Assignment questions only; Chapters 4 through 8
Chapter 4
1. Why do you think that futures markets were developed when banks were already offering forward contracts?
What might currency futures offer which forward contracts do not?
2. To what extent do margin requirements on futures represent an opportunity cost?
3. How does the payoff profile of a futures sale of a currency compare to the profile of a purchase of the same currency?
4. Why is a futures contract similar to a string of bets on the expected exchange rate, settled every day?
5. Do you think that a limit on daily price movements for currency futures would make these contracts more or less risky or liquid? Would a limitation on price movement make the futures contracts difficult to sell during highly turbulent times?
6. How could arbitrage take place between forward exchange contracts and currency futures? Would this arbitrage be unprofitable only if the futures and forward rates were exactly the same?
7. Does the need to hold a margin make forward and futures deals less desirable than if there were no margin requirements?
Does your answer depend on the interest paid on margins?
8. How does a currency option differ from a forward contract? How does an option differ from a currency future?
9. Suppose a bank sells a call option to a company making a takeover offer where the option is contingent on the offer being accepted. Suppose the bank reinsures the option on an options exchange by buying a call for the same amount of foreign currency. Consider the consequences of the following four outcomes or “states”:
a. The foreign currency increases in value, and the takeover offer is accepted.
b. The foreign currency increases in value, and the takeover offer is rejected.
c. The foreign currency decreases in value, and the takeover offer is accepted.
d. The foreign currency decreases in value, and the takeover offer is rejected.
Consider who gains and who loses in each state, and the source of gain or loss. Satisfy yourself why a bank that reinsures on an options exchange might charge less for writing the takeover-contingent option than the bank itself pays for the call option on the exchange. Could this example help explain why a bank-based over-the-counter options market coexists with a formal options exchange market?
10. What is the payoff profile from buying and writing a call option? Ignore the transactions costs.
11. What type(s) of option would speculators buy if they thought the euro would increase more than the market believed?
12. What type(s) of option would speculators write if they thought the Swiss franc would increase more than the market believed?
Chapter 5
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
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?
Possibly
Chapter 7
1. Since gold is a part of official reserves, how would the balance-of-payments statistics show the sale of domestically mined gold to the country’s central bank? What happens if the mining company sells the gold to foreign private buyers?
2. Can all countries collectively enjoy a surplus, or must all surpluses and deficits cancel against each other? What does gold-mining mean for the world’s balance?
3. Under what conditions would inflation increase the value of exports?
4. Even if inflation did increase the value of exports, would the balance of trade and the exchange rate necessarily improve from inflation that is higher than in other countries?
5. How do we know that an exogenous increase in exports will cause a currency to appreciate even though the balance of payments is always zero? How does your answer relate to the law of supply and demand whereby supply equals demand even after demand has increased?
6. What is the difference between the immediate and the long-run effect of the sale of bonds to foreign investors?
7. What is the difference between the immediate and the long-run effect of direct investment by foreigners when the direct investment is in a heavily export-oriented activity such as oil exploration and development? Would it make any difference if the industry into which direct investment occurred were involved in the production of a good the country previously had been importing?
8. If the balance of payments of Alaska were prepared, what do you think it would look like? How about the balance of payments of New York City? What do you think the net investment position of these locations will be? Should we worry if Alaska is in debt?
9. If the overall level of interest rates in all countries increased, how would this affect the balance of payments of the US as a net debtor nation?
10. Which item(s) in the balance-of-payments account, Table 7.1,would be most affected by an expected appreciation of the US dollar, and how would the item(s) and the current spot value of the dollar be affected by the expected appreciation? Do you believe that the higher expected future value of the US dollar could increase the spot value immediately?
Chapter 8
1. Assume that the foreign currency amount of interest and dividend earnings from abroad is fixed. Show how the horizontal addition of interest and dividend earnings to a currency’s demand curve will appear when consideration is given to the effect of exchange rates on the translated values of these earnings.
2. Are debt-service imports as likely to be affected by exchange rates as are debt-service exports? [Hint: It depends on the currency of denomination of debt-service earnings and payments.]
3. What is the slope of the currency supply curve when the demand for imports is unit-elastic; that is, equal to 1.0?
4. What is the intuitive explanation for the fact that a decrease in demand for a currency can cause it to appreciate if import and export demand are sufficiently inelastic?
5. How can speculators cause the foreign exchange market to be stable even when the economy is moving along the downward-sloping part of a J curve?
6. Why is the import demand curve likely to be more elastic in the long run than in the short run?
7. Why are exports likely to be more elastic in the long run than in the short run?
8. Does only the equilibrium exchange rate change with inflation, or is the quantity of currency traded also affected; if so, why?