Cost of carry
Also written Carrying cost · Cost of carry (financing cost)
The cost of holding an asset until a future date — financing interest plus storage, less any income it pays. It links spot to futures: fair futures price = spot + cost of carry − inflows.
In plain language
You can get a share on a future date in two ways. Buy a futures contract today. Or buy the share in the cash market today and carry it until that date.
Carrying it is not free. You have to pay for the money you used — interest. For a commodity you also pay storage and insurance. Against that, the asset may pay you something while you hold it — a dividend on a share, interest on a bond.
Cost of carry = what it costs to hold the asset − what the asset pays you while you hold it.
For equity derivatives, the workbook puts it simply: carrying cost is the interest paid to finance the purchase less the dividend earned.
That number is the bridge between the spot price and the futures price. If both routes deliver the same share on the same date, they should cost the same — so the futures price should equal the spot price plus the cost of carry. The workbook adds a realistic note: cost of carry may be different for different participants, because they borrow at different rates.
How it works
The cost of carry model — also called the no-arbitrage model — assumes that in an efficient market arbitrage opportunities cannot persist, so the futures price settles at the fair price.
Its important assumptions (Chapter 3, section 3.7): the underlying is available in abundance in the cash market; demand and supply are not seasonal; holding the asset is easy and feasible; the asset can be sold short; and there are no transaction costs, no taxes and no margin requirements.
Where those fail, the model weakens. Seasonal commodities, assets that cannot be stored or sold short, and situations where convenience yield dominates can make futures trade at a discount that reverse arbitrage cannot correct. Because margins are ignored, the workbook says the model is more suitable for pricing forwards than futures.
Basis links it to the calendar. The difference in basis between a one-month and a two-month futures contract should essentially equal the cost of carrying the asset between the first and second month.
The formula
Fair futures price = Spot price + Cost of carry − Inflows
Discrete: F = S × (1 + r − q)^T
Continuous: F = S × e^((r − q) × T)
S = spot price, r = cost of carry (financing rate), q = income yield, T = time in years
A worked example
1. A single share. ABC Ltd trades at Rs 100. The buyer borrows Rs 100 at 6% p.a. and holds for one year. The company pays a 200% dividend on Rs 1 face value, i.e. Rs 2.
Interest paid = 6% × 100 = Rs 6
Dividend received = Rs 2
Net cost of carry = 6 − 2 = Rs 4
Break-even futures = 100 + 4 = Rs 104
2. An index, three months. Index at 17,500, financing cost 12%, index return 4% p.a., 90 days to expiry.
Discrete: 17,500 × (1 + 0.12 − 0.04)^(90/365) = 17,835.26
Continuous: 17,500 × e^((0.12 − 0.04) × 90/365) = 17,848.63
The workbook says that if index futures trade above 17,848.63, one can buy the index stocks and sell futures to lock in the difference — ignoring transaction costs, taxes and margins.
3. Gold. Spot Rs 62,130 per 10 g; financing, storage and insurance for three months Rs 100. Fair three-month price Rs 62,230. If three-month futures trade at Rs 62,280, buying spot and selling futures earns Rs 50 per 10 g before costs.
Why NISM asks about it
Chapter 3, section 3.4, defines cost of carry with the ABC Ltd example; section 3.7 builds the cost of carry model, its assumptions, the dividend-adjusted formula with the 17,500 index example, and convenience yield. Chapter 5, section 5.1, applies it to cash-and-carry, reverse cash-and-carry and calendar spread arbitrage. Expect a fair-price calculation and an assumptions question.
Common exam traps
- Dividends reduce the cost of carry. Fair futures price = spot + carry − inflows, not + inflows.
- Discrete and continuous compounding give different answers — 17,835.26 and 17,848.63 in the workbook's own example. Use the method the question specifies.
- The model ignores transaction costs, taxes and margins. Those create no-arbitrage bounds around the fair price.
- The cost of carry model is also called the no-arbitrage model — not the expectations model, which is a different pricing approach.
- The workbook says the model is better suited to forwards than futures, because margins are ignored.
- Convenience yield mainly arises in commodities, not in financial assets such as equities.
Where this is taught
- Series IV · Chapter 3: Exchange Traded Interest Rate Futuresintroduced here
- Series XVI · Chapter 3: Commodity Futuresintroduced here
- Series V-D · Chapter 15: Introduction to Forwards and Futuresintroduced here
- Series VIII · Chapter 3: Introduction to Forwards and Futuresintroduced here
Related terms
- BasisThe difference between the spot price and the futures price of an asset — positive when spot exceeds futures, negative when futures exceeds spot, and zero at expiry.
- ArbitrageSimultaneously buying and selling an asset, or a replica of it, in different markets to profit from a price discrepancy — a trade that aims to lock in a profit rather than bet on direction.
- Futures contractA standardised forward traded on an exchange, where the exchange fixes every term except the price and the clearing corporation guarantees settlement, so neither side carries the other's default risk.
