Assume the interest rate is 16% on pounds sterling and 7% on the Euro. At the same time, inflation is running at an annual rate of 3% in Germany and 9% in England.
- If the Euro is selling at a one-year forward premium of 10% against the pound, is there an arbitrage opportunity? Explain.
- What is the real interest rate in Germany? in England?
- Suppose that during the year the exchange rate changes from Euro2.7/£1 to Euro2.65/£1. What are the real costs to a German company of borrowing pounds? Contrast this cost to its real cost of borrowing Euro.
- If the Euro is selling at a one-year forward premium of 10% against the pound, is there an arbitrage opportunity? Explain.
Answer. According to interest rate parity, with a Euro rate of 7% and a 10% forward premium on the Euro against the pound, the equilibrium pound interest rate should be
1.07 x 1.10 – 1 = 17.7%
Since the pound interest rate is only 16%, there is an arbitrage opportunity. It involves borrowing pounds at 16%, converting them into Euro, investing them at 7%, and then selling the proceeds forward, locking in a pound return of 17.7%.
- What is the real interest rate in Germany? in England?
Answer. The real interest rate in Germany is 1.07/1.03 -1 = 3.88%. The real interest rate in England is 1.16/1.09 -1 = 6.42%.
- Suppose that during the year the exchange rate changes from Euro2.7/£1 to Euro2.65/£1. What are the real costs to a German company of borrowing pounds? Contrast this cost to its real cost of borrowing Euro.
Answer. At the end of one year, the German company must repay ,1.16 for every pound borrowed. However, since the pound has devalued against the Euro by 1.85% (2.65/2.70 – 1 = -1.85%), the effective cost in Euro is 1.16 x (1 – 0.0185) – 1 = 13.85%. In real terms, given the 3% rate of German inflation, the cost of the pound loan is found as 1.1385/1.03 -1 = 10.54%.
As shown above, the real cost of borrowing Euro equals 3.88%, which is significantly lower than the real cost of borrowing pounds. What happened is that the pound loan factored in an expected devaluation of about 9% (16% – 7%), whereas the pound only devalued by about 2%. The difference between the expected and actual pound devaluation accounts for the approximately 7% higher real cost of borrowing pounds.
- What are the real costs to a British firm of borrowing Euro? Contrast this cost to its real cost of borrowing pounds.
Answer. During the year, the Euro appreciated by 1.89% (2.70/2.65 – 1) against the pound. Hence, a Euro loan at 7% will cost 9.02% in pounds (1.07 x 1.0189 – 1). In real pound terms, given a 9% rate of inflation in England, this loan will cost the British firm 0.02% (1.0902/1.09 – 1) or essentially zero. As shown above, the real interest on borrowing pounds is 6.42%.
