Commodity carry connects financing, storage timing and the benefit of available inventory to delivery prices. See why a USD 2 storage bill can cost more when prepaid.
Commodity carry
Commodity carry is the cost or benefit of maintaining exposure to a commodity over time, before the effect of an unexpected price change. For physical inventory, the starting point is the cash cost of financing, storing and protecting the goods, adjusted for any income and the benefit of having usable stock available. It helps explain why buying a commodity for delivery later need not cost the same as buying it in the spot market today.
The word carry needs a sign convention. A positive cost of carry is a burden on the holder; a positive net carry benefit is an advantage. A futures strategy’s quoted carry measure is also different from a warehouse’s cash budget. State which measure is being used before comparing commodities or strategies.
Start with a dated storage bill
Consider one unit of a fictional, storable commodity. Its spot price is USD 100 per unit. The holder can borrow for exactly one year at a 5% simple annual rate, and storage costs USD 2 per unit, payable at the end of that year. Assume no income, physical loss, insurance or other charges, and that the stored unit remains deliverable at the required grade and location.
Buying the unit with borrowed money creates a year-end debt of USD 105. The storage bill then adds USD 2:
100(1+0.05×1)+2=USD 107 per unit.
This is the terminal cash amount needed to fund the purchase and storage. It is not an observed forward quote or a prediction of the spot price.
If the same USD 2 storage charge must instead be paid today and financed, the initial loan is USD 102. Its year-end repayment is
(100+2)(1+0.05×1)=USD 107.10 per unit.
The extra USD 0.10 is interest on the prepaid storage charge. Treating every storage bill as an addition to today’s spot price would overstate the first case; adding every bill only at maturity would understate the second.
Synthetic one-unit commodity ledger: financing USD 100 at 5% for one year and paying USD 2 storage at maturity costs USD 107; financing USD 102 when storage is prepaid costs USD 107.10. The timing difference is USD 0.10 per unit.
Original synthetic payment timeline. All amounts are USD per physical unit, using one-year simple financing. The two rows differ only in the payment date of the storage charge.
Inventory supplies a service as well as a price exposure
A factory may need its physical input tomorrow. A forward contract delivering next year cannot keep production running tomorrow. That operational advantage of accessible inventory is called convenience yield. It is not generally a cash coupon that can simply be entered as a guaranteed receipt in the funding ledger. CME’s explanation links this benefit to keeping production running and to inventory scarcity. CME Group.
A common model for a storable commodity writes
F0,T=S0e(r+u−y)T,
where F0,T is today’s delivery price for time T, S0 is spot, r is financing, u is proportional storage cost and y is convenience yield. Here the rates are continuously compounded annualised model rates, and T is in years. This is a different convention from the simple-rate cash ledger above. The model treats storage as a proportional rate; it does not justify replacing a dated dollar bill by the same numerical percentage.
The formula organises the economics: financing and storage raise the cost of carrying stock, while the service from immediate inventory offsets that burden. An inferred convenience yield depends on the storage and funding assumptions used; prices alone do not reveal a directly paid yield.
When does carry constrain a forward price?
A feasible cash-and-carry trade buys the physical unit, stores it and sells it for future delivery. Under the fictional ledger’s assumptions, a contracted delivery receipt can be compared with the USD 107 total obligation. An apparent excess becomes an arbitrage claim only if executable quotes, committed financing, storage capacity, delivery eligibility, settlement and other costs support the entire trade.
The reverse direction is more demanding. A participant must be able to sell or borrow the physical commodity now and replace it later. Inventory owners may refuse to give up stock needed for production. Short availability and convenience benefits therefore matter to whether a two-sided pricing equality is defensible. A forward price below fully funded storage cost is not sufficient evidence of a free profit.
Commodity identity also matters: grade, location, quantity and delivery date must match. EIA’s natural-gas discussion shows how storage both absorbs surplus supply and supplies the market when demand is stronger. EIA. The unchanged-unit ledger cannot be applied automatically to perishables that lose deliverable quantity or quality. Electricity storage likewise requires actual technology, capacity and an allowance for energy losses; it is not equivalent to putting an unchanged unit in a warehouse. U.S. EPA.
For a worked introduction connecting these inputs to contract specifications and a producer’s hedge, see Commodities. The full lesson is available with a free signed-in account.
Carry is not realised futures profit
A futures contract gives price exposure without requiring the investor to own warehouse inventory. Its realised result depends on the position’s entry and exit prices, contract size and costs; collateral returns and margin funding also matter. Rolling positions adds another sequence of trades. A carry signal or a curve in contango or backwardation does not lock in the investor’s eventual return.
Sources
John C. Hull, Options, Futures, and Other Derivatives, 9th Global Edition, Pearson, 2018, Chapter 5, §§5.11–5.12, pp. 143–145: dated storage costs, consumption commodities, convenience yield and cost of carry.
