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CFA Level II Exam · Introduction to Commodities and Commodity Derivatives

Theories of Commodity Futures Returns for CFA Level II

Updated 7 October 2026 · Fact-checked

Three theories explain commodity futures prices and returns. Insurance theory says hedgers pay speculators a risk premium. The hedging pressure hypothesis says the premium depends on whether hedgers are net short or net long. The theory of storage links futures prices to storage costs and the convenience yield. Match the clue in the vignette to the theory.

Understand Theories of Commodity Futures Returns

A commodity futures contract is a bet on a future spot price. The question is whether the futures price is an unbiased forecast of that spot price, or whether it sits above or below it. If it sits away from the expected spot price, the long side earns a risk premium. The three theories give different reasons for that gap.

Insurance theory (also called normal backwardation, from Keynes) starts with producers. Producers want to lock in prices, so they sell futures. Speculators take the long side, and they must be paid for bearing price risk. So the futures price is set below the expected future spot price. Speculators then earn a positive return as the futures price converges up to the spot price. The curve is in normal backwardation: futures price below expected spot price. Note that this is a statement about futures versus expected spot, not about the shape of the futures curve itself.

The hedging pressure hypothesis extends this. Hedgers can be on either side. Producers tend to be net short hedgers. Consumers, such as airlines hedging fuel, tend to be net long hedgers. If hedgers are mostly short, speculators go long and earn a premium (normal backwardation). If hedgers are mostly long, speculators must go short, so the futures price is above the expected spot price. This is normal contango, and the long side earns a negative premium. The sign of the risk premium depends on the net hedger position. With net short hedgers, it gives the same result as insurance theory, but it is a separate and broader theory.

The theory of storage focuses on physical inventory instead of risk. Holding a commodity costs money for storage, insurance and financing. Holding it also gives a benefit, the convenience yield: the value of having the physical good on hand to avoid a stockout or to keep production running. In rate form, the futures price is F₀ = S₀ × (1 + r + c − y), where r is the interest rate, c is the storage cost rate and y is the convenience yield rate, all for the same period. The curve is in backwardation (F₀ < S₀) only when the convenience yield exceeds interest plus storage costs (y > r + c). It is in contango when y < r + c.

The convenience yield is high when inventories are low and falls when inventories are high. High inventory means a low convenience yield, so the futures price is above spot and the curve is in contango. Low inventory means a high convenience yield, and the curve can move to backwardation. This theory explains the shape of the curve, while the first two explain the risk premium.

Key formulas to remember

Theory of storage (cost of carry with convenience yield)
F₀ = S₀ × (1 + r + c − y)
Rates form: r, c and y are rates for the same period (interest, storage cost, convenience yield). In money terms, the discrete form is F₀ = S₀ × (1 + r) + FV(storage costs) − FV(convenience yield). Do not mix the two forms. Continuous form: F₀ = S₀ × e^((r + c − y)T). Backwardation (F₀ < S₀) needs y > r + c.
Insurance theory (normal backwardation)
Futures price < Expected future spot price
Hedgers are net short, speculators are net long and earn a positive risk premium.
Hedging pressure: net short hedgers
Futures price < Expected future spot price
Speculators are long and earn a positive premium.
Hedging pressure: net long hedgers
Futures price > Expected future spot price
Speculators are short. This is normal contango. The long side earns a negative premium.
Convenience yield and inventory
Low inventory → high convenience yield → backwardation if y > r + c; High inventory → low convenience yield → contango
Convenience yield is a benefit of holding the physical commodity, not of holding the futures.

How to solve Theories of Commodity Futures Returns questions

Use this method for any item set question on the theories of commodity futures returns.

  1. 1Identify what the question asks about: the risk premium (futures versus expected spot price) or the shape of the futures curve (futures versus spot price).
  2. 2Find the data in the vignette: who is hedging (producers or consumers), their net position, and inventory levels.
  3. 3If the clue is the net hedger position, use the hedging pressure hypothesis. Net short hedgers mean backwardation and a positive premium for the long side. Net long hedgers mean contango and a negative premium for the long side.
  4. 4If the clue is inventory, storage costs or convenience yield, use the theory of storage. Low inventory means high convenience yield, and backwardation when the yield exceeds interest plus storage costs. High inventory means contango.
  5. 5If the vignette says only that speculators are paid for taking on hedgers' risk, with producers hedging, use insurance theory.
  6. 6Check the direction of each comparison: futures versus expected spot for the risk premium, futures versus spot for the curve shape.
  7. 7Choose the option that matches the theory and the direction. Reject options that mix the two comparisons.

Quickest way: Clue-to-theory shortcut

When to use it: Use it when time is short and the answer options name a theory or a curve shape.

