Cost of carry
Encyclopedia
The cost of carry is the cost of "carrying" or holding a position. 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
; the cost of purchasing a particular security
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 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). Storage costs (generally expressed as a percentage of the spot price) should be added to the cost of carry for physical commodities such as corn, wheat, or gold.
The cost of carry model expresses the forward price
(or, as an approximation, the futures price) as a function of the spot price
and the cost of carry.
where
is the forward price
,
is the spot price
,
is the base of the natural logarithm
s,
is the risk-free interest rate
,
is the storage cost,
is the convenience yield
, and
is the time to delivery of the forward contract
(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
on the Chicago Mercantile Exchange
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
s in the S&P 500 and receiving any dividend
s that they might pay, since the e-mini 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.
Opportunity cost
Opportunity cost is the cost of any activity measured in terms of the value of the best alternative that is not chosen . It is the sacrifice related to the second best choice available to someone, or group, who has picked among several mutually exclusive choices. The opportunity cost is also the...
; the cost of purchasing a particular security
Security (finance)
A security is generally a fungible, negotiable financial instrument representing financial value. Securities are broadly categorized into:* debt securities ,* equity securities, e.g., common stocks; and,...
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 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). Storage costs (generally expressed as a percentage of the spot price) should be added to the cost of carry for physical commodities such as corn, wheat, or gold.
The cost of carry model expresses the forward price
Forward price
The forward price 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, we can express the forward price in terms of the spot price and any dividends etc...
(or, as an approximation, the futures price) as a function of the spot price
Spot price
The spot price or spot rate of a commodity, a security or a currency is the price that is quoted for immediate settlement . Spot settlement is normally one or two business days from trade date...
and the cost of carry.
where
is the forward priceForward price
The forward price 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, we can express the forward price in terms of the spot price and any dividends etc...
,
is the spot priceSpot price
The spot price or spot rate of a commodity, a security or a currency is the price that is quoted for immediate settlement . Spot settlement is normally one or two business days from trade date...
,
is the base of the natural logarithmNatural logarithm
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
s,
is the risk-free interest rateRisk-free interest rate
Risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. The risk-free rate represents the interest that an investor would expect from an absolutely risk-free investment over a given period of time....
,
is the storage cost, is the convenience yieldConvenience yield
A convenience yield is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints....
, and
is the time to delivery of the forward contractForward 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 today. This is in contrast to a spot contract, which is an agreement to buy or sell an asset today. It costs nothing to enter a...
(expressed as a fraction of 1 year).
The same model in currency markets is known as interest rate parity
Interest rate parity
Interest rate parity is a no-arbitrage condition representing an equilibrium state under which investors will be indifferent to interest rates available on bank deposits in two countries. Two assumptions central to interest rate parity are capital mobility and perfect substitutability of domestic...
.
For example, a US investor buying a Standard and Poor's 500 e-mini futures contract
Futures contract
In finance, a futures contract is a standardized contract between two parties to exchange a specified asset of standardized quantity and quality for a price agreed today with delivery occurring at a specified future date, the delivery date. The contracts are traded on a futures exchange...
on the Chicago Mercantile Exchange
Chicago Mercantile Exchange
The Chicago Mercantile Exchange is an American financial and commodity derivative exchange based in Chicago. The CME was founded in 1898 as the Chicago Butter and Egg Board. Originally, the exchange was a non-profit organization...
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
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...
s in the S&P 500 and receiving any dividend
Dividend
Dividends are payments made by a corporation to its shareholder members. It is the portion of corporate profits paid out to stockholders. When a corporation earns a profit or surplus, that money can be put to two uses: it can either be re-invested in the business , or it can be distributed to...
s that they might pay, since the e-mini 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.
See also
- Carry (investment)Carry (investment)The carry of an asset is the return obtained from holding it , or the cost of holding it .For instance, commodities are usually negative carry assets, as they incur storage costs or may suffer from depreciation, but in some circumstances, appropriately hedged commodities can be positive carry...
- Carrying chargeCarrying chargeA carrying charge is the cost of storing a physical commodity, such as grain or metals, over a period of time. The carrying charge includes insurance, storage and interest on the invested funds as well as other incidental costs. In interest rate futures markets, it refers to the differential...
- Interest rate parityInterest rate parityInterest rate parity is a no-arbitrage condition representing an equilibrium state under which investors will be indifferent to interest rates available on bank deposits in two countries. Two assumptions central to interest rate parity are capital mobility and perfect substitutability of domestic...
- Covered interest arbitrageCovered interest arbitrageCovered interest arbitrage is the investment strategy where an investor buys a financial instrument denominated in a foreign currency, and hedges his foreign exchange risk by selling a forward contract in the amount of the proceeds of the investment back into his base currency...
- Spot-future paritySpot-future paritySpot-future parity is a parity condition that should theoretically hold, or opportunities for arbitrage exist. Spot-future parity is an application of the law of one price...
- ContangoContangoContango is the market condition wherein the price of a forward or futures contract is trading above the expected spot price at contract maturity. The resulting futures or forward curve would typically be upward sloping , since contracts for further dates would typically trade at even higher prices...
- Demurrage (currency)Demurrage (currency)Demurrage is a cost associated with owning or holding currency over a given period of time. It is sometimes referred to as a carrying cost of money. For commodity money such as gold, demurrage is in practice nothing more than the cost of storing and securing the gold...