Commodity Future

Commodity futures are how the world puts a price on physical things. Each contract is an agreement to buy or sell a fixed amount of a raw material, of a fixed quality, on a fixed date. A thousand barrels of WTI crude oil. Five thousand bushels of wheat. A hundred ounces of gold. The terms are standard, so the contracts are interchangeable and easy to trade.

They were invented so that farmers and millers could agree a price before the harvest came in — in Chicago in the 1800s, and in Osaka for rice long before that. That is still what they are for. Producers sell futures to fix what they will earn. Users buy them to fix what they will pay. Speculators stand in the middle and carry the risk, in the hope of being paid for it.

Most of these contracts can end in actual delivery, at named warehouses, ports or pipelines. Hardly any of them do. But the fact that they could is what keeps the price honest: on the last day the contract has to be worth the same as the real barrel or the real bushel, or traders make free money until it is. April 2020 showed this at its most dramatic, when the oil price went below zero — buyers were paying to get out of taking delivery, because there was nowhere left to put the oil.

The forward curve tells the story

• Contango: later months pricier — the market pays for storage; typical when supply is ample.
• Backwardation: later months cheaper — immediate scarcity; owning physical now has value (the "convenience yield").
• Curve shape, not spot level, is the professionals' read on physical tightness.

Roll yield

Futures investors must roll expiring contracts. In contango, each roll buys dear and sells cheap — a systematic drag (why oil ETFs long underperform spot oil); in backwardation, rolling earns. Long-run commodity index returns are dominated by this, not by spot moves.

Hedgers vs. speculators

Commitments-of-Traders data shows the ecology: producers net short, index money net long. The normal backwardation hypothesis (Keynes): hedgers pay speculators an insurance premium, visible as positive expected roll returns in producer-hedged markets.

Pricing: storage arbitrage with a twist

with storage cost \(u\) and convenience yield \(y\) — the option-like value of holding physical inventory (keep the refinery running, meet a delivery). Unlike equities, \(y\) is unobservable and volatile: it's backed out of the curve and spikes with scarcity. Cash-and-carry arbitrage bounds only the contango side (storage is real and finite); backwardation has no arbitrage ceiling — scarcity can price anything.

Term-structure models

Two-factor models (Gibson–Schwartz: spot + mean-reverting convenience yield; Schwartz–Smith: short-term deviations + long-term equilibrium) capture the curve's dynamics for real-asset valuation and hedging. Seasonality (gas, power, agriculture) adds deterministic curve shape; power markets push further — non-storability breaks the arbitrage link entirely, making expectations + risk premia the whole price.

Spreads as the real market

• Calendar spreads: storage economics distilled (the "cash-and-carry" trade at full tanks = April 2020).
• Crack/crush/spark spreads: refinery, soybean and power-plant margins as tradable objects — processors hedge the spread, not the legs.
• Location/quality bases: WTI–Brent, hub differentials; pipeline shocks trade here.

Financialisation debates

Index-fund flows, position limits, and the empirical question of whether paper money moves physical prices — the literature says: levels rarely, curve shape and correlations measurably.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.