Define the two curve shapes precisely, because loose definitions are exactly where errors creep in. Line up a commodity's futures contracts by delivery month and look at price versus time-to-delivery:
- Contango: the futures curve slopes upward with maturity, a longer-dated contract costs more than a nearer-dated one (near month cheaper, far month pricier). Rolling a long position, selling the cheaper expiring contract, buying the pricier next one, means selling low and buying high, a cost each time you roll. This produces a negative roll yield.
- Backwardation: the futures curve slopes downward with maturity, a longer-dated contract is cheaper than the nearer one. Rolling now means selling the pricier expiring contract and buying the cheaper next one, selling high, buying low, a gain each roll. This produces a positive roll yield.
Roll yield formula and what shapes the curve
A clean, snapshot way to compute the roll yield captured at any single roll event, matching the sign convention above exactly:
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Roll Yield (per roll) ≈ (F_near − F_far) / F_near
In contango, F_far > F_near, so this comes out negative (a cost); in backwardation, F_far < F_near, so it comes out positive (a gain), exactly matching the two bullets above, and exactly matching the Spot-vs-ER decomposition in commodities as an asset class, which is the same fact viewed from the index-level side rather than the single-roll side.
Why does the curve take one shape or the other? Two complementary explanations, both worth carrying, because they answer slightly different questions.
The cost-of-carry / convenience-yield model answers "what should the fair futures price be, given the economics of holding the physical good instead." A textbook cost-of-carry relationship: F ≈ S × [1 + (r + u − y) × T], where S is the spot price, r is the financing (risk-free) rate, u is the storage-and-insurance cost, y is the convenience yield, the benefit of holding the physical good rather than a paper claim on it (not running out of crude at a refinery; not missing a delivery deadline). If r + u > y (financing and storage costs dominate any benefit of physical possession), the curve is in contango, this is the normal state for storable financial assets like gold, whose convenience yield is close to zero (nobody "needs" physical gold on hand the way a refiner needs crude), so r + u − y stays reliably positive. If y > r + u (physical possession is valuable enough (because inventories are tight and running out would be costly), the curve flips into backwardation) this is common in tightly supplied industrial and energy commodities during periods of low inventory, because the convenience yield of having the barrel now outweighs the carrying cost of holding the paper claim instead.
What is Keynes's theory of normal backwardation?
Keynes's theory of normal backwardation (extended by later work into the hedging-pressure hypothesis) answers a different question: "who is on the other side of the trade, and what do they have to pay for it." Keynes's original story: commodity producers are natural hedgers who want to sell forward to lock in a price, so they are net short futures; to induce speculators to take the other (long) side and bear the price risk, the futures price must sit below the expected future spot price, a long futures holder earns a risk premium for providing that insurance, which shows up as the curve trending toward spot over time (i.e., backwardation, on average, is "normal"). The hedging-pressure extension makes the theory more honest: the sign of the risk premium depends on who dominates the hedging demand in a given market, not always producers. In some markets the consumers are the dominant natural hedgers, an airline hedging jet-fuel costs by going long futures, for instance, which flips the logic: consumers, not producers, are paying to offload risk, and the curve tends toward contango instead, with the long side (the consumer-hedgers) paying the premium rather than collecting it. Neither theory is "the" answer, they describe the same curve shape from the financing-and-storage side and the who-needs-insurance side respectively, and a careful analyst checks both before asserting why a given commodity's curve looks the way it does.
Has the curve shape changed over time?
One durable, sobering empirical fact worth carrying forward, honestly dated: many commodities (especially energy and some industrial metals) spent long historical stretches in backwardation through the twentieth century, which is exactly why "normal backwardation" earned its name and why early commodity-index investors (pre-2000s) collected a positive average roll yield as a matter of course. The so-called financialization of commodities era, roughly from the mid-2000s onward, coincided with far more persistent contango in several major commodities (crude oil prominently among them, especially around periods of storage gluts), turning the roll yield from a tailwind into a headwind for long-only index investors in some regimes. Treat this as a real historical pattern, not a law of nature, the sign of roll yield is a function of physical market conditions and hedging demand at a point in time, and it can and does flip; anyone asserting "commodities always/never earn positive roll yield" has skipped exactly the mechanism this section just built.
{
"skill": "Reading a commodity fund's or CTA strategy's marketing claim about roll yield or 'normal backwardation' without accepting it on tone alone",
"use": "Have a chat assistant draft a first-pass explanation of why a specific commodity's futures curve is shaped the way it currently is (cost-of-carry drivers vs hedging-pressure drivers), then use the explanation as a checklist of what to verify against the actual curve and inventory data — never as the verdict itself.",
"tools": ["Chat assistants — Claude, ChatGPT, for a first-pass mechanism explanation", "Exchange/data terminals — CME Group's own settlement and curve data, MCX's contract data, or a Bloomberg/Refinitiv terminal for the actual quoted curve"],
"prompt": "Explain why <COMMODITY>'s futures curve is currently in <contango/backwardation>, using both the cost-of-carry/convenience-yield model and Keynes's hedging-pressure framework. State which explanation is more likely dominant right now and what inventory or hedging-flow data would confirm it. Flag if you are not certain of the current curve shape.",
"verify": "Pull the actual current futures settlement prices for at least two contract months directly from the exchange (CME/NYMEX for US contracts, MCX for Indian ones) and compute the roll yield yourself using (F_near-F_far)/F_near — do not accept the model's claimed curve shape or 'current' inventory levels, both of which may be stale relative to its training cutoff (Guardrail #4, Date-check, applies with force here because curves move daily).",
"diy": "You must already be able to define contango/backwardation by curve shape and compute roll yield from two prices by hand — this section. AI can accelerate drafting the 'why', but the curve itself and the sign of the roll yield must be read off real, current, verified prices, not recalled from memory.",
"market": "US"
}