Question

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

a. If the spot exchange rate decreases by $0.10, what is the dollar loss on the futures position?

b. In order to hedge its futures exposure, should the bank borrow in the UK or invest in the UK? How much?

c. If the bank hedges the futures contract, what is the total value of the bank’s portfolio?

Answer 1

a.

USE THE FORMULA:

1 + i_d) = (S / F) * (1 + i_f).

The formula above could be rearranged to determine the forward foreign exchange rate, in which F = S * ((1 + i_f) / (1 + i_d)).

Where:

i_d is the interest rate in the domestic currency, or the base currency

i_f is the interest rate in the foreign currency, or the quoted currency

S is the current spot foreign exchange rate

F is the forward foreign exchange rate

THEN FUTURE RATE IS:

1+0.04=((1/1.85)/F)*(1+0.03)

0R, F=0.535 AND 1 USD= 0.535 GBP

SPOT RATE: 1USD= (1/1.185) GBP=0.5405 GBP

NEW SPOT RATE: 1 GBP= 1.75 USD OR, 1 USD= 0.5714 GBP

VALUE OF 1000000 POUNDS IS=1.75*1000000=1.75 MILLION

DOLLAR LOSS= 1.8-1.75= 0,5 MILLION

b.

SINCE DOLLAR RATE HAS DECREASED, HENCE POUND HAS APPRECIATED WITH RESPECT TO DOLLAR AND HENCE COMPANY MUST INVEST IN UK.

c.

IF THE BANK HEDGES WITH A FUTURES CONTRACT THEN IT BUYS 1000000 POUNDS FOR 1.8 MILLION DOLLARS AND HENCE VALUE OF THE PORTFOLIO IS 1000000 POUNDS.