# Chapter 6 International Parity Relationships

**Topics:**Exchange rate, United States dollar, Foreign exchange market

**Pages:**6 (1660 words)

**Published:**February 2, 2013

PROBLEMS

1. Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 to invest for six months. The six-month interest rate is 8 percent per annum in the United States and 7 percent per annum in Germany. Currently, the spot exchange rate is €1.01 per dollar and the six-month forward exchange rate is €0.99 per dollar. The treasurer of IBM does not wish to bear any exchange risk. Where should he/she invest to maximize the return?

If $100,000,000 is invested in the U.S., the maturity value in six months will be $104,000,000. Alternatively, $100,000,000 can be converted into euros and invested at the German interest rate, with the euro maturity value sold forward. In this case the dollar maturity value will be $105,590,909

Clearly, it is better to invest $100,000,000 in Germany with exchange risk hedging.

2. While you were visiting London, you purchased a Jaguar for £35,000, payable in three months. You have enough cash at your bank in New York City, which pays 0.35% interest per month, compounding monthly, to pay for the car. Currently, the spot exchange rate is $1.45/£ and the three-month forward exchange rate is $1.40/£. In London, the money market interest rate is 2.0% for a three-month investment. There are two alternative ways of paying for your Jaguar. (a) Keep the funds at your bank in the U.S. and buy £35,000 forward. (b) Buy a certain pound amount spot today and invest the amount in the U.K. for three months so that the maturity value becomes equal to £35,000. Evaluate each payment method. Which method would you prefer? Why?

Option a: Thus, the cost of Jaguar as of today is $48,489.

Option b: Thus the cost of Jaguar as of today is $49,755.

You should definitely choose to use “option a”, and save $1,266, which is the difference between $49,755 and $48489.

3. Currently, the spot exchange rate is $1.50/£ and the three-month forward exchange rate is $1.52/£. The three-month interest rate is 8.0% per annum in the U.S. and 5.8% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or £1,000,000. 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.

a. Thus, IRP is not holding exactly.

b. Arbitrage profit will be $12,040 .

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 is restored.

4. Suppose that the current spot exchange rate is €0.80/$ and the three-month forward exchange rate is €0.7813/$. The three-month interest rate is 5.60 percent per annum in the United States and 5.40 percent per annum in France. Assume that you can borrow up to $1,000,000 or €800,000. 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. b. Assume that you want to realize profit in terms of euros. Show the covered arbitrage process and determine the arbitrage profit in euros. a. Arbitrage profit = $23,758.

b. Arbitrage profit = €18,562.

5. In the issue of October 23, 1999, the Economist reports that the interest rate per annum is 5.93% in the United States and 70.0% in Turkey. Why do you think the interest rate is so high in Turkey? Based on the reported interest rates, how would you predict the change of the exchange rate between the U.S. dollar and the Turkish lira?

E(e) = -64.07%; The Turkish lira thus is expected to...

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