S-95
Introduction to Exchange Rates
and the Foreign Exchange Market
1. Refer to the exchange rates given in the following table:
Based on the table provided, answer the following questions:
a. Compute the U.S. dollar–yen exchange rate E$/¥ and the U.S. dollar–
Canadian dollar exchange rate E$/C$ on June 25, 2010, and June 25, 2009.
Answer:
b. What happened to the value of the U.S. dollar relative to the Japanese yen and
Canadian dollar between June 25, 2009, and June 25, 2010? Compute the per–
centage change in the value of the U.S. dollar relative to each currency using the
U.S. dollar-foreign currency exchange rates you computed in (a).
Answer: Between June 25, 2009 and 2010, both the Canadian dollar and the
June 25, 2010 June 25, 2009
Country (currency) FX per $ FX per £ FX per € FX per $
Australia (dollar) 1.152 1.721 1.417 1.225
Canada (dollar) 1.037 1.559 1.283 1.084
Denmark (krone) 6.036 9.045 7.443 5.238
Euro 0.811 1.215 1.000 0.703
Hong Kong (dollar) 7.779 11.643 9.583 7.750
India (rupee) 46.36 69.476 57.179 48.16
Japan (yen) 89.35 134.048 110.308 94.86
Mexico (peso) 12.697 18.993 15.631 13.22
Sweden (krona) 7.74 11.632 9.577 7.460
United Kingdom (pound) 0.667 1.000 0.822 0.609
United States (dollar) 1.000 1.496 1.232 1.000
Source: U.S. Federal Reserve Board of Governors, H.10 release: Foreign Exchange Rates.
10
S-96 Solutions n Chapter 10 Introduction to Exchange Rates & the Foreign Exchange Market
c. Using the information in the table for June 25, 2010, compute the Danish
d. Visit the website of the Board of Governors of the Federal Reserve System at
http://www.federalreserve.gov/. Click on “Economic Research and Data” and
then “Statistics: Releases and Historical Data.” Download the H.10 release For-
eign Exchange Rates (weekly data available). What has happened to the value of
the U.S. dollar relative to the Canadian dollar, Japanese yen, and Danish krone
since June 25, 2010?
Answer: Answers will depend on the latest data update.
e. Using the information from (d), what has happened to the value of the U.S.
dollar relative to the British pound and the euro? Note: The H.10 release quotes
these exchange rates as U.S. dollars per unit of foreign currency in line with
long-standing market conventions.
2. Consider the United States and the countries it trades with the most (measured in
trade volume): Canada, Mexico, China, and Japan. For simplicity, assume these are
the only four countries with which the United States trades. Trade shares and ex-
change rates for these four countries are as follows:
a. Compute the percentage change from 2009 to 2010 in the four U.S. bilateral
exchange rates (defined as U.S. dollars per unit of foreign exchange, or FX) in
the table provided.
b. Use the trade shares as weights to compute the percentage change in the nominal
effective exchange rate for the United States between 2009 and 2010 (in U.S.
dollars per foreign currency basket).
Country (currency) Share of Trade $ per FX in 2009 $ per FX in 2010
Canada (dollar) 36% 0.9225 0.9643
Mexico (peso) 28% 0.0756 0.0788
China (yuan) 20% 0.1464 0.1473
Japan (yen) 16% 0.0105 0.0112
Solutions n Chapter 10 Introduction to Exchange Rates & the Foreign Exchange Market S-97
c. Based on your answer to (b), what happened to the value of the U.S. dollar against
this basket between 2009 and 2010? How does this compare with the change in
the value of the U.S. dollar relative to the Mexican peso? Explain your answer.
Answer: The dollar depreciated by 4.01% against the basket of currencies. Vis-à-
3. Go to the website for Federal Reserve Economic Data (FRED): http://research.
stlouisfed.org/fred2/. Locate the monthly exchange rate data for the following:
Look at the graphs and make your own judgment as to whether each currency was
fixed (peg or band), crawling (peg or band), or floating relative to the U.S. dollar
during each time frame given.
a. Canada (dollar), 1980–2012
Answer: Floating exchange rate
b. China (yuan), 1999–2004, 2005–2009, and 2009–2010
Answer: 1999–2004: Fixed exchange rate. 2005–2010: Gradual appreciation
vis-à-vis the dollar. Again fixed for 2009–2010
c. Mexico (peso), 1993–1995 and 1995–2012
Answer: 1993–1995: crawl; 1995–2012: floating (with some evidence of a
managed float)
d. Thailand (baht), 1986–1997 and 1997–2012
e. Venezuela (bolivar), 2003–2012
4. Describe the different ways in which the government may intervene in the forex
market. Why does the government have the ability to intervene in this way, while
private actors do not?
