The cost of carry or carrying charge is the cost of holding a

security Security is protection from, or resilience against, potential harm (or other unwanted coercion). Beneficiaries (technically referents) of security may be persons and social groups, objects and institutions, ecosystems, or any other entity or ...

or a physical

commodity In economics, a commodity is an economic goods, good, usually a resource, that specifically has full or substantial fungibility: that is, the Market (economics), market treats instances of the good as equivalent or nearly so with no regard to w ...

over a period of time. The carrying charge includes

insurance Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to protect ...

, storage and

interest In finance and economics, interest is payment from a debtor or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct f ...

on the

invest Investment is traditionally defined as the "commitment of resources into something expected to gain value over time". If an investment involves money, then it can be defined as a "commitment of money to receive more money later". From a broade ...

ed funds as well as other incidental costs. In interest rate

futures market A futures exchange or futures market is a central financial exchange where people can trade standardized futures contracts defined by the exchange. Futures contracts are derivatives contracts to buy or sell specific quantities of a commodity or f ...

s, it refers to the differential between the yield on a

cash In economics, cash is money in the physical form of currency, such as banknotes and coins. In book-keeping and financial accounting, cash is current assets comprising currency or currency equivalents that can be accessed immediately or near-i ...

instrument and the cost of the funds necessary to buy the instrument. If long, the cost of carry is the cost of interest paid on a margin account. Conversely, if short, the cost of carry is the cost of paying dividends, or rather the

opportunity cost In microeconomic theory, the opportunity cost of a choice is the value of the best alternative forgone where, given limited resources, a choice needs to be made between several mutually exclusive alternatives. Assuming the best choice is made, ...

; the cost of purchasing a particular

rather than an alternative. For most investments, the cost of carry generally refers to the risk-free interest rate that could be earned by investing currency in a theoretically safe investment vehicle such as a

money market account A money market account (MMA) or money market deposit account (MMDA) is a deposit account that pays interest based on current interest rates in the money markets. The interest rates paid are generally higher than those of savings accounts and tra ...

minus any future cash flows that are expected from holding an equivalent instrument with the same risk (generally expressed in percentage terms and called the

convenience yield A convenience yield is an implied return on holding inventories. It is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints. Let F_ be the forward price of an asset with ...

). Storage costs (generally expressed as a percentage of the

spot price In finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement (payment and delivery) on the spot date, which is normally two business days after t ...

) should be added to the cost of carry for physical commodities such as corn, wheat, or gold.

Formula

The cost of carry model expresses the

forward price The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in ...

(or, as an approximation, the futures price) as a function of the

and the cost of carry. :

F = S e^\,

where :

F

is the

, :

S

is the

, :

e

is the base of the

natural logarithm The natural logarithm of a number is its logarithm to the base of a logarithm, base of the e (mathematical constant), mathematical constant , which is an Irrational number, irrational and Transcendental number, transcendental number approxima ...

s, :

r

is the

risk-free interest rate The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free r ...

, :

s

is the storage cost, :

c

is the

, and :

t

is the time to delivery of the

forward contract In finance, a forward contract, or simply a forward, is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on in the contract, making it a type of derivative instrument.John C Hu ...

(expressed as a fraction of 1 year). The same model in currency markets is known as interest rate parity. For example, a US investor buying a Standard and Poor's 500 e-mini

futures contract In finance, a futures contract (sometimes called futures) is a standardized legal contract to buy or sell something at a predetermined price for delivery at a specified time in the future, between parties not yet known to each other. The item tr ...

on the

Chicago Mercantile Exchange The Chicago Mercantile Exchange (CME) (often called "the Chicago Merc", or "the Merc") is an American derivatives marketplace based in Chicago and located at 20 S. Wacker Drive. The CME was founded in 1898 as the Chicago Butter and Egg Board ...

could expect the cost of carry to be the prevailing risk-free interest rate (around 5% as of November, 2007) minus the expected dividends that one could earn from buying each of the

stock Stocks (also capital stock, or sometimes interchangeably, shares) consist of all the Share (finance), shares by which ownership of a corporation or company is divided. A single share of the stock means fractional ownership of the corporatio ...

s in the

S&P 500 The Standard and Poor's 500, or simply the S&P 500, is a stock market index tracking the stock performance of 500 leading companies listed on stock exchanges in the United States. It is one of the most commonly followed equity indices and in ...

and receiving any

dividend A dividend is a distribution of profits by a corporation to its shareholders, after which the stock exchange decreases the price of the stock by the dividend to remove volatility. The market has no control over the stock price on open on the ex ...

s that they might pay, since the

e-mini E-minis are futures contracts that represent a fraction of the value of standard futures. They are traded primarily on the Chicago Mercantile Exchange. As of April, 2011, CME lists 44 unique E-mini contracts, of which approximately 10 have average ...

futures contract is a proxy for the underlying stocks in the S&P 500. Since the contract is a futures contract and settles at some forward date, the actual values of the dividends may not yet be known so the cost of carry must be estimated.

References

{{reflist Derivatives (finance) Financial economics

Formula

See also

References