Question

Currently, the spot exchange rate is $1.50/£ and the three-month forward exchange rate is $1.52/£. The three-month interest rate is 8.0% per annum in the U.S. and 5.8% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000. Calculate your arbitrage profit in USD

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 $/£ = 1.52 as against the spot rate of 1.50

So we will try to make arbitrage .

Given  $1,500,000.

Let borrow  $1,500,000 in US. So that after 3 months we end up paying  $1,500,000 +  $1,500,000* (8%)*3/12

= $1530000

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

hence we get  $1,500,000/1.50 = 1,000,000 pounds

We invest this and at the end we get. 1000,000 + 1,000,000*(5.8%) * 3/12 = 1014500

Convert this into USD =1014500*1.52 = 1542040

hence the net profit will be 1542040 - 1530000 = 12040

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* 5.8% *3/12
= 1014500

We will convert this into dollars = 1014500 * 1.52 = $1542040

We will invest the 15,00,000

After 3 months we get

= 15,00,000 + 15,00,000 * 8% * 3/12

1530000

Hence we make a loss = 12040

This is because we are borrowing in high rate country and investing in low rate country