Question

Assignment 2

CHAPTER 5

INTERNATIONAL PARITY RELATIONSHIPS AND

FORECASTING FOREIGN EXCHANGE RATES

PROBLEMS

PROBLEMS

1. Suppose that the treasurer of General Electric has an extra cash reserve of $10,000,000 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 France. Currently, the spot exchange rate is $1.40/€ and the six-month forward exchange rate is $1.44/€. The treasurer of General Electric does not wish to bear any exchange risk. Where should he/she invest to maximize the return?

2. While you were visiting Frankfurt, you purchased a BMW for €50,000, payable in three months. You have enough cash in U.S. dollars 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 $1.35/€ and the three-month forward exchange rate is $1.30/€. In Frankfurt, the money market interest rate is 2.0% for a three-month investment. There are two alternative ways of paying for your BMW.

(a) Keep the funds at your bank in the U.S. and buy €50,000 forward.

(b) Buy a certain euro amount spot today and invest the amount in Germany for three months so that the maturity value becomes equal to €50,000.

Evaluate each payment method. Which method would you prefer? Why?

  

3. Currently, the spot exchange rate is $1.50/£ and the three-month forward exchange rate is $1.53/£. 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.

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 8 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.

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?

8. Suppose that the current spot exchange rate is €1.50/₤ and the one-year forward exchange rate is €1.58/₤. The one-year interest rate is 6.0% in euros and 5.2% in pounds. You can borrow at most €1,000,000 or the equivalent pound amount, i.e., ₤666,667, at the current spot exchange rate.

1. Show how you can realize a guaranteed profit from covered interest arbitrage. Assume that you are a euro-based investor. Also determine the size of the arbitrage profit.
2. Discuss how the interest rate parity may be restored as a result of the above

      transactions.

3. Suppose you are a pound-based investor. Show the covered arbitrage process and

      determine the pound profit amount

Answer 1

Since, multiple questions have been posted, I have answered the first one.

______

Question 1:

The treasurer has following two options:

1) Invest $10,000,000 in United States at the prevailing interest rate of 8% per annum of 4% for a period of 6 months.

2) Convert $10,000,000 into euros at the spot exchange rate, invest the converted amount in France at the prevailing interest rate (which is 7%/2 or 3.5%) for 6 months and forward sell the euro maturity value.

To take a decision, we will have to calculate the future/maturity value of both the options at the end of 6 months as below:

Maturity Value of Option 1 = Amount of Cash Reserve*(1+Interest Rate in U.S. for 6 Months) = 10,000,000*(1+4%) = $10,400,000

Maturity Value of Option 2 = Amount of Cash Reserve*(1/Spot Exchange Rate)*(1+Interest Rate in France for 6 Months)*Forward Exchange Rate = 10,000,000*(1/1.40)*(1+3.5%)*(1.44) = $10,645,714

Based on the above calculations it can be concluded that it is better to invest in France as it results in a higher return at the time of maturity.