Why can't a barrel in December cost whatever the market feels like?

Because there are two ways to have a barrel in six months' time, and if one is cheaper than the other, someone will do both.

• Route A. Buy a barrel today at spot, borrow the money to pay for it, rent a tank, insure the contents, and sit there for six months.
• Route B. Buy the six-month futures contract, leave your cash on deposit, and take delivery in six months.

Both routes end in exactly the same place: you, holding a barrel, in six months. So the price of Route B cannot wander far from the all-in cost of Route A. That cost has a name — cost of carry — and it is the entire skeleton of a commodity curve.

The relationship, written out in full

F = S + financing + storage + insurance − convenience yield

Every term is a real cash cost or benefit of holding the physical good:

• S — today's spot price, the money you tie up on day one.
• Financing — interest on that money for the holding period: S × r × t.
• Storage — tank rental, warehouse rent, elevator charges, gas injection and withdrawal fees. Quoted per unit per month in most physical markets.
• Insurance — cover on the value of the inventory, usually a small annual percentage.
• Convenience yield — the benefit of having the physical good on hand rather than a promise of it. This is the term that does not behave, and it gets the next lesson to itself.

Note the signs. The first three all push the deferred price up. The last one pushes it down, exactly the way a dividend pushes an equity future below where financing alone would put it.

Worked: crude oil, six months out

• Spot S = $78.00 a barrel
• Financing r = 5.0% a year, t = 0.5 years → 78.00 × 0.05 × 0.5 = $1.95
• Storage quoted at $0.40 per barrel per month → 6 × 0.40 = $2.40
• Insurance 0.5% a year on value → 78.00 × 0.005 × 0.5 = $0.20
• Convenience yield: assume zero for now

Full carry = 1.95 + 2.40 + 0.20 = $4.55, and F = 78.00 + 4.55 = $82.55.

That is roughly $0.76 a barrel a month, and it is the number the rest of this course keeps returning to.

Watch the arbitrage bite

Suppose the six-month contract trades at $85.00 instead. Then anyone with tank space and a credit line does this, today, all at once:

• Buy a barrel at spot: −$78.00
• Sell the six-month future at $85.00
• Pay six months of carry: −$4.55
• Deliver the stored barrel into the contract in six months: +$85.00

Locked in, before frictions: 85.00 − 78.00 − 4.55 = $2.45 a barrel, or $2,450 on a 1,000-barrel contract, with no exposure to what oil does in between. This is the cash-and-carry trade, and it is not exotic — it is the day job of physical trading houses, refiners with spare tankage and storage operators. The moment a curve offers more than full carry, storage gets hired and the trade gets done, which sells the deferred contract and bids up spot until the gap closes.

So $82.55 is not a prediction. It is a ceiling, enforced by anyone who owns a tank.

Where the model breaks

Now run it the other way. Suppose the six-month contract trades at $76.00 — below spot. Plug it in:

76.00 = 78.00 + 4.55 − c → c = $6.55

The arithmetic says something is subtracting $6.55 a barrel over six months, and no cost line explains it. That residual is the convenience yield, and it is where the commodity curve stops behaving like an index curve.

In the data

The financing term is the one piece of full carry that is published every day. The latest thirty-day average of SOFR, the dollar secured lending rate, is below.

It read 3.73% on 28 September 2026. Check what kind of rate a benchmark is before you use it: this one is a trailing average, other SOFR figures are single nights, and one is a compounded index near 1.26 that is not a rate at all. Storage and insurance are not published anywhere in daily data, which is why full carry is always part observed and part assumed.

Try it now

1. Financing is the thirty-day SOFR average above; spot is WTI at Cushing, below. Compare the two dates, then redo the financing line of the worked example with them: spot × rate ÷ 100 × 0.5 for a six-month hold.

2. Add storage at the worked example's $0.40 a barrel a month and insurance at half a percent a year on today's spot. No public daily series carries storage costs, so that $0.40 is an assumption and should be written down as one. You now have full carry, and today's ceiling is spot plus it.
3. Compare your number to the actual six-month contract on the exchange's settlement page. Whatever the arithmetic cannot explain is the interesting part, and it has a name.