Futures term structure: what the price curve across expiries reveals about supply, demand, and carry
A futures market does not offer a single price—it offers a schedule of prices across different expiry dates for the same underlying. That schedule, the term structure (also called the forward curve), encodes whether maintaining a long futures position currently costs or earns money at each roll. For a systematic investor, reading the term structure correctly is not optional: it determines a meaningful component of long-run returns before a single directional bet is placed.
What the term structure is
The theoretical framework for futures term structure pricing was established by Black (1976) in The Pricing of Commodity Contracts, Journal of Financial Economics, which extended the Black-Scholes model to futures and formalised the cost-of-carry relationship between spot prices and futures prices across different maturities. Gorton and Rouwenhorst (2006) in Facts and Fantasies about Commodity Futures, Financial Analysts Journal, subsequently documented that the slope of the futures term structure—whether a commodity is in contango or backwardation—is a significant predictor of subsequent roll returns.
The futures term structure is the set of prices quoted for contracts with different expiry dates on the same underlying instrument. For crude oil, for example, there are simultaneously tradeable contracts expiring every month out to several years. Plotting those prices against their expiry dates produces the term structure.
An upward-sloping curve—where contracts further in time are priced higher than nearer ones—is called contango. A downward-sloping curve—where near-dated contracts are priced above further-dated ones—is called backwardation. Most real-world term structures are neither flat nor uniformly sloped. They can be steep in contango in the near months and flatten or invert for longer-dated expiries. The shape shifts continuously as supply-demand conditions, interest rates, storage availability, and seasonal factors change.
Two drivers: financial futures vs commodity futures
The forces that shape the term structure differ fundamentally between financial futures and commodity futures.
Financial futures. For equity index futures, government bond futures, and currency futures, the term structure is governed by the cost-of-carry model. The theoretical futures price is F ≈ S × (1 + r − d) × T, where S is the spot price, r is the risk-free rate, d is the dividend or yield on the underlying, and T is time to expiry in years. For equity index futures, this means the futures price should trade at a premium to spot when interest rates exceed dividend yields. In most interest-rate environments over the past decade, equity index futures have been in contango because central bank rates exceeded typical equity dividend yields. A three-month S&P 500 E-mini contract with a spot level of 5,000, a risk-free rate of 5%, and a dividend yield of 1.4% should theoretically trade at approximately 5,045—a 45-point premium that must be paid at each quarterly roll.
Commodity futures. The term structure is driven by the interplay of storage costs, convenience yield, and supply-demand fundamentals. Storage costs push the curve toward contango: if it costs money to store a barrel of oil or a bushel of wheat, the forward price must be higher than spot to cover those costs. Convenience yield pulls the curve toward backwardation: the benefit of physically possessing a commodity today—being able to sell it immediately if spot prices spike, or use it in production without waiting for delivery—has economic value not available to the holder of a futures contract. When convenience yield is high relative to storage costs, the curve is in backwardation. Agricultural commodities exhibit strong seasonal patterns in their term structure, reflecting the harvest cycle: prices for immediate delivery spike ahead of the harvest as inventories draw down, then fall as new supply arrives.
What the term structure tells you
The shape of the term structure has a direct and practical implication for any investor holding a long futures position through time: it determines the roll yield. A long position in a contango market loses money at each roll—the investor sells the expiring (lower-priced) contract and buys the next (higher-priced) one. A long position in a backwardated market earns money at each roll—the investor sells the expiring (higher-priced) contract and buys the next (lower-priced) one.
The total return from a long futures position therefore has three components: spot return (the change in the spot price), roll yield (positive in backwardation, negative in contango), and collateral yield (return on the cash posted as margin). In sustained contango markets, the roll yield can be large enough to turn a positive spot-price return into a negative total return. This is precisely what happened to many long-only commodity funds in crude oil during 2009–2011, when spot prices recovered but persistent contango eroded gains at each monthly roll.
Limitations
The term structure changes continuously and cannot be reliably predicted. A market may be in contango today and shift to backwardation within weeks if a supply disruption tightens spot availability. Systematic strategies that attempt to harvest roll yield by rotating into backwardated markets bear the risk that the term structure state changes after position entry.
The cost-of-carry relationship holds cleanly for financial futures under normal conditions but breaks down under liquidity stress. During market dislocations, futures can trade at discounts or premiums to their theoretical cost-of-carry value because of funding constraints, forced liquidations, or broken arbitrage. S&P 500 futures traded at a significant discount to spot for several days in March 2020, as selling pressure in futures outpaced the ability of arbitrageurs to buy futures and sell the index. The divergence corrected within days, but during the dislocation the spread was large enough to matter for any strategy relying on carry relationships.
Futures term structure in pfolio
pfolio displays the live term structure for futures instruments in the platform, allowing users to observe the current state of the forward curve before constructing a position. The continuous futures chain builder incorporates actual roll prices into the constructed price series, so term structure effects—positive roll yield in backwardated periods, negative roll yield in contango periods—are embedded in backtested performance rather than obscured by adjusted prices. This means what the backtest shows is what an investor following that roll schedule would have earned, roll costs included.
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