Question

Currently, the spot exchange rate is $1.50/£ and the six-month forward exchange rate is $1.52/£. The six-month interest rate is 8.0% per annum in the U.S. and 3% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000.

Answer The Following:

a. Determine whether the interest rate parity is currently holding?

b. If the IRP is not holding, how would you carry out covered interest arbitrage? (Show all the steps and determine the arbitrage profit.)

c. Explain how the IRP will be restored as a result of covered arbitrage activities (What factors could change and how?)?

Answer 1

Given:
Spot Exchange Rate, S=1.50
Forward exchange rate, F= 1.52
Interest rate in US, Ius=8%
Interest rate in UK, Iuk= 3%
Credit, C= 1,500,000 or 1,000,000

a) Now, (1+Ius) = 1.08
(1+Iuk)*(F/S) = 1.058*(1.52/1.50) = 1.072
Since, both are not equal hence Interest rate parity is not holding exactly.

b) Steps:
(1) Borrow $1,500,000 then the repayment will be $1,530,000.
(2) Buy £1,000,000 spot using $1,500,000.
(3) Invest £1,000,000 at the pound interest rate of 3%;
maturity value will be £1,030,000.
(4) Sell £1,030,000 forward for $1,565,600 (Euro*1.52)
Arbitrage profit will be $35,600 (1,565,600 - 1,530,000)

c) Following the arbitrage transactions described above,
The dollar interest rate will rise;
The pound interest rate will fall;
The spot exchange rate will rise;
The forward exchange rate will fall.
These adjustments will continue until IRP holds.