CHAPTER 4: PARITY CONDITIONS IN INTERNATIONAL FINANCE AND CURRENCY FORECASTING
- Inflation is the logical outcome of an expansion of the money supply in excess of real output growth. As the supply of one commodity increases relative to supplies of all other commodities, the price of the first commodity must decline relative to the prices of other commodities. In other words, its value in exchange or exchange rate must decline. Similarly, as the supply of money increases relative to the supply of goods and services, the price of money in terms of goods and services must decline, i.e., the exchange rate between money and goods declines.
- The international parallel to inflation is domestic currency depreciation relative to foreign currencies. To maintain the same exchange rate between money and goods both domestically and abroad, the exchange rate must decline by (approximately) the difference between the domestic and foreign rates of inflation. This is purchasing power parity, which is itself based on the law of one price.
- Although the nominal or actual money exchange rate may fluctuate all over the place, we would normally expect the real, or inflation-adjusted exchange rate, to remain relatively constant over time. The same is true for nominal versus real rates of interest. However, although the prediction that real interest and exchange rates will remain constant over time is a reasonable one ex ante, ex post we find that these real rates wander all over the place. A changing real exchange rate is the most important source of exchange risk for companies.
- Four additional equilibrium economic relationships tend to hold in international financial markets: Purchasing Power Parity (PPP), the Fisher Effect, International Fisher Effect (IFE), Interest Rate Parity (IRP), and the forward rate as an unbiased estimate of the future spot rate.
1.a. What is purchasing power parity (PPP)?
- b. What are some reasons for deviations from purchasing power parity?
- Comment on the following statement: “It makes sense to borrow during times of high inflation because you can repay the loan in cheaper dollars.”
- Which is likely to be higher, a 150% ruble return in Russia or a 15% dollar return in the U.S.?
- The interest rate in England is 12%, while in Switzerland it is 5%. What are possible reasons for this interest rate differential? What is the most likely reason?
- Over the period 1982-1988, Peru and Chile stand out as countries whose interest rates are not consistent with their inflation experience. Specifically, Peru’s inflation and interest rates averaged about 125% and 8%, respectively, over this period, whereas Chile’s inflation and interest rates averaged about 22% and 38%, respectively.
7.a. How would you characterize the real interest rates of Peru and Chile (e.g., close to zero, highly positive, highly negative)?
7.b. What might account for Peru’s low interest rate relative to its high inflation rate? What are the likely consequences of this low interest rate?
7.c. What might account for Chile’s high interest rate relative to its inflation rate? What are the likely consequences of this high interest rate?
7.d. During the same period, Peru had a small interest differential and yet a large average exchange rate change. How would you reconcile this experience with the IFE and with your answer to part b?
- Over the period 1982-1988 numerous countries (e.g., Pakistan, Hungary, Venezuela) had a small or negative interest rate differential and a large average annual depreciation against the dollar. How would you explain these data? Can you reconcile these data with the IFE?
- What factors might lead to persistent covered interest arbitrage opportunities among countries?
- In early 1989, Japanese interest rates were about 4 percentage points below U.S. rates. The wide difference between Japanese and U.S. interest rates prompted some U.S. real estate developers to borrow in yen to finance their projects. Comment on this strategy.
- In late December 1990, one‑year German Treasury bills yielded 9.1%, whereas one‑year U.S. Treasury bills yielded 6.9%. At the same time, the inflation rate during 1990 was 6.3% in the U.S., double the German rate of 3.1%.
12.a. Are these inflation and interest rates consistent with the Fisher Effect?
12.b. What might explain this difference in interest rates between the U.S. and Germany?
- The spot rate on the euro is $0.91 and the 180‑day forward rate is $0.93. What are possible reasons for the difference between the two rates?
- If the dollar is appreciating against the Polish zloty in nominal terms but depreciating against the zloty in real terms, what do we know about Polish and U.S. inflation rates?
- Suppose the nominal peso/dollar exchange rate is fixed. If the inflation rates in Mexico and the U.S. are constant (but not necessarily equal), will the real value of the peso/dollar exchange rate also be constant over time?
- If the average rate of inflation in the world rises from 5% to 7%, what will be the likely effect on the U.S. dollar’s forward premium or discount relative to foreign currencies?
- Comment on the following quote from the Wall Street Journal (August 27, 1984, p. 6) that discusses the improving outlook for Britain’s economy: “Recovery here will probably last longer than in the U.S. because there isn’t a huge budget deficit to pressure interest rates higher.”
- Comment on the following headline that appeared in the Wall Street Journal (December 19, 1990, p. C10): “Dollar Falls Across the Board as Fed Cuts Discount Rate to 6.5% From 7%.” (The discount rate is the interest rate the Fed charges member banks for loans.)
- In an integrated world capital market, will higher interest rates in, say Japan, mean higher interest rates in, say, the U.S.?
- From base price levels of 100 in 2000, Japanese and U.S. price levels in 2006 stood at 98 and 109, respectively.
1.a. If the 2000 $:¥ exchange rate was $0.00928, what should the exchange rate be in 2006?
1.b. In fact, the exchange rate in 2006 was ¥1 = $0.00860. What might account for the discrepancy? (Price levels were measured using the consumer price index.)
- Two countries, the U.S. and England, produce only one good, wheat. Suppose the price of wheat is $3.25 in the U.S. and is £1.35 in England.
2.a. According to the law of one price, what should the $:£ spot exchange rate be?
2.b. Suppose the price of wheat over the next year is expected to rise to $3.50 in the U.S and to £1.60 in England. What should the one‑year $:£ forward rate be?
- If expected inflation is 100% and the real required return is 5%, what will the nominal interest rate be according to the Fisher Effect? (exact and approximate!)
- Suppose the short-term interest rate in France was 3.7%, 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%.
4.a. Based on these figures, what were the real interest rates in France and Germany?
- In July, the one‑year interest rate is 12% on British pounds and 9% on U.S. dollars.
5.a. If the current exchange rate is $1.63:£1, what is the expected future exchange rate in one year?
5.b. 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?
- 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?
- Suppose three‑year deposit rates on Eurodollars and Eurofrancs (Swiss) are 12% and 7%, 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?
- Assume 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.
10.a. If the euro is selling at a one-year forward premium of 10% against the pound, is there an arbitrage opportunity? Explain.
10.b. What is the real interest rate in Germany? In England?
- Suppose that three-month interest rates (annualized) in Japan and the U.S. are 7% and 9%, respectively. If the spot rate is ¥142:$1 and the 90-day forward rate is ¥139:$1:
13.a. Where would you invest?
13.b. Where would you borrow?
13.c. What arbitrage opportunity do these figures present?
13.d. Assuming no transaction costs, what would be your arbitrage profit per dollar or dollar-equivalent borrowed?
- Suppose today’s exchange rate is $1.35/€. The six-month interest rates on dollars and euros are 6% and 3%, respectively. The six-month forward rate is $1.3672. A foreign exchange advisory service has predicted that the euro will appreciate to $1.375 within six months.
15.a. How would you use forward contracts to profit in the above situation?
15.b. How would you use money market instruments (borrowing and lending) to profit?
15.c. Which alternatives (forward contracts or money market instruments) would you prefer? Why?