The commodity curve — course checkpoint

You arrived able to see that commodity curves slope. You leave able to say why, by how much, what holding a position through one costs, and what it reveals about storage.

Unit 1 — the storage model

A curve is a cross-section, not a time series. Its skeleton: F = S + financing + storage + insurance − convenience yield.

• House numbers: spot $78.00, financing 5%, storage $0.40 a barrel a month, insurance 0.5% → six-month full carry $4.55, ceiling $82.55.
• Convenience yield is the value of holding the physical good — the refinery that keeps running. It subtracts, like a dividend, and it is a residual.
• It breaks the arbitrage one way only: cash-and-carry enforces the ceiling, while the reverse trade needs borrowable physical, which mostly does not exist. Contango is capped, backwardation is not — and the cap floats up as storage gets dear, then vanishes when capacity runs out.

Unit 2 — contango and backwardation as outcomes

• Measure contango as percent of full carry: $82.55 is 100%, $80.30 is 51%, $78.60 is 13% — three physical situations, one adjective. A commodity curve is the price of storage, quoted in the commodity.
• Backwardation requires convenience yield > carry; a six-month contract at $74.50 implies $8.05 a barrel, near 20.6% annualised. Convenience yield is convex in inventory: high stocks → full carry, low stocks → backwardation.
• Seasonality is the same model on a calendar; the old-crop/new-crop boundary is no carry relationship at all.
• The curve is not a forecast: F = E[S] − risk premium, only the left side is observable, and normal backwardation (below expected spot) is a different claim from backwardation (below today's spot).

Unit 3 — the roll, and what it costs

A roll is one trade, a calendar spread across a published window. It books nothing on roll day and is paid over the following month by convergence. Spot flat at $80.00, each roll buying $81.50 into $80.00:

• Fixed one contract: −$1,500 × 12 = −$18,000, or −22.5% of an $80,000 notional.
• Resizing fund: −1.50 ÷ 81.50 = −1.84% a month → (1 − 0.0184)¹² ≈ −20.0%.
• Backwardated: buy at $78.50 → +1.91% a month → +25.5%. A 45-point swing from shape alone.

Roll return is not a fee — it is the storage bill, transferred. A fund holds contracts plus collateral, so its gap to spot is arithmetic: 0.800 × 1.05 × 0.9925 ≈ 0.834, a −16.6% year against flat spot, the fee the smallest term by an order of magnitude.

Unit 4 — reading the curve

• April 2020: the expiring WTI May contract settled at −$37.63 on 20 April — physical delivery at Cushing, working capacity near 76 million barrels, stocks around 55 million, and all remaining capacity already leased. Compulsory obligation, no bid, no executable cash-and-carry: the ceiling did not rise, it disappeared. Brent, waterborne and index-settled, did not go negative. A negative price is the market pricing disposal.
• Implied carry = [(F₂ ÷ F₁) − 1] × 12 ÷ months, then implied convenience yield = financing + storage + insurance − implied carry. A curve at 8.46% at the front and 5.73% at twelve months pays about $0.19 a barrel a month for near storage and nothing a year out.
• The calendar spread is the cleanest instrument on the board: two markets at an identical $78.00 flat price can be −$0.55 (comfortable) or +$0.80 (tight) on the prompt spread.

The card worth keeping

• F = S + financing + storage + insurance − convenience yield
• Percent of full carry = (F − S) ÷ full carry
• Implied carry = [(F₂ ÷ F₁) − 1] × 12 ÷ months
• Implied convenience yield = financing + storage + insurance − implied carry
• Monthly roll return = (converged price − entry price) ÷ entry price
• Compounded roll = (1 + monthly roll)¹²
• Total return factor = spot factor × roll factor × collateral factor × fee factor (the terms compound; adding them is close but wrong)

The one sentence to keep

A commodity curve is the price of storage and of prompt delivery, quoted in the commodity itself — and rolling a position through it turns that price into realised money, month after month, whatever spot does.

The framing, stated plainly

Everything here is education, not advice. This course contains no forecast of any commodity price, no view on any curve, and no suggestion that anyone hold or trade any instrument. The 2020 exchange-traded-product case is mechanics — how convergence generates a tracking gap — and neither a warning about nor an endorsement of any product. Commodity futures are leveraged contracts whose risks are covered in Leverage and liquidation; a curve is a thing to read, never a signal to act on. Figures were rounded illustrations, chosen so the arithmetic stays visible.

Before you sit it

Each of these is a minute at your desk. Any one that is not names the lesson to reopen first.

• Say what caps a commodity curve from above, and why nothing caps it from below — Why can't a barrel in December cost whatever the market feels like?
• Say what has to be true for December oil to cost less than today's — What has to be true for December oil to cost less than today's oil?
• Say why a long position bleeds while the spot price goes nowhere — Why does a long position bleed when the price goes nowhere?
• Say what the front spread tells you that the outright price does not — Why do traders watch the front spread more closely than the price?

Try it now

1. Pick one commodity and write six sentences: today's curve shape, its full carry, its contango as a percent of full carry, its implied convenience yield, the sign of its roll, and what its prompt spread says about inventories.
2. Verify each against the data in this course and the exchange's public settlement pages: the monthly spot series for the cash price, the continuous futures series for the rolled one (front-month crude, the most traded of them, is below) and the thirty-day SOFR average for the financing leg.

3. Then say the line this course was built around: the curve is a price list for storage — and the roll is the invoice.

Checkpoint quiz next.