Cost of Carry formula and interpretation

By | August 9, 2013

A future Contract is an agreement between two parties to BUY or SELL an underlying asset, including stocks, indices,commoditities or currency, at a certain time in the future at a certain price. Futures contracts are standardized and are traded on the exchange. To facilitate liquidity in futures contracts, the exchange defines certain standard specifications for  a particular contract , including a standard underlying instrument, a standard quantity and quality of that underlying assest ( to be delivered or cash settled), and a standard timing for such a settlement.  If you have taken position in equity futures, whether long or short, you have to close the position by entering in an equal and opposite transaction anytime prior to expiry of the contract as there is no delivery of the underlying assets.
The Relationship between Futures Prices and Spot Prices can be summarized in terms of what is commonly known as the COST-OF-CARRY.

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 opportunity cost the cost of purchasing a particular security rather than an alternative.

Typically,in equity futures,there is no incidence of storage costs as in commodity futures. Moreover, equity has a dividend stream, which is a negative cost if one is long on the futures of the underlying and positive if one is short.

The theoretical way of pricing any Future is to factor in the current price and holding costs or cost of carry.

The Futures Price = Spot Price + Cost of Carry

Cost of carry is the sum of all costs incurred if a similar position is taken in cash market and carried to maturity of the futures contract less any revenue which may result in this period. The costs typically include interest in case of financial futures (also insurance and storage costs in case of commodity futures). The revenue may be dividends in case of index futures.

Apart from the theoretical value, the actual value may vary depending on demand and supply of the underlying at present and expectations about the future. These factors play a much more important role in commodities, especially perishable commodities than in financial futures.

In general, the Futures price is greater than the spot price. In special cases, when cost of carry is negative, the Futures price may be lower than Spot prices.
The Pricing of a futures contract is a simple process. Using the cost-of-carry logic mentioned below,one can calculate the fair value of a futures contract, The cost-of -carry model used for pricing futures is given below:

F = S * exp (r*t) – D.
So, r = ln((F+D)/S)/t
Where F – Futrues price
S – spot price
r – cost of carry
t – time to expiry
D – dividends to be paid during the life of the futures contract
e is 2.71828

Suppose ABC Ltd trades in the spot market @ 1150 .The money can be invested @11% p.a. The fair value of a one-month futures cintract in ABC is calculated as follow:-

F=1150×2.718280X11x(1/12) =1160
The above example show how to  calculate the futures price when no dividend is expected.
Now we shall see how the futures price is  calculated when dividends are expected. Suppose the Interest rate is 10% and the market price of ABC Ltd is Rs.140. The  company will be declaring a dividend of Rs.10 after 15 Days of purchasing a two-month contract, then the Rs.10 dividend will  be compounded for the remaining 45 days of the Contract.

F=140×2.718280X.1X(60/362)-10×2.718280.1x(45/365) =132.20
Although cost-of-carry is a critical indicator to judge the movement in the futures market, cost-of-carry in conjunction with open interest is a good indicators of the prevailing market Sentiments.

 

2 thoughts on “Cost of Carry formula and interpretation

  1. Saumya

    Just curious to know whether your post and articles are of copywrite nature.

    Can I quote your post or article (in part or in full) somewhere else, with or without quoting your reference or with or without your permission.

    Thanks

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