Cost of carry

If you acquire a position on the spot market, the entire holding costs – primarily the financing costs – must be borne by the buyer. If, on the other hand, you choose a derivative (eg. a future), then the purchase obligation and consequently also the financing requirement is postponed. Therefore one saves the holding costs (costs of carry).

For that reason, it is possible to pay more for a future than for the corresponding instrument on the spot market. (Otherwise, there would be a possibility for arbitrage).

This higher price can be calculated with the following formula:

F = S · (1 + r )^(T -t)

F . . . price of the future
S . . . spot price
c . . . cost of carry-Satz
t . . . valuation day
T . . . maturity of the future
(T-t) . . . duration of the contract

In this case, the cost of carry rate (1+c)^(T-t) includes all the holding costs till the maturity of the future.

In the case of securities also returns from the holdings (dividends, or interests) need to be accounted for. These returns don’t belong to the buyer of the future, therefore they minimize the advantages in the cost of carry for the future.

Their price can be calculated like this:

F = S · (1 + r – e)^(T -t)

F . . . price of the future
S . . . spot price
c . . . cost of carry
t . . . valuation day
T . . . maturity of the future
(T-t) . . . duration of the contract

e… returns from security

As you can see if the duration (T-t) = 0 then the cost of carry is 1. Remember x^0 is always 1. For that reason, we can say that on the expiration date the spot market price and the future price is the same: F = S * ( 1)