Question

A currency dealer has good credit and can borrow either € 1,000,000 or £ 750,000 for two years. The 2-year euro interest rate is 5%, and the 2-year pound interest rate is 6%.  The spot exchange rate is
£0.75/€, and the 2-year forward exchange rate is £0.80/€.

1. Show how to realize a certain profit via covered interest arbitrage.
2. How do interest rates, the spot currency market, and the forward currency market adjust to produce an equilibrium?  Provide some explanation of the adjustment process.

Answer 1

Current Spot Rate = £ 0.75 / €, € Interest Rate = 5 % and  £ Interest Rate = 6 %

A covered interest arbitrage can be executed as desrcibed below:

- Borrow £ 750000 for two years at the £ interest rate of 6 % per annum. This borrowing results in a liability of 750000 x (1.06)^(2) = £ 842700

- Convert the borrowing of £ 750000 into € at the current spot rate of £0.75/€ to yield = (750000 / 0.75) = € 1000000

- Invest this € 1000000 for two years at the € interest rate of 5 % per annum. This investment would produce a total value = 1000000 x (1.05)^(2) = € 1102500

- Convert this € investment proceed into £ at the forward exchange rate of € 0.8 / £ to yield (1102500 x 0.8) = £ 882000

- Covered Interest Arbitrage Profit = £ 882000 - 842700 = £ 39300

As an increasing number of people realize the possibility of making this arbitrage profit, their is an increase demand to borrow pounds, thereby pushing up pound interest rates. An increased pound interest rate in comparison to the euro interest rate will result in pound devaluing relative to the euro, pushing the forward exchange rate towards the equilibirum expected spot exchange rate two years later. This, in turn, would lead to the covered interest arbitrage gains getting wiped out.