Question

A foreign exchange trader working for a bank enters into a long position in a forward contract to buy one million pounds of sterling at an exchange rate of 1.6000 in three months. At the same time, another trader on the next desk takes a long position in 16 three month futures contracts on sterling. The futures price is 1.6000, and a futures contract is on £62,500. The forward and the futures prices both increase to 1.6040 at the end of the day the trades being executed. Both traders claim the same profit, but the bank’s accounting system shows that the forward trader has made a smaller profit than the futures trader has made. The forward trader immediately picks up the phone to complain to the accounting department. If you work in the accounting department, answers to the following questions are the explanations you need to give to the forward trader. (Assume that the interest rate is 6%.)

(a) What are the value of the futures and the value of the forward when the futures price and the forward price both increase to 1.6040?

(b) Why are the two values different?

(c) If the forward price and futures price both go down by 0.0040, instead of going up, what will be the profit (or loss) of the two traders in their positions and which trader’s profit (or loss) is bigger?

Answer 1

Given:

Trader 1 - Forward Contract (1,000,000 Pounds of Sterling)

Exchange Rate: 1.6 (3 months)

Trader 2 - Futures Contract (16* 62,500 pounds = 1,000,000 Pounds of Sterling)

Exchange Rate: 1.6 (3 months)

a.> Exchange rate increases to 1.6040.

Suppose both trader enter a short position at 1.6040,

Profit realised by both traders:

=

= 4000

As futures contract has daily settlement, therefore when the exchange rate rises, the futures trader realizes the profit of 4000 immediately.

The same profit is realised by the forward trader at the end of the contract, i.e., after 3 months.

Therefore, the present value of the forward contract profit =

b.> The two values are different because, the profit realised by the futures trader is due to the daily settlement of the futures contract. The futures trader immediately realises the profit of 4000 pounds by entering a short contract with a rate of 1.6040.

The forward trader cannot realise the same profit because, if he decides to close his position by entering a short position, the position will only be closed after 3 months. Forward contracts do not have daily settlement. He can then realise the profit of 4000 pounds at the end of the contract.

c. Given: Prices go down by 0.0040.

New price = 1.5960

Futures Loss:

Loss= 4000 pounds realised immediately

Forward Loss:

=Present value of

=Present value of [4000 pounds]

Loss = 3941 pounds