Question

An asset is selling for $250. A Futures contract with the asset as underlying, expires in 8 months (assume 365 day year). Interest rates are 5% per annum and the future value of cost of carry has been calculated to be $5.35 and is net any convenience yield earned over the time period.

(A) Calculate the arbitrage free futures price.

(B) A month has passed; the contract expires in 7 months. The asset sells for $239, and net cost of carry is $4.00. Interest rates are stable at 5% Calculate price and profit or loss over the one month period of time.

(C) At expiration the cash market is showing a price of $229. Interest rates are 5%, contracts with 6 months till expiration, are showing cost of carry of $6.16. Calculate price and profit from the futures contract.

Answer 1

A) Calculation of arbitrage free future price:

Arbitrage free future Price = Spot price * e^rT + Future value of cost of carry

Arbitrage free future Price = 250*e^0.05*(8/12) + 5.35

Arbitrage free future price = 250*1.0339 + 5.35

Arbitrage free future price = 263.82

B) Calculation of future price at initiation for contract expiring in 1 month:

Future price = Spot price * e^rT + Future value of cost of carry

Future price = 250*e^0.05*(1/12)+ 4 = $ 255.04

Here we see that the future price calculated at initiation for contract expiring in 1 month is coming to $ 255.04 and the asset is selling at $ 239, which implies that there is a loss of $ 16.04 because it is cheaper to buy the asset from the market in 1 month rather than to execute the future contract in 1 month.

C) At expiration the asset can be brought at $ 229.

In part A above, we calculated what would be the future price of the 8 month contract at expiration and it came to $ 263.82 which means that buying asset from the market at $ 229 is cheaper rather than entering into future contract. There would be a loss of $ 34.82 because of future contract.