1.1) Between 1994 and 1995, the Mexican peso moved from $3.38 to $6.44.
a) How many dollars did the Mexican peso buy in 1994? And in 1995?
b) How many Mexican pesos did the U.S. dollar buy in 1994? And in 1995?
c) Compute the 1994-1995 percentage change in the value of the Mexican peso relative to the U.S. dollar ($/MXN).
d) Given your answer in c), did the Mexican peso appreciate or depreciate against the U.S. dollar over the 1994-1995 period?
e) Given your answer in d), did the U.S. dollar appreciate or depreciate against the Mexican peso over the 1994-1995 period?
f) Compute the 1994-1995 percentage change in the value of the U.S. dollar relative to the Mexican peso (MXN/$).
1.2) On June 18, 2007, one U.S. dollar bought ¥124.09. On June 18, 2012, one U.S. dollar was worth ¥80.52. By June 18, 2015, the U.S. dollar moved to ¥123.53.
a) Did the yen appreciate or depreciate against the U.S. dollar between June 2007 and June 2012? Did such trend continue between June 2012 and June 2015?
b) How many U.S. dollars did one yen buy on June 18, 2007? And on June 18, 2012? What was the U.S. dollar value of the yen on June 18, 2015?
c) By what percentage has the yen appreciated/depreciated against the U.S. dollar between June 2007 and June 2012? And between June 2012 and June 2015?
d) By what percentage has the U.S. dollar appreciated/depreciated against the yen between June 2007 and June 2012? And between June 2012 and June 2015?
e) Do your answers to questions d) and c) change if you consider the entire sample period (2007-2015)?
1.3) The Brazilian real devalues by 40% against the U.S. dollar. By how much does the U.S. dollar appreciate against the Brazilian real?
1.4) Assume Euro Area inflation increases relative to U.S. inflation. Define the (nominal) exchange rate as the dollar value of one euro. What is the impact on the equilibrium exchange rate (all else unchanged)? Describe the impact of this relative change on the demand for and supply of euros. Present a graphical solution.
Topic 2: Parity Conditions and Currency Forecasting (Chapter 4)
2.1) Suppose the Swiss franc is worth $0.40 at the beginning of the year. During the year, U.S. inflation is 5% and Swiss inflation is 3%.
a) Does economic theory predict an appreciation or a depreciation of the Swiss franc over the year? Why? By how much approximately?
Suppose the Swiss franc is worth $0.44 at the end of the year.
b) By how much did the nominal value of the Swiss franc change over the year? Does your answer confirm or disprove the prediction of economic theory?
c) Does your answer in b) imply a change in the competitiveness of Switzerland relative to the United States? Why?
d) Compute the real value of the Swiss franc relative to the U.S. dollar at the end of the year.
e) The real exchange rate at the beginning of the year equals the nominal spot rate. Compute
the change in the real value of the Swiss franc over the year.
f) Verify that the real percentage change in the exchange rate (answer d) equals the difference between the nominal percentage change in the exchange rate (answer b) and the inflation rate differential between the two countries.
2.2) The following table shows the price of a Big Mac in a variety of countries and the nominal bilateral exchange rate between such countries and the United States in January 2017. Prices are denominated in local currencies (LOC); any exchange rate is expressed as LOC/$.
|
Country
|
Big Mac local price (LOC)
|
Exchange Rate (LOC/$)
|
Implied PPP exchange rate (LOC/$)
|
Big Mac dollar price ($)
|
Under/over valuation against $ (%)
|
|
United States
|
5.06
|
1
|
1
|
5.06
|
0
|
|
Euro Area
|
3.88
|
0.96
|
|
|
|
|
United Kingdom
|
3.09
|
0.83
|
|
|
|
|
China
|
19.60
|
6.93
|
|
|
|
|
Mexico
|
49
|
21.95
|
|
|
|
|
Japan
|
380
|
116.67
|
|
|
|
|
Switzerland
|
6.50
|
1.02
|
|
|
|
a) For each country, compute the implied PPP exchange rate, the dollar price of the local BigMac and quantify the resulting under/over valuation of the currency of interest against the U.S. dollar (in percentage terms). Please fill the table and report all intermediate steps in your solution sheet.
b) In which countries is the U.S. dollar weaker than the domestic currency? And stronger?
2.3) On January 1, 1990, the annual inflation rates in the U.S. and Greece were expected to be 3% and 8%, respectively. Assume the drachma was worth $.007 on that day. What was the expected spot rate in three years according to economic theory?
