Chapter 5:
Assignment
1. Why might the law of one price hold even in the presence of import tariffs?
2. Assume that the prices of a standard basket of goods and services in different countries are as follows
• United States $400
• Canada C$500
• United Kingdom £220
• Japan ¥60,000
a. What are the implied PPP exchange rates?
b. How would the presence of a high sales tax in Britain, such as the value added tax (VAT), influence your guess of where the actual value of S($/£) would be vis-à-vis the PPP value of S($/£)?
3. Why might there be departures from PPP even if the law of one price holds for every commodity?
4. a. Assume PMex
= 50 percent and PUS
= 2 percent. Calculate S(Ps/$) and S($/Ps) according to the precise
and approximate dynamic PPP conditions.
b. Assume that Mexican inflation increases to 100 percent, while US inflation remains at 2 percent. Calculate S(Ps/$) and S($/Ps) according to the precise and approximate PPP conditions.
c. How does the error in the approximate condition depend on whether you are measuring S(Ps/$) or S($/Ps)?
d. How would a constant percentage sales tax in Mexico affect your answers above?
5. If speculators are risk-averse, could this affect the accuracy of the link between the expected change in the exchange rate and the difference between expected inflation rates?
6. Is the accuracy of the approximate PPP condition negatively affected by the level of inflation?
7. Why might the relative form of PPP hold even though the absolute form does not?
8. Assume inflation in Brazil is 15 percent and in China is 2 percent. What is the percent change in the exchange rate of Brazilian reals per Chinese RMB, and Chinese RMB per Brazilian real, and why do these two percent changes differ?
9. What is required for price discrimination between markets to cause departures from the law of one price?
10. What is the relevance of a “goodness of fit” measure such as the R2 statistic for judging PPP?
11. What is one-way versus two-way arbitrage in the context of PPP, and how do the implications of the two types of arbitrage differ?
12. Specialization, which has accompanied freer trade, has caused countries to produce larger amounts of each of a narrower range of products, trading these for the wider range of products that people consume. How might this have affected PPP?
13. What characteristics of a Big Mac® led The Economist to choose it as a basis for their alternative PPP exchange rate measure? Can you suggest any other items which might be used?
14. Several possibilities, both theoretical and empirical, have been raised to explain the apparent failure of PPP.
List and explain at least three of these. Comment on the validity of the explanation.
15. Does empirical evidence suggest PPP may be more likely to hold in the short run or the long run? Can you suggest an explanation for why this might be true?
Chapter 6:
Assignment
1. Derive the criteria for making covered money-market investment and borrowing decisions when the exchange
rates are given in European terms. Derive the equivalent of equation (6.4).
2. You have been given the following information:
where: r$
= annual interest rate on three-month US dollar commercial paper
r£
= annual interest on three-month British-pound commercial paper
S($/£) = number of dollars per pound, spot
F¼($/£) = number of dollars per pound, three months forward
On the basis of the precise criteria:
a. In which commercial paper would you invest?
b. In which currency would you borrow?
c. How would you arbitrage?
d. What is the profit from interest arbitrage per dollar borrowed?
3. a. Use the data in Question 2 and the precise formula on the right-hand side of equation (6.4) to compute the covered yield on investment in pounds. Repeat this using the approximate formula on the right-hand side of equation (6.5).
b. Compare the error between the precise formula and the approximate formula in a above with the error in the situation where r$
= 15 percent, r£
= 16 percent, and S($/£) and F3($/£) are as above.
c. Should we be more careful to avoid the use of the “interest plus premium or minus discount” approximation in equation (6.5) at higher or at lower interest rates?
d. If the interest rates and the forward rate in Question 2 are for twelve months, is the difference between equation (6.4) and equation (6.5) greater than when we are dealing with three-month rates?
4. Derive the equivalent of Table 6.1 where all covered yields are against pounds rather than dollars.This will require computing appropriate cross spot and forward rates.
5. Draw a figure like Figure 6.4 to show what interest arbitrage will do to interest-rate differentials and the forward premiums at points A to F in the table below. If all the adjustment to the interest parity occurs in the forward exchange rate, what will F1/12($/£) be after interest parity has been restored?
6. Write down the expectations form of PPP, the uncovered interest parity condition, and the Fisher-open condition.
Derive each one from the other two.
7. Assuming that there are a large number of third-country borrowers and investors, do you think that political risk will cause larger deviations from interest parity than are caused by transaction costs?
8. If banks are as happy to advance loans that are secured by domestic currency money-market investments as they are to advance loans secured by similar foreign currency covered money-market investments, will firms prefer domestic currency investments over foreign currency investments on grounds of liquidity?
9. How does the importance of liquidity relate to the probability that cash will be needed?
10. Use the framework of Figure 6.7 to show how the band within which one-way arbitrage is unprofitable compares to the band within which round-trip arbitrage is unprofitable.
11. Why might a borrower want to borrow in a currency that is at a forward discount if that borrower faces a higher tax rate on interest income than on capital gains?
12. Why does the Fisher-open condition relate to countries rather than currencies?
13. In general, are transaction costs higher in spot or forward markets? Does this hold any implications for whether interest parity will hold exactly?
14. What role does the rest of the world play in determining whether covered interest parity will hold between any two currency-denominated securities?
15. Suppose that real interest rates are equal for all countries in the world. Does this imply anything for the relationship between covered interest rate parity and the PPP condition?
Chapter 13:
Assignment
1. In what sense is the sign – positive versus negative – of the slope coefficient which measures exposure relevant for exposure versus risk, and in what sense is it irrelevant?
2. How can exposure exceed the face value of a foreign currency-denominated asset or liability?
3. If the Bank of Canada “leans against the wind,” which means increasing interest rates when the Canadian dollar depreciates and lowering interest rates when the Canadian dollar appreciates, what would this mean for the exposure of
a. Canadian residents holding Canadian dollar-denominated bonds?
b. US residents holding Canadian dollar bonds?
Relate your answer to Question 2 above.
4. How does PPP relate to:
a. Exposure on real, fixed assets?
b. Operating exposure?
5. Would it make sense to add a firm’s exposures in different currencies at the spot exchange rate to obtain a measure of the firm’s aggregate exposure? If not, why not?
6. What is the problem in using the standard deviation of exchange rates as a measure of foreign exchange risk?
7. If a company has used its currency of debt denomination and/or forward contracts to make its exposure zero, what would measured exposure be from the β of a regression line, if in calculating b the debt and/or forward contracts were omitted from the regression equation?
8. Would the distinction between real and actual changes in exchange rates be important if inflation and interest rates were everywhere the same and were also small?
9. By studying the stock price of a US-based publicly traded company you have noticed that when the dollar drops against various currencies the company’s value on the stock exchange increases. By averaging the link between exchange rates and the company’s value you have determined the size of the change in each exchange rate that increases the value of the company by $1 million:
∆Su(€/$) = 0.1
∆Su(¥/$) = 5
∆Su(SFr/$) = 0.05
∆Su(C$/$) = 0.04
What is the company’s exposure to the various currencies?
10. Redo the analysis in this chapter of the effect of exchange-rate changes on an exporter by allowing the quantity sold, q, to change with the exchange rate instead of holding it constant. Use calculus to make the problem easier, and note that pUK
and q should be at profit-maximization levels in every period. [Note:This is a very difficult question.]