  1. Hedgers are named: think hedging pressure. Short hedgers mean the long side earns a premium.
  2. Inventory or convenience yield is named: think theory of storage. Low inventory means backwardation.
  3. Only producers hedging and speculators paid: think insurance theory, so futures are below expected spot.
  4. Write down the one-line result and match it to an option.

Common mistakes in Theories of Commodity Futures Returns

  • Treating backwardation as the same thing in all three theories.

    The word is used for two different comparisons: futures below expected spot (risk premium) and futures below spot (curve shape).

    Fix: Always ask what the futures price is being compared with. Expected spot relates to the risk premium theories. Spot price relates to the storage theory.

  • Saying insurance theory allows a negative premium for the long side.

    Candidates blend it with the hedging pressure hypothesis.

    Fix: Insurance theory assumes hedgers are net short, so the long speculator earns a positive premium. The possibility of a negative premium comes from hedging pressure.

  • Claiming a high convenience yield produces contango.

    Confusing the benefit of holding the physical with the cost of carry.

    Fix: Convenience yield reduces the futures price in the formula. A yield that exceeds interest plus storage costs means backwardation.

  • Assuming high inventory means high convenience yield.

    Thinking more stock means more benefit.

    Fix: Convenience yield is the value of having the commodity when it is scarce. Ample inventory makes it low.

  • Treating consumers as net short hedgers.

    Mixing up who needs to protect against rising prices.

    Fix: Consumers fear price rises, so they buy futures and are net long. Producers fear price falls, so they sell futures and are net short.

Worked examples

Example 1

A vignette says gold-mining firms and oil producers hold large net short futures positions to lock in prices. Speculators hold the offsetting long positions. Q1: Which theory best describes this? Q2: What is the relationship between the futures price and the expected spot price? Q3: What return do the long speculators expect from the premium? A) Positive B) Negative C) Zero

Show the solution
  1. Q1: Producers hedge by selling futures and speculators take the other side for compensation. That is insurance theory (normal backwardation). The hedging pressure hypothesis with net short hedgers gives the same result, but it is a separate theory.
  2. Q2: Speculators must be paid for bearing risk, so the futures price is below the expected spot price.
  3. Q3: As the futures price converges up to the expected spot price, long positions gain. The risk premium for the long side is positive.

Answer: Q1: insurance theory (normal backwardation); hedging pressure with net short hedgers gives the same result. Q2: futures price below expected spot price. Q3: A) Positive.

Example 2

A vignette on a copper market reports that inventories have fallen to very low levels and manufacturers say having metal on hand is highly valuable. Futures prices are below the spot price. Q1: What does the theory of storage say about the convenience yield? Q2: What does the below-spot futures price imply about the convenience yield relative to interest and storage costs? Q3: If inventories later rebuild to high levels, what happens to the convenience yield? A) Rises B) Falls C) Stays the same

Show the solution
  1. Q1: Low inventory makes physical stock valuable, so the convenience yield is high.
  2. Q2: In the rates form F₀ = S₀ × (1 + r + c − y), F₀ < S₀ only if y > r + c. Futures below spot is backwardation, so the convenience yield exceeds interest plus storage costs.
  3. Q3: Ample inventory lowers the value of holding extra stock, so the convenience yield falls. Once y drops below r + c, the curve moves to contango.

Answer: Q1: high convenience yield. Q2: the convenience yield exceeds interest plus storage costs (backwardation). Q3: B) Falls.

Exam tips

  • Read the question stem for what is being compared: futures versus expected spot, or futures versus spot.
  • Underline in the vignette who is hedging and whether they are net long or net short. That decides the sign of the premium.
  • Inventory words in the vignette point to the theory of storage and the curve shape.
  • Remember the theories are not exclusive. Storage explains curve shape and the others explain risk premiums.
  • There is no penalty for wrong answers, so answer every question.

Theories of Commodity Futures Returns in other exams

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

Theories of Commodity Futures Returns: frequently asked questions

What is the difference between the theory of storage and the hedging pressure hypothesis?

The theory of storage explains the futures curve through storage costs, interest and convenience yield tied to inventory. The hedging pressure hypothesis explains the risk premium through the net positions of hedgers. One is about physical stock, the other about who bears risk.

What is normal backwardation?

It is the condition where the futures price is below the expected future spot price, so long speculators earn a positive risk premium. It arises when hedgers are net short. It is a different idea from a downward sloping futures curve.

When do long speculators earn a negative risk premium?

When hedgers are mostly net long, such as consumers buying futures to protect against rising prices. Speculators must then go short, and the futures price is above the expected spot price. This is normal contango under the hedging pressure hypothesis.

How does convenience yield affect the futures price?

Convenience yield is a benefit of holding the physical commodity and it lowers the futures price relative to spot. Futures fall below spot (backwardation) when the yield exceeds interest plus storage costs, which is usually when inventories are low. A lower yield leads to contango.