Question

Currently, the spot exchange rate is 1.50 USD/GBP and the three-month forward exchange rate is 1.510 USD/GBP. The three-month interest rate is 5.0% per annum in the U.S. and 2.0% per annum in the UK. Assume that you can borrow as much as $1,500,000 or £1,000,000.

a/ What is the implied three-month U.S.per annuminterest rate? (round to 2 decimals in %)

b/ Does Interest Rate Parity hold?

c/ Determine the arbitrage profit (if any, otherwise type "0") and report it in the currency in which you borrow. Remember that you should have a three month investment horizon.

In______(fill in "USD" or "GBP"), the arbitrage profit is ______(round to the nearest currency unit)

Answer 1

As per interest rate parity, forward rate = Spot rate*(1+ interest rate US)/(1+ Interest rate UK)

1.510 = 1.50*(1+ interest rate US*3/12)/(1+2%*3/12)

Implied interest rate in US = 4.68%

B. No, since actual interest rate is different

C. Borrow GBP 1,000,000

Convert into USD at Spot rate and get 1,000,000*1.50 =$1,500,000

Invest for 3 months and get =1500,000*(1+5%*3/12) =$1,518,750

Convert back into GBP and get 1,518,750/1.510 = GBP 1,005,794.70

Repay loan = GBP 1,000,000*(1+2%*3/12) = GBP 1,005,000

arbitrage gain = GBP 794.70