5. Suppose quotes for the dollar–euro exchange rate, E$/€, are as follows: in New York,
$1.50 per euro; and in Tokyo, $1.55 per euro. Describe how investors use arbitrage
to take advantage of the difference in exchange rates. Explain how this process will
affect the dollar price of the euro in New York and Tokyo.
6. Consider a Dutch investor with 1,000 euros to place in a bank deposit in either the
Netherlands or Great Britain. The (one-year) interest rate on bank deposits is 2% in
Britain and 4.04% in the Netherlands. The (one-year) forward euro–pound exchange
rate is 1.575 euros per pound and the spot rate is 1.5 euros per pound. Answer the
following questions, using the exact equations for UIP and CIP as necessary.
S-98 Solutions n Chapter 10 Introduction to Exchange Rates & the Foreign Exchange Market
a. What is the euro-denominated return on Dutch deposits for this investor?
b. What is the (riskless) euro-denominated return on British deposits for this inves-
tor using forward cover?
c. Is there an arbitrage opportunity here? Explain why or why not. Is this an equi-
librium in the forward exchange rate market?
Answer: Yes, there is an arbitrage opportunity. The euro-denominated return
d. If the spot rate is 1.5 euros per pound, and interest rates are as stated previously,
what is the equilibrium forward rate, according to covered interest parity (CIP)?
Answer: CIP implies: F€/£ 5 E€/£ (1 1 i€)/(1 1 i£) 5 1.5 3 1.0404/1.02 5
€1.53 per £.
e. Suppose the forward rate takes the value given by your answer to (d). Compute
the forward premium on the British pound for the Dutch investor (where ex-
change rates are in euros per pound). Is it positive or negative? Why do investors
require this premium/discount in equilibrium?
Answer: Forward premium 5 (F€/£/E€/£ 2 1) 5 (1.53/1.50) 2 1 5 0.02 5 2%.
f. If uncovered interest parity (UIP) holds, what is the expected depreciation of the
euro (against the pound) over one year?
Answer: If the UIP holds, expected euro/pound exchange rate is the same as the
g. Based on your answer to (f ), what is the expected euro–pound exchange rate
one year ahead?
7. You are a financial adviser to a U.S. corporation that expects to receive a payment
of 40 million Japanese yen in 180 days for goods exported to Japan. The current spot
rate is 100 yen per U.S. dollar (E$/¥ = 0.01000). You are concerned that the U.S.
dollar is going to appreciate against the yen over the next six months.
a. Assuming the exchange rate remains unchanged, how much does your firm
expect to receive in U.S. dollars?
b. How much would your firm receive (in U.S. dollars) if the dollar appreciated to
110 yen per U.S. dollar (E$/¥ = 0.00909)?
Answer: The firm would receive $363,636 (5 ¥40,000,000/110).
Solutions n Chapter 10 Introduction to Exchange Rates & the Foreign Exchange Market S-99
c. Describe how you could use an options contract to hedge against the risk of
losses associated with the potential appreciation in the U.S. dollar.
8. Consider how transactions costs affect foreign currency exchange. Rank each of the
following foreign exchanges according to their probable spread (between the “buy
at” and “sell for” bilateral exchange rates) and justify your ranking.
a. An American returning from a trip to Turkey wants to exchange his Turkish lira
for U.S. dollars at the airport.
b. Citigroup and HSBC, both large commercial banks located in the United States
and United Kingdom, respectively, need to clear several large checks drawn on
accounts held by each bank.
c. Honda Motor Company needs to exchange yen for U.S. dollars to pay American
workers at its Ohio manufacturing plant.
d. A Canadian tourist in Germany pays for her hotel room using a credit card.