Commodity markets · RiskAtoms Academy

By the end you will be able to

1Explain the difference between spot and futures prices for a commodity, and how futures are traded and settled.
2Price a commodity future from spot, interest, storage cost and the convenience yield.
3Explain contango and backwardation and what each says about supply.
4Work out the cost or gain of rolling a futures position.

Why it matters

On 20 April 2020 the price of a barrel of US crude oil for May delivery fell below zero. Sellers paid buyers to take their oil. To see how that can happen, you need two ideas: futures, and the cost of storing something physical.

Core explanation

Things you can drop on your foot

Commodities are raw materials: energy (crude oil, natural gas), metals (gold, copper, aluminium), and agricultural products (wheat, coffee, cattle). Unlike a share or a bond, they are physical. They must be shipped, stored, insured, and sometimes they rot. That single fact explains most of what is special about their prices.

Spot and futures. The spot price is the price for delivery now. A futures contract fixes today the price for delivery on a later date. Commodity futures trade on exchanges such as CME Group in the US (for example WTI crude oil and grains), ICE (Brent crude) and the London Metal Exchange (copper, aluminium, nickel). Each contract has a set size and grade, for example 1,000 barrels of a given crude delivered at a given place. Most traders close their contracts before expiry; only a small share end in physical delivery. Lesson L1.7.03 explains how futures margins work.

Who uses them. An airline buys jet fuel futures to fix its fuel bill. A wheat farmer sells futures before harvest to lock in a price. A mining company sells copper forward. Traders and investors take the other side, and some funds hold commodity futures as an investment.

The cost of carry

Suppose you need oil in six months. You could buy it today and store it, or buy a six-month future. If you buy today, you pay interest on the money (or give up the interest you could have earned), and you pay for storage. So the future should cost about the spot price plus those costs. This is the cost of carry, the same “two routes must meet” logic as FX forwards in L1.6.02.

There is a twist. Owning the physical barrel has a benefit the future does not give: if supplies run short, a refinery that holds oil keeps running and a trader can sell into high prices. This benefit is the convenience yield. It pulls the futures price down. When supplies are plentiful it is close to zero; in a shortage it can be large.

Contango

Futures above spot

Plenty of supply, little convenience yield. Futures sit near spot plus the full cost of carry. Storing is rewarded.

Backwardation

Futures below spot

Tight supply, high convenience yield. Having the commodity now is worth more than the cost of carrying it.

The words describe the shape of the futures curve: the line of futures prices against delivery dates. A curve in contango slopes up; one in backwardation slopes down.

Rolling. Futures expire, so an investor who wants to stay exposed must roll: sell the expiring contract and buy the next. In contango the next contract costs more, so each roll loses a little; in backwardation it costs less, so rolling gains. This is why a fund tracking oil futures can lag the spot price of oil for long periods.

Not every commodity behaves the same. Gold is plentiful in vaults and cheap to store, so its curve sits close to full carry. Natural gas and electricity are hard to store, so their prices swing with the seasons. Crops have a harvest cycle.

Read the curve

Oil futures far above spot, and tankers anchored at sea, full of crude. What is going on?

Read the curve

Copper for delivery now is well above copper for delivery in three months. What does it tell you?

Read the curve

Natural gas for January delivery costs much more than for the following May.

Read the curve

A futures price above spot plus interest plus storage. Can that last?

The formal version

This extends the forward price from L1.6.02. Let $S$ be spot, $r$ the annual interest rate, $u$ the storage cost per unit per month, $y$ the convenience yield and $m$ the months to delivery. With simple interest:

F = \text{Spot} + \text{Financing} + \text{Storage} - \text{Convenience}

F = S + S \times r \times \tfrac{m}{12} + u \times m - S \times y \times \tfrac{m}{12}

F = S \times \left(1 + (r - y)\tfrac{m}{12}\right) + u \times m

Setting $y = 0$ gives the full-carry price, the ceiling on $F$ . A curve is in contango when $F > S$ and in backwardation when $F < S$ . Real contracts use exact days and, often, continuous compounding; the logic is the same.

Try it

Start with the glut. Raise the convenience yield slowly and find the point where the curve turns flat, then into backwardation. Then cut storage costs to zero and see how much of the contango was storage.

