Cost of Carry, Explained

Financing, storage, and yield in one number.

Cost of carry is the net cost of holding an asset from today to some future delivery date. It sounds simple, but it is the single number that links a spot price to a futures price — and understanding it precisely is the difference between knowing why a curve is shaped the way it is and just reading it. Every futures pricing calculator is ultimately an implementation of the cost-of-carry model. Get the carry right and the fair value follows mechanically; misread it and every relative-value judgment built on top is off.

The cost-of-carry formula

The theoretical futures price under continuous compounding is:

F = S · e^{(r + u − q)T}

where S is the current spot price, r is the continuously compounded risk-free rate, u is the continuously compounded storage or carrying cost, q is the continuously compounded income or yield paid by the asset, and T is time to delivery in years. The exponent (r + u − q) is the net cost of carry. When it is positive, futures trade above spot — contango. When it is negative, futures trade below spot — backwardation.

The intuition is arbitrage. If you could buy the spot asset today, finance the purchase, pay any carrying costs, collect any income, and deliver at expiration, the breakeven delivery price is exactly F. Any other futures price creates a riskless profit for someone with access to the financing and the physical asset.

Components by asset class

The terms inside the exponent change their character depending on what you are holding.

• Equities. Storage is negligible. Income is the continuous dividend yield q. Net carry = r − q. When dividend yield is below the risk-free rate, carry is positive and the futures price exceeds spot. When yields are high relative to rates — common in certain markets — the index future can trade at a discount to spot.
• Commodities. Storage costs are real and material — warehousing, insurance, spoilage. There is no dividend, but there can be a convenience yield: the implicit value to a holder of having physical supply on hand (refinery throughput, delivery certainty). Net carry = r + u − convenience yield. When convenience yield dominates, carry turns negative and backwardation results.
• Foreign exchange. The cost of carry for a currency pair is the interest rate differential. Holding foreign currency earns the foreign rate r_f while you finance in the domestic rate r_d. The covered interest parity relation gives F = S · e^{(r_d − r_f)T}. If the domestic rate exceeds the foreign rate, the forward rate is above spot; if below, the forward is at a discount — this is precisely what carry trades exploit when they assume parity holds imperfectly short-term.

This is also why futures fair value is not the same number across asset classes — the yield term is structurally different in each market.

Positive vs. negative carry — what it implies

Carry is positive when the costs of holding the asset (financing plus storage) exceed the income it generates. It is negative when income exceeds holding costs. The sign has direct implications for how the forward curve is shaped and what position you implicitly take when you hold a futures contract versus the spot.

• Positive carry (F > S): The curve slopes upward. A long futures position systematically rolls into higher-priced contracts as expiry approaches — roll yield is negative. Holders of the physical asset are compensated for incurring costs; futures buyers are paying for the privilege of deferred delivery.
• Negative carry (F < S): The curve slopes downward. Rolling a long position generates positive roll yield as you sell the expiring contract at a lower price and re-buy a further-dated one at an even lower price. Commodity markets with supply tightness frequently exhibit this — spot scarcity and high convenience yield overwhelm financing costs.

The shape of the curve — contango and backwardation — is carry made visible across the term structure.

Worked example: S&P 500 index future

Suppose the S&P 500 spot index is 5,400, the 3-month (T = 0.25) risk-free rate is 5.25% continuously compounded, and the index dividend yield is 1.40% continuously compounded. Net carry = 5.25% − 1.40% = 3.85%.

Fair value: F = 5,400 · e^{(0.0385 × 0.25)} = 5,400 · e^0.009625 ≈ 5,400 · 1.00967 ≈ 5,452

If the futures contract is trading at 5,460, it is rich to fair value by 8 points. If it is at 5,440, it is cheap by 12 points. These deviations create the basis trades that index arbitrageurs run continuously — buying the cheap leg, shorting the expensive leg, and unwinding at expiry when spot and futures converge.

Asset class	Carry formula	Typical sign
Equity index	r − dividend yield	Positive when rates > yield
Energy commodity	r + storage − convenience yield	Varies; often negative in backwardation
Currency pair	rdomestic − rforeign	Positive or negative by rate differential
Gold	r + storage (near zero convenience yield)	Almost always positive — persistent contango

Where carry analysis breaks down

The cost-of-carry model is an arbitrage bound, not a forecast. A few practical limits matter.

• Barriers to arbitrage. The model assumes you can finance at the risk-free rate, borrow and lend the physical commodity freely, and transact without friction. In practice, financing costs vary by counterparty, short-selling physical commodities may be impossible, and bid-ask spreads widen the no-arbitrage band. Futures can deviate from carry-implied fair value within that band without creating a clean trade.
• Stochastic convenience yield. In commodity markets the convenience yield is not observable directly and it fluctuates with supply conditions. A model that treats it as constant will misprice long-dated contracts whenever scarcity dynamics shift.
• Dividend uncertainty. For single-stock futures, the dividend yield is an estimate. A surprise cut or special dividend will move the fair value discontinuously and wrong-foot a carry model built on consensus estimates.

None of this makes carry analysis less useful — it remains the baseline against which every futures price is measured. But it is a framework for identifying deviation, not a guarantee that deviation will close on your schedule. The model tells you where the price should be; the market tells you where it is.