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FRM Part I · FRM Exam Part I

Commodity Forwards and Futures for FRM Part I

Commodity forwards and futures fix a price today for delivery of a commodity later. You price them with cost of carry: F = S × e^((r + u − y) × T), where u is storage cost and y is convenience yield. Then you read the curve shape and measure hedge effectiveness and basis risk.

What this chapter covers

This chapter covers how commodity forwards and futures are priced, why their curves slope up or down, and how firms use them to hedge. It starts with contract basics, then builds the cost-of-carry pricing model. It then adds the features that make commodities different from financial assets: storage costs, convenience yield and lease rates.

The central idea is that the forward price is linked to the spot price by the cost of holding the physical commodity. Storage and financing push the forward price up. Convenience yield, the benefit of holding the physical good, pulls it down. The balance of these forces decides whether the curve is in contango or backwardation.

The chapter connects to other parts of the paper. The pricing logic is the same no-arbitrage reasoning you use for financial forwards and futures. The hedging section links to minimum-variance hedge ratios in Quantitative Analysis and to basis risk in Foundations of Risk Management. Questions are usually numerical, so you need to be quick with exponentials and continuous compounding.

Commodity pricing questions are formula-driven, short and predictable, so they are marks you can secure with practice. The same cost-of-carry logic also appears in other forward and futures chapters, so mastering it here pays off several times. Many questions test whether you understand the direction of effects, for example what happens to the forward price when convenience yield rises. Candidates who only memorise formulas lose these marks. Candidates who understand the economics gain them quickly.

Commodity Forwards and Futures: topics in the order to study them

  1. 1Commodity Forward and Futures BasicsYou need the contract terms, margining and the difference between forwards and futures before any pricing makes sense.
  2. 2Commodity Forward Pricing and Cost of CarryThis is the core pricing formula. Everything later in the chapter is an adjustment to it.
  3. 3Convenience YieldIt is the main extra term in the pricing formula, and it explains why commodities break the simple carry model.
  4. 4Contango and BackwardationOnce you know carry and convenience yield, you can explain why the curve slopes up or down.
  5. 5Commodity Lease Rates and Forward CurvesLease rates give another way to read the curve, since they act like the commodity's own dividend yield.
  6. 6Hedging with Commodity Futures and Basis RiskHedging applies everything above, so it comes last. It also brings in hedge ratios and the basis.

How to prepare Commodity Forwards and Futures

Treat this chapter as one pricing formula with a few moving parts, followed by an application. Practise numbers early, because the arithmetic is where marks are lost.

  1. Read the basics and write down in your own words how a forward differs from a futures contract, including daily settlement and counterparty risk.
  2. Learn the cost-of-carry formula in continuous form, F = S × e^((r + u − y) × T), and in the discrete form with storage costs added. Solve at least five examples by hand and with your calculator's e^x key.
  3. For each input (r, u, y, T), state in one sentence whether raising it raises or lowers F. Test yourself without notes.
  4. Link convenience yield and lease rate to curve shape. Practise reading a table of futures prices and saying whether it is contango or backwardation, and what that implies about y.
  5. Rearrange the formula to solve for implied convenience yield from observed spot and futures prices. Examiners often ask for this.
  6. Work through hedging problems: choose the number of contracts, compute the hedge result, and identify the basis at the start and end of the hedge.
  7. Finish with timed mixed sets of 10 questions. Review every wrong answer and note whether the error was conceptual or arithmetic.

Common mistakes in Commodity Forwards and Futures

  • Adding convenience yield to the forward price instead of subtracting it.

    Fix: Remember that holding the physical asset gives a benefit. Benefits reduce F, so y enters with a minus sign.

  • Mixing continuous and discrete compounding in the same calculation.

    Fix: Read the wording first. Use e^(rT) for continuous rates and (1 + r)^T for annual rates, and do not combine them.

  • Saying contango always means storage costs exceed convenience yield in a literal sense for every commodity.

    Fix: Say that contango is consistent with r + u exceeding y, and backwardation with y exceeding r + u, under the carry model.

  • Reversing the sign convention for basis.

    Fix: Use the definition given in the question or in the GARP reading, and check it before judging whether the basis strengthened or weakened.

  • Forgetting to scale the hedge by the hedge ratio and contract size.

    Fix: Compute h* first, then multiply by the exposure and divide by contract size. Round to a whole number of contracts only at the end.

  • Assuming a perfect hedge removes all risk.

    Fix: State that hedging replaces price risk with basis risk. The hedge is only perfect if the basis at close is known in advance.

Last-day revision: Commodity Forwards and Futures

  • Cost of carry (continuous): F = S × e^((r + u − y) × T), with u as storage cost rate and y as convenience yield.
  • Higher interest rates or storage costs raise the forward price; higher convenience yield lowers it.
  • Contango: futures prices rise with maturity, so F is above S.
  • Backwardation: futures prices fall with maturity, so F is below S.
  • Convenience yield is the benefit of holding the physical commodity, not the futures contract.
  • Implied convenience yield: y = r + u − ln(F ÷ S) ÷ T.
  • Futures are marked to market daily; forwards usually settle at maturity.
  • Basis = spot price of the asset being hedged − futures price.
  • Basis risk arises when the hedged asset and the futures contract do not move together perfectly.
  • A short hedge gains if the basis strengthens; a long hedge gains if it weakens.
  • Minimum-variance hedge ratio h* = ρ × σS ÷ σF.
  • Match contracts to exposure: number of contracts = h* × exposure ÷ contract size.

Commodity Forwards and Futures practice questions

Commodity Forwards and Futures in other exams

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

Commodity Forwards and Futures: frequently asked questions

What is the cost-of-carry formula for commodities?

In continuous compounding, F = S × e^((r + u − y) × T). Here S is the spot price, r the risk-free rate, u the storage cost rate, y the convenience yield and T the time to delivery in years. Check whether the question gives storage as a rate or as a fixed amount, because the formula changes.

What is the difference between contango and backwardation?

In contango, futures prices are higher for longer maturities. In backwardation, they are lower for longer maturities. The shape reflects the balance between financing and storage costs on one side and convenience yield on the other.

How do I find the implied convenience yield?

Rearrange the carry formula: y = r + u − ln(F ÷ S) ÷ T. Use the natural log key on your calculator. A higher observed futures price relative to spot gives a lower implied yield.

Why does basis risk matter for hedgers?

Hedgers use futures that may differ from their exposure in grade, location or maturity. The basis can change between the start and end of the hedge, so the hedge outcome is not fully certain. This leftover uncertainty is basis risk.

Are calculations heavy in this chapter?

They are moderate. Most questions need one formula, an exponential and careful reading of the inputs. Practise with your approved calculator so you do not lose time on exam day.