SOLUTIONS TO CHAPTER 4 PROBLEMS
1. From base price levels of 100 in 2000, Japanese and S. price levels in 2003 stood at 102 and 106, respectively.
- If the 2000 $:¥ exchange rate was $0.007692, what should the exchange rate be in 2003? ANSWER. If e2003 is the dollar value of the yen in 2003, then according to purchasing power parity e2003/0.007692 = 106/102 or e2003 = $0.007994.
- b. In fact, the exchange rate in 2003 was ¥ 1 = $0.008696. What might account for the discrepancy? (Price levels were measured using the consumer price in)
- Two countries, the United States and England, produce only one good, wheat. Suppose the price of wheat is $3.25 in the United States and is £1.35 in England.
- According to the law of one price, what should the $:£ spot exchange rate be?
- Suppose the price of wheat over the next year is expected to rise to $3.50 in the United States and to £1.60 in England. What should the one-year $:£ forward rate be?
- If the U.S. government imposes a tariff of $0.50 per bushel on wheat imported from England, what is the maximum possible change in the spot exchange rate that could occur?
- 3. If expected inflation is 100 percent and the real required return is 5 percent, what will the nominal interest rate be according to the Fisher effect?
- 4. In early 1996, the short-term interest rate in France was 7%, and forecast French inflation was 1.8%. At the same time, the short-term German interest rate was 2.6% and forecast German inflation was 1.6%.
- Based on these figures, what were the real interest rates in France and Germany?
- To what would you attribute any discrepancy in real rates between France and Germany?
- 5. In July, the one-year interest rate is 12% on British pounds and 9% on U.S. do
- If the current exchange rate is $1.63:£1, what is the expected future exchange rate in one year?
- Suppose a change in expectations regarding future U.S. inflation causes the expected future spot rate to decline to $1.52:£1. What should happen to the U.S. interest rate?
- 6. Suppose that in Japan the interest rate is 8% and inflation is expected to be 3%. Meanwhile, the expected inflation rate in France is 12%, and the English interest rate is 14%. To the nearest whole number, what is the best estimate of the one-year forward exchange premium (discount) at which the pound will be selling relative to the French franc?
- 7. Chase Econometrics has just published projected inflation rates for the United States and Germany for the next five yea U.S. inflation is expected to be 10 percent per year, and German inflation is expected to be 4 percent per year.
- If the current exchange rate is $0.95/€, what should the exchange rates for the next five years be?
- Suppose that U.S. inflation over the next five years turns out to average 3.2%, German inflation averages 1.5%, and the exchange rate in five years is $0.99/€. What has happened to the real value of the euro over this five- year period?
- 8. During 1995, the Mexican peso exchange rate rose from Mex$5.33/U.S.$ to Mex$7.64/U.S.$. At the same time, U.S. inflation was approximately 3% in contrast to Mexican inflation of about 48.7%.
- By how much did the nominal value of the peso change during 1995?
- By how much did the real value of the peso change over this period?
- Suppose three-year deposit rates on Eurodollars and Eurofrancs (Swiss) are 12 percent and 7 percent, respectively. If the current spot rate for the Swiss franc is $0.3985, what is the spot rate implied by these interest rates for the franc three years from now?
- 10. Assume the interest rate is 16 percent on pounds sterling and 7 percent on euros. At the same time, inflation is running at an annual rate of 3 percent in Germany and 9 percent in England.
- If the euro is selling at a one-year forward premium of 10 percent against the pound, is there an arbitrage opportunity? Explain.
- b. What is the real interest rate in Germany? in England?
- Suppose that during the year the exchange rate changes from €1.8/£1 to €1.77/£1. 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.
- 11. Suppose the Eurosterling rate is 15 percent, and the Eurodollar rate is 11.5 p What is the forward premium on the dollar? Explain.
- 12. Suppose the spot rates for the euro, pound sterling, and Swiss franc are $1.52, $2.01, and $0.98, respectively. The associated 90-day interest rates (annualized) are 8 percent, 16 percent, and 4 percent; the U.S. 90- day rate (annualized) is 12 percent. What is the 90-day forward rate on an ACU (ACU 1 = €1 + £1 + SFr 1) if interest parity holds?
- 13. Suppose that three-month interest rates (annualized) in Japan and the United States are 7 percent and 9 percent, respectiv If the spot rate is ¥142:$1 and the 90-day forward rate is ¥139:$1:
- Where would you invest?
- b. Where would you borrow?
- What arbitrage opportunity do these figures present?
- d. Assuming no transaction costs, what would be your arbitrage profit per dollar or dollar-equivalent borrowed?
- 14. Here are some prices in the international money markets:
Forward rate (one year) Interest rate (€)
Interest rate ($)
= 7% per year
= 9% per year
- Assuming no transaction costs or taxes exist, do covered arbitrage profits exist in the above situation? Describe the flows.
- Suppose now that transaction costs in the foreign exchange market equal 0.25% per transaction. Do unexploited covered arbitrage profit opportunities still exist?
- Suppose no transaction costs exist. Let the capital gains tax on currency profits equal 25%, and the ordinary income tax on interest income equal 50%. In this situation, do covered arbitrage profits exist? How large are they? Describe the transactions required to exploit these profits.
- 15. Suppose today’s exchange rate is $1.55/€. The six-month interest rates on dollars and euros are 6 percent and 3 percent, respectively. The six-month forward rate is $1.547 A foreign exchange advisory service has predicted that the euro will appreciate to $1.5790 within six months.
- How would you use forward contracts to profit in the above situation?
- How would you use money market instruments (borrowing and lending) to profit?
- Which alternatives (forward contracts or money market instruments) would you prefer? Why?