Cost of carry combines financing, storage, income, and ownership benefits when comparing spot and forward or futures prices.
Cost of carry is the net cost or benefit of owning an asset from today until a future date. It commonly includes financing and storage costs, less income or other benefits received while holding the asset. In forward and futures pricing, carry helps explain the difference between a comparable Spot Price and a price for later delivery.
There is no single cost-of-carry formula for every market. Commodities can require storage and insurance, equity indexes can distribute dividends, bonds can pay coupons, and currencies involve two interest rates.
| Component | Typical sign | Examples |
|---|---|---|
| Financing cost | Increases carry | Interest or opportunity cost of funding the spot asset |
| Storage cost | Increases carry | Warehouse, tank, vault, or inventory expense |
| Insurance and handling | Increases carry | Coverage, inspection, transport, and operational expense |
| Income | Reduces carry | Dividends, coupons, lease income, or foreign-currency interest |
| Convenience yield | Reduces net commodity carry | Operational benefit of having physical inventory available |
| Borrowing or shorting friction | Can increase or block carry | Securities borrow fees, commodity availability, or position constraints |
Costs and benefits must be measured over the same horizon and on a consistent annualized or total-period basis.
Under simplified no-arbitrage assumptions, a forward price is the spot price carried to maturity:
where:
The exponential form assumes continuous compounding. Market conventions may instead use simple interest, discrete compounding, day-count rules, quoted forward points, or product-specific invoice calculations.
Before applying a formula, define each input on the same basis:
| Input | Question to resolve |
|---|---|
| Spot price | Which asset, grade, location, currency, quantity, and settlement date? |
| Forward or futures price | Which contract, expiration, delivery terms, and quotation? |
| Time | Actual days, a stated year fraction, or another day-count convention? |
| Interest rate | Simple, annually compounded, or continuously compounded? |
| Income | Known cash amount, expected cash flow, or annualized yield? |
| Storage and insurance | Paid upfront, through time, or at delivery? |
| Currency quote | Domestic currency per foreign unit, or the inverse? |
Combining a simple annual financing rate with a continuously compounded dividend yield can create a small but real modeling error. Mixing a spot price for immediate retail delivery with a wholesale futures contract for another grade or location can create a much larger conceptual error.
A common framework is:
where \(r\) is the financing rate, \(u\) is proportional storage and related cost, and \(y\) is convenience yield.
Convenience yield is not normally a separately invoiced cash payment. It represents the operational or scarcity benefit of controlling usable inventory. Estimating it from market prices can absorb omitted costs, constraints, and measurement differences.
For an asset with a continuous income yield \(q\):
For an equity index, \(q\) commonly represents expected dividend yield over the contract horizon. Actual dividends, tax treatment, and futures conventions can differ from the simplifying assumptions.
Assume a hypothetical equity index has:
| Input | Value |
|---|---|
| Spot index level | 5,000 |
| Annual financing rate | 5.0% |
| Expected annual dividend yield | 1.5% |
| Time to expiration | 0.25 years |
Using continuous compounding:
The model places the future about 43.94 index points above spot because the assumed financing rate exceeds the expected dividend yield. The premium does not mean the index is forecast to rise by 43.94 points.
If expected dividends increase while other inputs remain unchanged, modeled futures fair value falls. If financing increases while other inputs remain unchanged, modeled fair value rises.
For an actual index future, dividend timing, tax, index composition, market liquidity, and the contract’s settlement methodology can affect the comparison. The Stock Index Futures guide explains the contract mechanics and hedge implications.
When the spot quote expresses domestic currency per unit of foreign currency:
where \(r_d\) is the domestic rate and \(r_f\) is the foreign rate. The foreign currency is itself an interest-bearing asset, so its yield offsets part of the domestic financing cost.
Assume the spot quote is 1.1000 units of domestic currency per unit of foreign currency. The continuously compounded domestic rate is 4%, the foreign rate is 2%, and the term is six months.
Under these assumptions, the foreign currency trades at a forward premium in this quote because the domestic rate is higher. The approximately 0.0111 difference reflects the rate differential over the term; it is not a guaranteed currency gain.
If the market displays the reciprocal quote, the numerical direction reverses. A modeler must identify the base and quote currencies before assigning domestic and foreign rates. The rates should also match the relevant funding curves, maturity, day count, and collateral assumptions rather than unrelated policy or deposit rates.
Assume a hypothetical storable commodity has:
| Input | Value |
|---|---|
| Spot price | $100.00 |
| Annual financing rate | 4% |
| Annual storage and insurance rate | 3% |
| Annual convenience yield | 1% |
| Time to maturity | 0.5 years |
The net annual carry rate is:
The model-implied six-month forward price is:
The $3.05 premium is a modeled result, not a forecast that spot will rise. An observed futures price can differ because the storage estimate, convenience yield, funding access, deliverable grade, location, contract option, or arbitrage constraint differs from the assumptions.
When spot, futures, financing, storage, and time are observed or estimated, the commodity model can be rearranged to infer an annualized convenience yield:
Using the rounded values from the commodity example:
The result is close to the assumed 1%; the small difference comes from rounding the displayed forward price to $103.05.
An implied convenience yield is a residual, not a directly observed coupon. If storage cost or financing is wrong, the inferred convenience yield absorbs the error. Delivery options, location differences, inventory constraints, and inconsistent timestamps can also contaminate the estimate.