Try itFutures curve builder

Spot price ($/barrel)$70

Interest rate (a year)5.00%

Storage cost ($/barrel/month)$0.50

Convenience yield (a year)0.0%

Futures price by delivery month futures curve full carry (upper limit)

Curve shapecontango

Spot$70.00

6-month future$74.75

12-month future$79.50

12-month full carry$79.50

Futures above spot: the market pays you to store. Typical when stocks are plentiful.

F = S × (1 + (r − y) × months/12) + storage × months. Simple interest, a month taken as 1/12 of a year; real contracts use exact dates. Illustrative crude oil numbers.

Worked example

Six-month crude oil

Crude oil is $70.00 a barrel. Interest is 5.00% a year (simple, a month taken as 1/12 of a year) and storage costs $0.50 a barrel a month.

Pricing the six-month future

Step 1 of 5

1
Financing cost
$70 \times 0.05 \times 6/12 = 1.75$ dollars a barrel.

The roll in numbers

A fund holds 100 contracts of 1,000 barrels. At expiry it sells the old contract at $70.50 and buys the next at $71.20. The new position costs $70,000 more for the same oil. If spot oil does not move, the fund loses that amount each time it rolls in contango.

Regulatory lens

Because a few large traders could squeeze a physical market, regulators cap how big a position one trader may hold in some commodity derivatives: position limits, set by the Commodity Futures Trading Commission in the US and under MiFID II in the EU. Exchanges can also step in when trading becomes disorderly, as the LME did with nickel in 2022 (see Sparks).

Looking ahead: commodity price risk is one of the risk classes in the Basel market risk rules for banks, covered in later levels.

Sparks

SparkMinus $37.63

On 20 April 2020, the day before it expired, the May 2020 WTI crude oil future settled at minus $37.63 a barrel. Lockdowns had crushed demand, and storage at Cushing, Oklahoma, the contract's delivery point, was close to full. Holders who could not take delivery had to pay others to take the contract off their hands.

SparkThe nickel squeeze

In March 2022 nickel prices on the London Metal Exchange more than doubled within hours, briefly passing $100,000 a tonne, as traders with large short positions rushed to buy back. On 8 March the LME suspended trading and cancelled the trades done that day, a decision that was challenged in the courts.

Key takeaways

Commodities are physical: storing them costs money, and having them on hand can be valuable.
Futures fix a price today for later delivery; most are closed before expiry rather than delivered.
Futures price ≈ spot + financing + storage − convenience yield. Full carry is an upper limit.
Contango: futures above spot (plentiful supply). Backwardation: futures below spot (tight supply).
Rolling a long position costs money in contango and earns it in backwardation.

Reaction

Check what stuck

Glossary

Commodity: A raw material or basic product, such as oil, copper, wheat or gold, where one unit of a given grade is much like another.
Spot price: The price for delivery now, or within a few days.
Futures contract: An exchange-traded contract to buy or sell a set amount of a commodity on a set future date at a price agreed today.
Physical delivery: Settling a futures contract by actually handing over the commodity at an agreed place.
Cost of carry: The cost of holding a commodity until a future date: interest on the money tied up, plus storage and insurance.
Convenience yield: The benefit of having the physical commodity on hand, for example to keep a refinery running in a shortage. Expressed as a yearly % of spot.
Contango: Futures prices above spot, and rising with time to delivery. Usual when supply is plentiful.
Backwardation: Futures prices below spot, and falling with time to delivery. Usual when supply is tight.
Roll: Closing a futures contract that is about to expire and opening the next one, to keep a position going.

Deep Dives & Origins

Deep Dives

Hull, Options, Futures, and Other Derivatives, 11th edition (Pearson, 2021), the sections on commodity futures, storage costs and convenience yields. Intermediate.
Geman, Commodities and Commodity Derivatives (Wiley, 2005). Advanced.

Origins

Hull, Options, Futures, and Other Derivatives, 11th edition (Pearson, 2021).
US Commodity Futures Trading Commission, Interim Staff Report, Trading in NYMEX WTI Crude Oil Futures Contract Leading up to, on, and around April 20, 2020 (November 2020).
London Metal Exchange, notices on the suspension of nickel trading (March 2022), and the Independent Review of events in the nickel market in March 2022 (2023).

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