Question

Currently, the spot exchange rate is $1.52/£ and the three-month forward exchange rate is $1.54/£. The three-month interest rate is 5.84% per annum in the U.S. and 5.84% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000. If the IRP is not holding, determine the arbitrage profit in British Pound. Otherwise input your answer as 0 PS: Please input your answer without any currency information.

Answer 1

We know that as per IRP theory any interest rate arbitrage will be set off by change in the exchange rates between both the conuntries

Here interest rate in both the coun tries did not change

Hence as per IRP the forward rate should be equal to spot rate.

We have been given that the forward rate is $/£ = 1.54 as against the spot rate of 1.52

So we will try to make arbitrage .

Given  $1,500,000.

Let borrow  $1,500,000 in US. So that after 3 months we wnd up paying  $1,500,000 +  $1,500,000* (5.84%)*3/12

= 1521900 $

Pounds required to settle this transaction is 1521900/1.54 = 988246.7532

We have invested the borrowed  $1,500,000 in pounds

hence we get  $1,500,000/1.52 = 986842.105 pounds

We invest this and at the end we get. 1001250 pounds

hence the net profit will be 1001250 - 988246.7532 = 13003 Pounds

Let will try the other way also

Given ,1,000,000 Pounds

We will borrow This

And after 3 months we will end up paying 1,000,000 + 1,000,000* 5.84% *3/12
= 1014600

We will invest the 1,000,000 pounds converting it into USD

Amount invested 1,000,000*1.52 = 1520000$

After 3 months we get 1520000 + 1520000*5.84% *3/12

= 1542192 Dollars

Coverting this into pounds = 1542192/1.54

=1001423.377

That means we make a loss here

Hence we will borrow in dollars to make an arbitrage profit of 13003 pounds