When the observed forward price is materially above an executable carried spot cost, a theoretical cash-and-carry trade would:
A reverse cash-and-carry trade takes the opposite direction when the observed forward price is sufficiently low.
| Strategy | Spot leg | Forward leg | Critical constraint |
|---|---|---|---|
| Cash-and-carry | Buy and finance the asset | Sell forward | Asset must be deliverable and economical to store |
| Reverse cash-and-carry | Borrow and sell the asset | Buy forward | Asset must be available to borrow or short |
These are arbitrage frameworks, not guaranteed trades. Bid-ask spreads, balance-sheet charges, credit limits, margin, taxes, delivery options, storage capacity, and settlement timing can eliminate the apparent profit.
A theoretical price gap matters only if the complete trade can be executed. For a proposed cash-and-carry transaction, compare:
| Leg or cost | Evidence needed |
|---|---|
| Spot purchase | Firm price for the contract-deliverable asset and quantity |
| Financing | Committed rate, haircut, collateral, and maturity |
| Storage or custody | Capacity, location, insurance, handling, and withdrawal terms |
| Futures or forward sale | Executable price, depth, fees, and margin |
| Income | Coupon, dividend, lease, or foreign-currency interest actually available |
| Delivery | Eligibility, grading, transport, notice, and settlement deadlines |
| Exit and stress | Cost if financing, storage, or delivery assumptions fail |
Suppose a model shows a $1.20 premium above carried spot cost, but execution spreads total $0.35, storage uncertainty is $0.30, financing and balance-sheet charges are $0.25, and delivery costs are $0.20. The apparent residual is only $0.10 before tax, operational error, and adverse changes:
If any input is indicative rather than executable, the residual is not locked in. A trade described as arbitrage can still lose when a short sale is recalled, financing changes, storage is unavailable, quality fails inspection, or settlement does not occur as modeled.
| Market | Main carry inputs | Common analytical issue |
|---|---|---|
| Energy or metals | Funding, storage, insurance, convenience yield | Location and storage capacity |
| Agriculture | Funding, storage, quality, seasonality | Grade, harvest cycle, and delivery point |
| Equity index | Funding less expected dividends | Dividend timing and tax assumptions |
| Fixed income | Funding less coupon or income | Accrued interest and cheapest-to-deliver effects |
| FX | Domestic rate less foreign rate | Quote direction, value date, and funding curve |
| Volatility futures | Financing and expected underlying dynamics | Underlying may not be directly storable |
For non-storable or non-investable underlyings, no-arbitrage carry models can be incomplete. Expectations, risk premiums, replication limits, and contract methodology may dominate.
These terms are related but not interchangeable:
| Term | What it describes |
|---|---|
| Cost of carry | Modeled net cost or benefit of holding the spot asset through a future date |
| Basis | Observed difference between a cash price and a specified derivative price, under a stated sign convention |
| Forward or futures curve | Prices across several maturities at one observation time |
| Roll yield | Return attribution associated with replacing one futures contract with another while maintaining exposure |
| Spot return | Change in the price of the immediate-delivery asset |
A positive modeled carry can place a deferred contract above spot, yet an investor’s eventual total return can still be negative if spot falls. A futures strategy can also experience roll effects that differ from the initial curve because both contract prices move before the roll.
Always define the basis sign. Some analysts calculate futures minus spot, while others use cash minus futures. The same market can therefore be described with opposite signed numbers unless the convention is stated.
A forward and a future with the same underlying exposure and maturity are economically related, but they are not operationally identical.
| Feature | Forward | Future |
|---|---|---|
| Terms | Often customized | Standardized by an exchange |
| Cash-flow timing | Commonly concentrated at maturity, subject to collateral terms | Gains and losses generally settled daily |
| Credit structure | Bilateral or cleared under the agreement | Centrally cleared through the futures structure |
| Exit | Negotiated termination or offset | Offset in the listed market |
| Pricing consideration | Contract credit, collateral, and funding terms | Daily settlement and margin reinvestment |
Under simplified assumptions, modeled forward and futures values can be very close. When interest rates are uncertain and correlated with the underlying price, daily settlement and reinvestment can create a difference. Contract specifications, collateral remuneration, and timing must also match before comparing quotations.
Return to the hypothetical commodity example with a $100 spot price and six months to maturity. Holding all other inputs constant:
| Scenario | Net annual carry | Modeled forward price |
|---|---|---|
| Base: financing 4%, storage 3%, convenience yield 1% | 6% | $103.05 |
| Financing rises to 5% | 7% | $103.56 |
| Storage rises to 4% | 7% | $103.56 |
| Convenience yield rises to 2% | 5% | $102.53 |
The table is a model sensitivity, not a forecast. A one-percentage-point change has the same mathematical effect when every input is expressed as a proportional continuously compounded yield, but real storage bills, coupon cash flows, dividends, and financing arrangements may not follow that convention.
Sensitivity analysis should vary inputs independently and together. For example, nearby scarcity can raise spot prices, storage values, and implied convenience yield at the same time, making a one-variable shock unrealistic.
A commodity market is sometimes described as being at full carry when deferred prices compensate for the economically relevant cost of holding deliverable inventory. This is a market- and contract-specific comparison, not a fixed percentage.
Positive net carry can support an upward-sloping curve, or contango. A high convenience yield or nearby scarcity can support backwardation. The Contango and Backwardation guide explains why curve shape can also reflect seasonality, delivery constraints, expectations, and liquidity rather than carry alone.
This page is for financial education only. It does not provide a tradable fair-value quote or recommend a cash-and-carry, futures, forward, funding, or inventory strategy. Actual pricing requires current market data, contract specifications, and executable financing and transaction costs.