Why would a refinery pay more for a barrel today than for one in June?
Because a refinery with no crude in the tank stops. And a stopped refinery is not a cheaper refinery — restarting a cracking unit costs real money and takes real days, contracts go unfilled, and the plant burns fixed costs the whole time.
A futures contract does not keep a refinery running. Only a barrel does.
Convenience yield, defined without jargon
Convenience yield is the benefit that accrues to whoever holds the physical commodity, and does not accrue to whoever holds a claim on it.
It is not mystical. It is operational, and you can list it:
- The ability to keep producing without interruption.
- The ability to meet an unexpected order, or a cold snap, or a customer who needs delivery this week.
- Insurance against a supply disruption you cannot see coming.
- Optionality: inventory can be sold now into a spike, and a June contract cannot.
Economists call this the theory of storage. The plainer statement is that inventory is a running option on your own operations, it has value, and that value belongs to whoever is holding the stuff.
It behaves exactly like a dividend
In the equity world, a dividend accrues to the holder of the share and not to the holder of the future, so the future trades below where financing alone would put it. Convenience yield does the same job for commodities:
F = S + financing + storage + insurance − convenience yield
Every other term is a cost of holding the physical. Convenience yield is a benefit of holding the physical. Same slot, opposite sign.
Putting a number on the invisible
Take the crude example again: spot $78.00, full carry over six months $4.55, and the six-month contract quoted at $76.00.
c = 78.00 + 4.55 − 76.00 = $6.55 a barrel over six months
As a rate: 6.55 ÷ 78.00 = 8.4% over six months, roughly 16.8% a year.
Nobody publishes that number. It is a residual — what is left over when the observable pieces of the arithmetic refuse to add up. That makes it the most informative quantity on the curve and the least trustworthy one, both at the same time, and Unit 4 makes that tension explicit.
Why it breaks the arbitrage — the one-sided bound
Here is the part that most explanations skip.
The upper bound is enforceable. If the deferred contract trades above full carry, buy spot, sell the future, rent a tank, deliver. Anyone with storage and credit can do it, so contango cannot run far past full carry for long.
The lower bound is not enforceable. To push a too-cheap deferred contract back up, you would run the trade in reverse: sell the physical short today, invest the proceeds, buy the cheap future, and take delivery later to close the short. But to sell a physical commodity short you must first borrow barrels — and the people holding barrels are holding them precisely because they need them to keep operating. There is no deep, liquid lending market in physical crude the way there is in shares. (The Short Selling & Securities Lending course in Fixed Income & Rates shows what a functioning borrow market looks like; physical commodities mostly do not have one.)
So the arbitrage that would cap backwardation simply cannot be executed at scale. The consequence is structural:
- Convenience yield can be as low as zero — you can always decline to enjoy a benefit.
- It has no upper limit — nothing stops a market from paying enormously for prompt physical.
- Therefore contango is bounded and backwardation is not.
The gold contrast, which proves the point
Gold curves sit at very close to full carry almost all of the time. Two reasons, both structural: above-ground stock is vast relative to annual consumption, so nobody is ever short of gold operationally; and gold genuinely does lend, with quoted lease rates. Both blades of the arbitrage work, so the model holds tightly.
Crude, gas, wheat and copper are the opposite: consumed, awkward to store, and not lendable. That is why their curves are messy — and why the mess is information.
Try it now
- Read today's crude price off the chart below and compute full carry six months out, exactly as you did last lesson. Then drop a Level at that computed number. The distance between your line and the price is what storage and financing alone say the six-month contract should cost.
- Now look up the exchange's actual six-month settlement and subtract. What is left over is the convenience yield — the part nobody stores their way out of. Repeat the whole exercise for gold, where the residual should come out close to zero.
- Write one sentence explaining the difference using the word borrow — not the word sentiment.