Question

Assume that the interest rate is 16% on pounds sterling and 7% on euros. At the same time, inflation is running at an annual rate of 3% in Germany and 9% in England. a. If the euro is selling at a one-year forward premium of 202 | 10% against the pound, is there an arbitrage opportu- nity? Explain. b. What is the real interest rate in Germany? In England? C. Suppose that during the year the exchange rate changes from €1.8: £l to €1.77 :£l. What are the real costs to a German company of borrowing pounds? Contrast this cost to its real cost of borrowing euros. |d. What are the real costs to a British firm of borrowing euros? Contrast this cost to its real cost of borrowing pounds.

Answer 1

Solution :-

(A)

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 + 0.07) x (1 + 0.10) - 1 = 17.7%
Since the pound interest rate is only 16%, Means Arbitrage opportunity Exists. It involves borrowing pounds at 16%, converting them into euros, investing them at 7%, and then selling the
proceeds forward, locking in a pound return of 17.7%.

(B)

The real interest rate

In Germany is (1.07 / 1.03) - 1 = 0.0388 = 3.88%.

In England is (1.16 / 1.09) - 1 = 0.0642 = 6.42%.

(C)

At the end of one year, the German company must repay £1.16 for every pound borrowed. However, since the pound has depreciated against the euro by 1.67% ( 1.77 / 1.80 - 1 = -1.67%), the effective cost in euros is 1.16 x (1 - 0.0167) - 1 = 14.07%. In real terms, given the 3% rate of German inflation, the cost of the pound loan is found as (1.1407 / 1.03) - 1 = 10.74%.

(D)

The real cost of borrowing euros equals 3.88% [ ( 1.07 / 1.03 ) - 1 ], which is significantly lower than the real cost of borrowing pounds. What happened is that the pound loan factored in an expected depreciation of about 9% (16% - 7%), whereas the pound only depreciated by about 2%. The difference between the expected and actual pound depreciation accounts for the approximately 7% higher real cost of borrowing pounds.