Page 56 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Unit 5: Pricing of Future Contracts

5.2 Cost of Carry Model Notes

Cost-of-carry model is an arbitrage-free pricing model. Its central theme is that futures contract
is so priced as to preclude arbitrage profit. In other words, investors will be indifferent to spot
and futures market to execute their buying and selling of underlying asset because the prices
they obtain are effectively the same. Expectations do influence the price, but they influence the
spot price and, through it, the futures price. They do not directly influence the futures price. If the
investor does not book a futures contract, the alternative form to him is to buy at the spot market
and hold the underlying asset. In such a contingency he would incur a cost equal to the spot price
+ the cost of carry. The theoretical price of a futures contract is spot price of the underlying plus
the cost of carry. Please note that futures are not about predicting future prices of the underlying
assets.

This model stipulates that future prices equal to sum of spot prices and carrying costs involved
in buying and holding the underlying asset, and less the carry return (if any). We use fair value
calculation of futures to decide the no-arbitrage limits on the price of a futures contract. According
to the cost-of-carry model, the futures price is given by:

Futures price = Spot Price + Carry Cost – Carry Return ...(5.3)
This can also be expressed as: F= S(1+ r) t ...(5.4)
where: r is the cost of financing, t is the time till expiration.

!

Caution Carry cost (CC) is the interest cost of holding the underlying asset (purchased in
spot market) until the maturity of futures contract. Carry return (CR) is the income (e.g,
dividend) derived from underlying asset during the holding period.

The Cost of Carry is the sum of all costs incurred if a similar position is taken in cash market and
carried to expiry of the futures contract less any revenue that may arise out of holding the
underlying asset. The cost typically includes interest cost in case of financial futures (insurance
and storage costs are also considered in case of commodity futures). Revenue may be in the form
of dividend. Though one can calculate the theoretical price, the actual price may vary depending
upon the demand and supply of the underlying asset.
In simple words, the cost of carry refers to the difference between the costs and the benefits that
accrue while holding an asset. Suppose a sugarcane producer needs 1,000 kgs. of sugarcane for
processing in two months. To lock in the price of the sugarcane today, he can buy it and carry it
for two months. One cost of this strategy is the opportunity cost of funds. To come up with the
purchase price, he must either borrow money or reduce his earning assets by that amount.
Beyond interest cost, however, carry costs vary depending upon the nature of the asset. For a
physical asset such as wheat, he incurs storage costs (e.g., rent and insurance). At the same time,
by storing wheat, he avoids the costs of possibly running out of his regular inventory before
two months are up and having to pay extra for emergency deliveries. This benefit is called
convenience yield. Thus, the cost of carry for a physical asset equals interest cost plus storage
costs less convenience yield, that is:
Carry costs = Cost of funds + storage cost – convenience yield ... (5.5)
For a financial asset such as a stock or a bond, storage costs are negligible. Moreover, income
(yield) accrues in the form of quarterly cash dividends or semi-annual coupon payments. The
cost of carry for a financial asset is:
Carry costs = Cost of funds – income ...(5.6)

LOVELY PROFESSIONAL UNIVERSITY 51