts link to the sources above. Worked numbers are illustrative.