Understanding Cost of Carry: Key Definitions, Models, and Factors

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Cost of carry is the net cost of holding an asset over a period: financing (interest on the money tied up or borrowed), storage and insurance for physical goods, minus any income or benefit the asset provides while you hold it, such as dividends, coupons or convenience yield. In futures and forward markets, it links the spot (cash) price to the futures price. In direct investing, it is the set of holding costs that turns a gross return into a net one.

How Cost of Carry Works

Holding an asset ties up capital that could earn interest elsewhere, and physical goods must be stored and insured. Offsetting this, some assets pay income while held, and a physical commodity can carry a convenience yield: the benefit of having inventory on hand (for example, a refiner that avoids a production shutdown).

The net figure can be positive or negative. A positive net carry pushes the futures price above spot (contango). A negative one, often from a high convenience yield or high asset income, can push the futures price below spot (backwardation).

The Cost of Carry Formula

With continuous compounding, the futures cost of carry model is:

F = S × e^((r + s − c) × t)

• F = theoretical futures (or forward) price
• S = spot price
• e = base of natural logarithms (about 2.718)
• r = risk-free interest rate, annual
• s = storage cost as an annual percentage of spot
• c = convenience yield, annual
• t = time to delivery in years

The exponential form comes from replication: borrow S at r, buy the asset and hold it to delivery. Financing and storage grow the position’s cost continuously at r + s, while the benefit of holding offsets it at c. A forward delivering the same asset on the same date must cost the same, or there is a free profit. For a stock index, replace s − c with −q (the dividend yield). With simple annual compounding, F ≈ S × (1 + r + s − c)^t.

Worked example (hypothetical)

Assumptions: spot gold-style commodity at $100, r = 4%, s = 1%, c = 0.5%, six months to delivery (t = 0.5).

• Net carry rate: 4% + 1% − 0.5% = 4.5%
• Exponent: 0.045 × 0.5 = 0.0225
• F = 100 × e^0.0225 ≈ 100 × 1.02276 ≈ $102.28

When the Cash Price and Futures Price Don’t Match the Carry

The basis is the gap between the cash and futures prices (often quoted as spot minus futures, though conventions vary). Under the basis-of-carry view, the theoretical basis equals the net cost of carry. When the market basis departs from it, one side is mispriced.

Futures price greater than spot plus cost of carry (cash-and-carry): using the example, suppose the futures trades at $104. Buy the asset at $100 with borrowed money, pay storage and short the futures at $104. At delivery you hand over the asset for $104 against a total carry-inclusive cost of about $102.28, locking in roughly $1.72 per unit before commissions and fees.

Futures price below spot plus cost of carry (reverse cash-and-carry): suppose the futures trades at $101, so the cash asset is rich. Short the asset at $100, invest the proceeds at r, avoid storage, and buy the futures at $101. At delivery you take the asset back for $101, while the proceeds and avoided storage are worth about $102.28 net of the forgone convenience yield. The trade requires shorting or borrowing the physical asset. This is why commodities with a high convenience yield can stay in backwardation: holders will not give up inventory cheaply.

Because borrowing and lending rates differ and every leg costs money, these trades only pay outside a band around the theoretical price.

Cost of Carry in Forex and Bonds

For currencies, the carry is the interest rate differential, and the model becomes covered interest parity:

F = S × e^((r_quote − r_base) × t)

Hypothetical: EUR/USD spot 1.1000, USD rate 5%, EUR rate 3%, one year. F = 1.1000 × e^0.02 ≈ 1.1222. The currency with the higher interest rate trades at a forward discount. In spot forex, the same differential appears as the overnight rollover or swap charged or credited on positions held past the daily cut-off.

For a bond future, carry is the coupon income earned on the bond minus the repo (financing) cost of holding it. When coupon income exceeds financing, carry is positive and the futures price sits below the cash bond price after conversion-factor adjustments.

Carrying Costs and Net Returns

Outside futures pricing, carry is what separates gross from net returns on a held position:

• Margin interest: buying on margin is borrowing, so interest reduces the return.
• Short selling: a short seller pays the dividends of the borrowed shares plus any borrow fee.
• Other borrowing: any loan-funded investment carries its interest cost.
• Storage and insurance: relevant for physical metals, grain or energy.

Marginal carry is the carry of one additional unit or period: (r + s − c) × S × Δt for an added period, or per unit for an added position. It helps when deciding whether to roll or extend a holding.

Cost of Carry vs. Related Terms

• Cost of carry vs. futures price: carry is an input, and the futures price is the output after carry is applied to spot.
• Cost of carry vs. carry trade: a carry trade is a strategy, typically borrowing a low-rate currency to hold a high-rate one, betting the spot rate won’t offset the differential. A forward hedge removes the profit, because the forward already prices in the carry.
• Cost of carry vs. option pricing: models such as Black-Scholes include carry through the rate and dividend inputs, but option value also depends on volatility.

Limitations

The model assumes frictionless markets, borrowing and lending at a single risk-free rate, and free short selling. Convenience yield cannot be observed directly and is usually backed out of market prices. Dividend and storage costs can change during the contract. Some assets, such as electricity, cannot be stored at all, so the replication argument breaks down and futures prices reflect expected supply and demand instead.

The Bottom Line

Cost of carry matters to futures traders, forex traders holding positions overnight, and investors using margin or short sales. It explains where futures and forward prices should sit relative to spot and shows how holding costs turn gross returns into net ones. Arbitrage only pays outside a band set by fees and differing rates, and the model breaks down for assets like electricity that cannot be stored.