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What is cost-of-carry in pricing a futures contract?

Under normal conditions, the futures price is higher than the spot (or cash) price.

This is because the futures price generally incorporates costs that the seller would incur for buying and financing the commodity or asset, storing it until the delivery date, and for insurance. These costs are usually referred to as cost-of-carry. The rationale behind pricing a futures contract can be seen from the following equation:

\[Future \ price_t,_T = (1 + r + s)^{T-t} \times Spot \ price_t\]

where \(r\) refers to the interest rate between now, \(t\), and the delivery date \(T\) ; and \(s\) refers to the storage cost.

This situation of the futures price being higher than the spot price is known as contango. Under some conditions, however, the opposite situation might occur, and the futures price could be lower than the spot price. This could be due to a temporary scarcity of the commodity on the spot market, for example, due to a restricted current supply, making the price of the commodity unusually high. This situation is known as backwardation. If the market is in backwardation, the fair value of a futures contract is more difficult to calculate.

It is worth noting that cost-of-carry varies depending on what the underlying assets is. For example, if you buy a futures contract where the underlying assets are a firm’s shares, storage costs for these shares are not really a concern - they are at most some documents. In this case the cost-of-carry will be the interest paid to finance the asset. If there is a dividend payout from the shares, this reduces the cost-of-carry for such an underlying asset.

If we take another example, where the underlying asset is gasoline, then we can imagine that there will be a large cost-of-carry because of the need to find suitable storage for the gasoline, but also the need to take out an insurance policy for potential damage caused by the gasoline in the event of any accident or incident. However, ownership of the gasoline provides potential benefits (if it is held in inventory, it can be used), which are not available to holding the futures contract. This benefit of holding the physical asset is known as convenience yield, and it reduces the futures price.

But what if the underlying asset of the futures contract were a commodity like gold? How would this affect the cost-of-carry? Share your ideas with your fellow learners.

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This article is from the free online course:

Risk Management in the Global Economy

SOAS University of London