Determining interest rate parity

Question

Presently, spot exchange rate is $1.50/£ and three-month forward exchange rate is $1.52/£. Three-month interest rate is 8.0% per annum within the U.S. and 5.8% per annum within the U.K. Suppose that you can borrow as much as $1,500,000 or £1,000,000. 

a) Determine if the interest rate parity is presently holding.

b) In case IRP is not holding, how could you carry out the covered interest arbitrage? Display all steps and also compute the arbitrage profit.

c) Describe how IRP will be restored due to covered arbitrage activities.

Answer 1

Firstly, let summarize the given data:

   S = $1.5/£; F = $1.52/£;  I$ = 2.0%;  I£ = 1.45%

   Credit = $1,500,000 or £1,000,000.

a. (1+I$) = 1.02

    (1+I£)(F/S) = (1.0145)(1.52/1.50) = 1.0280

Hence, IRP is not holding exactly.

b. a) Borrow $1,500,000; repayment will be $1,530,000. 

    c) Buy £1,000,000 spot using $1,500,000.

    d) Invest £1,000,000 at pound interest rate of 1.45%;

         Maturity value will be £1,014,500.  

    e) Sell £1,014,500 forward for $1,542,040

    Arbitrage profit will be $12,040 

c. As per the, arbitrage transactions described above,

   Dollar interest rate will rise;

a) The spot exchange rate will rise;

b) The pound interest rate will fall;

c) These adjustments will continue until IRP holds.

d) The forward exchange rate will fall.