- Cash and carry arbitrageBuying the underlying in the cash market and simultaneously selling futures when futures trade above their fair price, carrying the asset to expiry to lock in the mispricing.
- ContangoA market in which the futures price sits above the spot price, normally because the futures buyer is paying for the cost of carrying the commodity through to delivery.
- No-arbitrage boundsThe band around the fair futures price, created by transaction costs, taxes and margins, within which a mispricing is too small to arbitrage profitably — so prices can sit there undisturbed.
- Reverse cash and carry arbitrageSelling the underlying in the cash market and simultaneously buying futures when futures trade below their fair price — the mirror image of cash and carry, and it needs stock to sell.
- Forward rateThe interest rate for a period that starts in the future, implied today by two spot rates — because rolling a short investment must return the same as locking in a long one, or arbitrage follows.
- ArbitragerA participant who locks a profit by entering opposite transactions in two markets at once — carrying no exposure and taking no view, and in the process pulling the two prices back together.
- Cash and carry pricingThe no-arbitrage model for bond futures: theoretical futures price = cash (dirty) price + financing cost − income on the cash position, which is accrued interest to the futures settlement date.
- Contango and backwardationThe two shapes a commodity futures curve can take — contango when the futures price is above spot, backwardation when it is below.
- BackwardationA market in which the futures price sits below the spot price — the cost of carry says futures should be dearer, and something is overriding it.
- Convenience yieldThe rupee benefit of physically holding a commodity rather than holding a futures contract on it — the term that lets a futures price fall below spot plus carry.
- Fair valueThe theoretical futures price — spot plus the cost of carrying the commodity to expiry — at which a buyer is indifferent between buying today and buying forward.
- Black-76 modelThe variant of the Black-Scholes model used to price Options on Futures, which substitutes the futures price F for the spot price and discounts the whole payoff at e^(-rT).
- Sectoral indexA commodity index built from the futures of a single segment — bullion, base metals, energy or the guar family — with fixed annual weights and no 30 per cent cap per constituent.
- Composite indexA commodity index spanning several segments — energy, metals, bullion — whose constituents must each weigh 1 to 30 per cent, with at least 80 per cent of the weight in sufficiently liquid futures.
- Price discoveryThe process by which the free interaction of buyers and sellers produces a price that reflects every participant's expectation of what the underlying will be worth at a future date.
- Break-even pointThe level of the underlying at which a position makes neither profit nor loss — for a bought call, strike plus premium; for a bought put, strike minus premium.
- RhoThe option Greek that measures interest rate sensitivity — the change in an option premium for a one percentage point change in the risk-free rate. It is positive for calls and negative for puts.
- Put-call parityThe arbitrage-free relationship binding a European call and put of the same strike and expiry to the spot and the discounted strike: c + X·e^(−rt) = p + S. Deviations create risk-free profit.
- UnderlyingThe asset a derivative contract derives its value from — the index, stock, bond or currency whose spot price drives the contract. The derivative has no value of its own without it.
- ConvergenceThe certainty that a futures price and the spot price of its underlying meet at expiry — because on the last trading day the contract settles at the cash market price, leaving no room for a difference.
- RolloverCarrying a derivatives position past expiry by closing the expiring contract and opening the same position in the next series simultaneously — the only way to hold a view longer than one contract cycle.
- Roll yieldThe gain or loss from rolling an expiring futures position into the next contract month, over and above the pure cost of carry.
- Expectations modelA futures pricing theory holding that the futures price is the market's expectation of the future spot price — unlike the cost-of-carry model, which prices futures off today's spot price plus financing cost.
- Hedge contract monthThe futures contract month chosen for a hedge — the thumb rule is to pick the contract expiring just after the date the hedger plans to unwind the underlying exposure.
- Fixed-for-floating swapA commodity swap in which one side pays a fixed price agreed at the outset and the other pays a floating price — a spot price, a nearest-futures price, or an average of either — reset each period.
- Futures carry effectThe reason a call on futures carries more intrinsic value than a call on goods, while a put on goods carries more than a put on futures — because before expiry the futures price sits above the spot price.
- METALDEXMCX's base metal sectoral index — for 2025, copper 40%, aluminium 30%, zinc 26% and lead 4% — which the workbook also reads as a rough inflation gauge for the metals family.
- Spot priceThe price at which the underlying asset trades in the cash market for immediate delivery — the anchor from which futures prices, basis, moneyness and final settlement are all measured.
- Calendar spreadA long position in futures of one maturity and a short position in futures of another maturity on the same underlying. It is a bet on the price gap between the two months, not on market direction.
- Cost of arbitrageThe financing cost an arbitrageur incurs while holding a cash-and-carry position until expiry, which reduces the gross arbitrage profit to the net gain actually earned.
- Carry costThe interest cost built into the gap between a stock's spot price and its futures price, reflecting the cost of funding a spot purchase until the futures contract's delivery date.