Basis, Contango & Backwardation: Reading the Curve

You now know what fixes the forward price (carry) and how it’s policed (arbitrage). This lesson zooms out from a single forward to the whole curve of futures prices across delivery months — and discovers that its shape has teeth. An upward-sloping curve quietly taxes anyone holding a long position over time; a downward-sloping one quietly pays them. There’s a famous case of an oil fund that lost money for years while oil itself rose, purely because of curve shape. By the end you’ll know exactly how that happens, and the two words every commodities trader lives by: contango and backwardation.

The basis: spot minus futures

Start with the gap between today’s spot and a futures price.

Definition. The basis is the difference between the spot price and the futures price: $\text{basis} = S_0 - F_0$ (conventions vary; we’ll use spot minus futures). It’s just the cost-of-carry wedge from last lesson, viewed as a single number. If carrying the asset is expensive (futures above spot), the basis is negative; if holding it is beneficial (futures below spot), the basis is positive.

The iron law — convergence. Whatever the basis is today, it must shrink to zero at expiry. On delivery day, “delivery now via the future” and “delivery now in the spot market” are the same transaction, so the futures price and the spot price must meet: $F_T = S_T$. The basis is a wedge that closes as expiry approaches — slowly at first, then snapping shut at the end. This convergence is guaranteed by arbitrage (if they didn’t converge, you’d buy the cheap one, sell the dear one, and pocket the gap at delivery), and it’s the engine behind everything else in this lesson.

Contango: the upward-sloping curve

Analogy. Contango is an escalator going up as you try to walk down it. Each month the price step you must buy is higher than the one you’re leaving — a built-in headwind for a long who keeps riding.

Definition. A market is in contango when futures prices are higher than spot, and farther-dated futures are higher still — an upward-sloping curve. This is the normal state for assets with positive net carry (financing + storage outweighing any convenience yield): gold, most equity indices, and well-supplied commodities. The curve slopes up because each extra month of delivery means another month of carry costs baked into the price.

Toggle the chart to Contango and you’ll see the curve climb away from spot, each delivery month dearer than the last:

Backwardation: the downward-sloping curve

Analogy. Backwardation is an escalator going down while you try to walk down it — it carries you along. Each month you roll into a cheaper contract, and the curve does some of your work for you.

Definition. A market is in backwardation when futures prices are lower than spot, and farther-dated futures lower still — a downward-sloping curve. It signals a high convenience yield: the market will pay a premium for the physical asset right now, typically because supply is tight (an oil shock, a harvest failure). The curve slopes down because the benefit of holding the asset today outweighs the cost of carrying it.

Toggle the chart to Backwardation to watch the curve fall away below spot — distant delivery is the bargain.

Roll yield: the cost (or gift) of staying in

Here’s where curve shape stops being trivia and starts moving your P&L. Futures expire, but exposures don’t — so a long-term holder must roll: close the expiring contract and open the next month’s. Curve shape decides whether that roll helps or hurts.

Definition. Roll yield is the return you earn (or lose) purely from rolling a futures position forward, holding spot constant.

• In contango, you roll by selling the cheaper expiring contract (which has converged down toward spot) and buying the pricier next month — selling low, buying high. The roll yield is negative: a steady bleed.
• In backwardation, you roll by selling the richer expiring contract and buying the cheaper next month — selling high, buying low. The roll yield is positive: a steady tailwind.

Worked example — bleeding in contango

Oil spot is $80, flat all year. The curve is in contango with each month $2 above the last. You’re long one contract (1,000 barrels) and roll monthly. Each roll, the contract you hold has converged toward spot ($80) while next month’s trades at $82, so you lose roughly $2/barrel = $2,000 per roll. Over 12 rolls, with spot unchanged, you’ve bled about $24,000 — entirely from curve shape, not from any move in oil. That’s the mechanism behind funds that lag spot in persistent contango.

Worked example — riding the tailwind in backwardation

Flip the curve: backwardation, each month $2 below the last, spot flat at $80. Now each roll sells the expiring contract (converged up toward $80) and buys next month at $78 — a $2/barrel gain, $2,000 per roll. Twelve rolls add about $24,000 of pure roll yield, again with spot dead flat. Same position, opposite curve, opposite outcome.

Basis risk: when your hedge doesn’t quite fit

One more consequence of the basis, this time for hedgers. Last lessons assumed a hedge perfectly offsets your exposure. In reality, the futures you use rarely match your actual risk exactly — different grade, different location, different date — so the basis between your asset and the contract can wander.

Definition. Basis risk is the risk that the basis (the gap between the price of the asset you’re hedging and the futures contract you’re hedging with) changes unpredictably before you close out. A hedge kills your exposure to the level of prices but leaves you exposed to the basis. The hedge is only as good as the correlation between your asset and the contract.

Worked example — the imperfect jet-fuel hedge

An airline wants to hedge jet fuel, but the liquid futures contract is on crude oil. They short crude futures to offset their fuel exposure. Crude and jet fuel usually move together — but not perfectly. If, over the hedge, jet fuel rises more than crude (the crack spread widens), the airline’s fuel bill climbs faster than its crude-futures hedge pays off, and they’re left with a residual loss. That leftover is basis risk: the hedge handled the big common move, but the gap between fuel and crude moved against them. The closer the contract matches your real exposure, the smaller this risk — which is one reason a perfectly-tailored forward (lesson 2) can beat a standardised future for a fussy hedger.

Putting it together

Zoom out from one forward to the whole curve and its shape becomes a force. The basis — spot minus futures — is the carry wedge, and arbitrage forces it to converge to zero at expiry. When the curve slopes up (contango, the positive-carry norm), a long who keeps rolling sells low and buys high every month, suffering a negative roll yield that can sink a fund even as spot rises. When it slopes down (backwardation, signalling a scarce-now asset), the roll pays the holder a positive yield. And because real hedges use contracts that don’t perfectly match the asset, basis risk — the wandering gap between your exposure and the contract — is the residual every hedger lives with. Here’s the curve on one card:

One mixed recap before we meet who’s actually using these things:

Key Takeaways