Question

Exchange rate is currently $1.85 US per 1 British pound. Interest rate is 3% in the US and 4% in the UK. A bank is long a futures contract on 1,000,000 pounds with F= $1.8 million in one year.

Write the expression for the present value of the bank’s short futures position, as a function of current spot exchange rate S

		Value = 1,000,000 (S (1.04/1.03) – 1.8) / 1.03
		Value = 1,000,000 (S (1.03/1.04) – 1.8) / 1.03
		Value = 1,000,000 (1.8 - S (1.03/1.04)) / 1.03
		Value = 1,000,000 (1.8 - S (1.04/1.03)) / 1.03

Answer 1

Banks Long futures contract is 1000000 pounds with $1.80 Million.

It means the bank has to buy 1000000 pounds by paying $1.80 Million.

Hence we can say that the bank will buy 1000000 pounds by selling $1.80 Million.($1.80 per pound)

Banks short position(Sell position) is $1.8 Million after one year.

Current exchange rate = Pound 1 = $1.85

$ INTEREST RATE = 3%

POUND INTEREST RATE =4%

According to interest rate parity Theory,

FR = SR (1+Interest rate of counrty 1)^t / (1+ interest rate of country 2)^t

=>FR after 1 year = Pound 1 = $1.85 per pound *(1.03)/(1.04) = $1.83

=> FR after 1 year = Pound 1 = S (1.03/1.04) $

Bank will sell $1.8 for Pound 1

and Bank will sell pound 1 received  for S(1.03/1.04)$ in the market after 1 year

Hence net gain / loss (in $)per Pound after 1 year= $1.8 -S(1.03/1.04)$.

$ INTEREST RATE =3%

Hence present gain/loss per Pound = ($1.8 -S(1.03/1.04)$) / (1.03)

Value of the contract for 1000000 pound = 1000000 (1.8 -S(1.03/1.04)) / (1.03)

Value = 1,000,000 (1.8 - S (1.03/1.04)) / 1.03