Question

3. 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 percent per annum in the U.S. and 5.8 percent per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000. a. Determine whether interest rate parity is currently holding. b. If IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit. c. Explain how IRP will be restored as a result of covered arbitrage activities.

Answer 1

Answer a)

Interest rate in 3 months , I_d = 8% = 8/4=2% , I_f = 5.8%= 5.8/4= 1.45%

S = $1.5/£; F = $1.52/£.

As per concept of IPR , Forward Rate = Spot Rate * (1+I_f )/ (1+I_d)

(1+I$) = 1.02, with concept of IPR (1+I£)(F/S) = (1.0145)(1.52/1.50) = 1.0280

As the actual interest rate $\neq$ calculated Interest rate.; IPR is not holding

Answer b) Step 1) Borrow $1,500,000 in US at rate of 8% per year for 3 months; repayment will be =$1,500,000*1.02 =$1,530,000.

Step 2) Buy £1,000,000 at spot rate = $1,500,000/1.50

Step 3) Invest £1,000,000 at the pound interest rate of 1.45% for 3 months ; maturity value = £1,000,000*1.0145= £1,014,500.

Step 4) Sell £1,014,500 at forward 1.52 = £1,014,500*1.52= $1,542,040

Arbitrage profit =$1,542,040 - $1,530,000= $12,040

Answer c) The covered arbitrage opportunity may create following impact which will help in restoration of IPR

• $ interest rate may rise;
• £ interest rate may fall;
• spot exchange rate may rise
• forward exchange rate may fall