2.4) Assume the prices indexes in Spain and the U.S are at 100 in January 1981 and at 117 and 105, respectively, in May 1981. Assume the peseta is worth $0.1320 in January 1981 and $0.1185 in May 1981.
a) Compute the PPP rate of the peseta over the period ($/PS).
b) Did the peseta appreciate or depreciate against the U.S. dollar in nominal terms over the period? By how much?
c) What is the real exchange rate for the peseta in May 1981?
d) By how much did the real value of the peseta change over the period?
e) Verify that the change in the nominal exchange rate ($/PS) is approximately equal to the inflation differential between the two countries.
You discover that your Professor was distracted and reported an incorrect nominal exchange rate. In May 1981, the correct exchange was PS1 = $0.1125.
f) Was the nominal depreciation of the peseta against the U.S. dollar larger, smaller or equal to the PPP prediction between January and May 1981? Was the peseta undervalued or overvalued relative to the U.S. dollar in May 1981?
g) What was the real exchange rate for the peseta in May 1981?
h) Did the peseta appreciate or depreciate against the U.S. dollar in real terms over the period? By how much?
i) What are the implications of your findings for Spanish exporters?
j) Compare the dollar price of a basket of Spanish goods in January 1981 to the dollar price of the same basket in May 1981. Verify that your answer in i) is correct.
2.5) The price of a BMW is $33000 in the United States and €28000 in Germany.
a) Where would you buy? Why?
b) What is the nominal exchange rate (€/$) implied by economic theory? At this exchange rate, where would you buy?
c) The actual nominal exchange rate is 0.93€/$. Is there any arbitrage opportunity? Where would you buy? Why?
2.6) Assume that the United States and the United Kingdom produce only one good, wheat. Suppose the price of wheat is $3.25 in the United States and £1.35 in the United Kingdom.
a) According to the Law of One Price, what should the nominal spot exchange rate ($/£) be?
b) Assume the U.S. government imposes a tariff of $0.50 per bushel on wheat imported from the United Kingdom. What is the nominal spot exchange rate ($/£) that ensures no arbitrage?
Suppose the price of wheat over the next year is expected to rise to $3.50 in the United States and £1.35 in the United Kingdom.
c) What should the one-year forward exchange rate ($/£) be? If the one-year forward exchange rate is $/£ 3, is there any arbitrage opportunity?
d) What is the change in the nominal exchange rate implied by these prices (approximately) ?
2.7) Assume annualized interest rates in the U.S. and Switzerland are 10% and 4%, respectively, and the Swiss franc can be exchanged for $0.3807. Assume covered interest rate parity holds. What is the 90day forward rate for the Swiss franc ($/Swiss franc)?
2.8) You want to invest $1,000,000,000 for one year. Assume the interest rate in the Australia is 6% and the interest rate in the United States is 1%. The current spot rate is AUD/$ 1.32 and the one-year forward rate is AUD/$ 1.3307. Would you prefer investing in Australia or in the United States? Why? Compute the proceeds of both strategies.
2.9) Assume the Australian dollar buys 0.75 U.S. dollars and the one-year forward rate is $/AUD 0.7515. Is the Australian dollar quoted at the forward discount or at the forward premium?
2.10) If annualized interest rates in the U.S. and Switzerland are 10% and 4%, respectively, and the 90day forward rate for the Swiss franc is $.3864, at what current spot rate will covered interest rate parity hold?
2.11) Annualized interest rates in the U.S. and France on January 1, 1991 are 9% and 13%, respectively. The spot value of the franc is 0.1109 per dollar.
a) What is the expected exchange rate (franc/$) in one year?
b) At what 180day forward rate will covered interest rate parity hold? [Note: You need to compute the 180day interest rates to work out the solution.]
c) At what one-year forward rate will covered interest rate parity hold?
d) Suppose the one-year exchange rate is expected to increase to $0.15 due to lower U.S. inflation. Do you want to buy or sell forward?
2.12) Suppose that three-month interest rates (annualized) in Japan and the United States are 7 percent and 9 percent, respectively. If the spot rate is $/¥142 and the 90-day forward rate is $/¥139, [Note: You need to compute the 90day interest rates to work out the solution.]
a) Where would you invest?
b) Where would you borrow?
c) What arbitrage opportunity do these figures present?
d) Assuming no transaction costs, what would be your arbitrage profit per unit borrowed?