Question

Suppose that the current spot exchange rate is $1.2/£ and the 1-year forward exchange rate is $1.3/£. The U.S. 1-year interest rate is 5 percent and the U.K. 1-year interest rate is 6 percent. Assume that you can borrow up to $1.2M or £1M.

a. Show how to realize a certain profit via covered interest arbitrage, assuming that you want to realize profit in terms of U.S. dollars. Also determine the size of your arbitrage profit in U.S. dollars.  Please show your step by step arbitrage strategy and calculation.

b. Assume that you want to realize profit in terms of British pounds. Show the size of covered arbitrage profit in British pounds.  Please show your calculation.

Answer 1

(a) Arbitrage Process

A Today's Transaction

1. Borrow $ 1,200,000 at interest rate of 5%

2. Convert $ into £ at spot rate i.e. 1,200,000/1.20 = £1,000,000

3. Invest £ 1,000,000 at interest rate of 6%

4. Take 1 Year forward sale contract of £ 1,060,000@ $1.30/£

B After One Year Transaction

1. Realised £ investment with interest and sale £ under forward contract = (1,000,000 * 1.06) * 1.30

= $ 1,378,000

2. Repay Borrowing of $ with interest = 1,200,000 * 1.05 = $ 1,260,000

3. Net Profit = Investment Proceed - Borrowing Payment

= 1,378,000 - 1,260,000 = $118,000

(b) Calculation of Net profit in £

Net profit = $ 118,000 / 1.30 = £ 90769

To realise such amount directly in pound we will have forward contract for required amount only that use to repay borrowin i.e. $ 1,260,000/1.30 = £969,231 instead of £1,060,000