Mini-Case Mrs. Watanabe and the Japanese Yen Carry Trade
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PART 2 Foreign Exchange Theory and Markets
Exhibit A The Trending JPY and AUD Spot Rate
Japanese yen ؍1.00 Australian dollar (monthly)
110
100
90
80
70
60
Ja
n0
Ju 0
l-0
Ja 0
n0
Ju 1
l-0
Ja 1
n0
Ju 2
l-0
Ja 2
n0
Ju 3
l-0
Ja 3
n0
Ju 4
l-0
Ja 4
n0
Ju 5
l-0
Ja 5
n0
Ju 6
l-0
Ja 6
n0
Ju 7
l-0
Ja 7
n0
Ju 8
l-0
Ja 8
n0
Ju 9
l-0
Ja 9
n1
Ju 0
l-1
Ja 0
n1
Ju 1
l-1
Ja 1
n1
Ju 2
l-1
Ja 2
n1
Ju 3
l-1
3
50
¥50 million at 1.00% interest per annum for one year. She
could then exchange the ¥50 million yen for Australian
dollars at ¥60.91/A$, and then deposit the A$820,883 proceeds for one year at the Australian interest rate of 4.50%
per annum. The investor could even have rationalized that
even if the exchange rate did not change, she would earn a
3.50% per annum interest differential.
As it turned out, the spot exchange rate one year later, in
January 2010, saw a much weaker Japanese yen against the
Aussie dollar, ¥83.19/A$. The one-year Aussie-Yen carry
Exhibit B The Aussie-Yen Carry Trade
Start
End
JPY50,500,000
71,362,297
JPY20,862,297
JPY50,000,000
1.0100
JPY to = 1 AUD
60.91
360 Days
JPY to = 1 AUD
83.19
AUS820,883
1.0450
AUS857,823
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Chapter 6 International Parity Conditions
trade position would then have earned a very healthy profit
of ¥20,862,296.83 on a one-year investment of ¥50,000,000,
a 41.7% rate of return.
Post 2009 Financial Crisis
The global financial crisis of 2008–2009 has left a marketplace in which the U.S. Federal Reserve and the European
Central Bank have pursued easy money policies. Both central banks, in an effort to maintain high levels of liquidity and
to support fragile commercial banking systems, have kept
interest rates at near-zero levels. Now global investors who
see opportunities for profit in an anemic global economy
are using those same low-cost funds in the U.S. and Europe
to fund uncovered interest arbitrage activities. But what is
making this “emerging market carry trade” so unique is not
the interest rates, but the fact that investors are shorting two
of the world’s core currencies: the dollar and the euro.
Consider the strategy outlined in Exhibit B. An investor
borrows EUR 20 million at an incredibly low rate, say 1.00%
per annum or 0.50% for 180 days. The EUR 20 million are
Questions
1.Purchasing Power Parity. Define the following terms:
a. The law of one price
b. Absolute purchasing power parity
c. Relative purchasing power parity
2.Nominal Effective Exchange Rate Index. Explain how
a nominal effective exchange rate index is constructed.
3.Real Effective Exchange Rate Index. What formula
is used to convert a nominal effective exchange rate
index into a real effective exchange rate index?
4.Real Effective Exchange Rates: Japan and the
United States. Exhibit 6.3 compares the real effective
exchange rates for the United States and Japan. If the
comparative real effective exchange rate was the main
determinant, does the United States or Japan have a
competitive advantage in exporting? Which of the two
has an advantage in importing? Explain why.
5.Exchange Rate Pass-Through. Incomplete exchange
rate pass-through is one reason that a country’s real
effective exchange rate can deviate for lengthy periods from its purchasing power equilibrium level of 100.
What is meant by the term exchange rate pass-through?
6.The Fisher Effect. Define the Fisher effect. To what
extent do empirical tests confirm that the Fisher effect
exists in practice?
7.The International Fisher Effect. Define the international Fisher effect. To what extent do empirical tests
confirm that the international Fisher effect exists in
practice?
159
then exchanged for Indian rupees (INR), the current spot
rate being INR 60.4672 = EUR 1.00. The resulting INR
1,209,344,000 are put into an interest-bearing deposit with
any of a number of Indian banks attempting to attract capital. The rate of interest offered, 2.50%, is not particularly
high, but is greater than that available in the dollar, euro, or
even yen markets. But the critical component of the strategy is not to earn the higher rupee interest (although that
does help), it is the expectations of the investor regarding
the direction of the INR per EUR exchange rate.
Case Questions
1.Why are interest rates so low in the traditional core
markets of USD and EUR?
2.What makes this “emerging market carry trade” so
different from traditional forms of uncovered interest
arbitrage?
3.Why are many investors shorting the dollar and the
euro?
8.Interest Rate Parity. Define interest rate parity. What
is the relationship between interest rate parity and forward rates?
9.Covered Interest Arbitrage. Define the terms covered
interest arbitrage and uncovered interest arbitrage.
What is the difference between these two transactions?
10. Forward Rate as an Unbiased Predictor of the Future
Spot Rate. Some forecasters believe that foreign
exchange markets for the major floating currencies are
“efficient” and forward exchange rates are unbiased
predictors of future spot exchange rates. What is meant
by “unbiased predictor” in terms of how the forward
rate performs in estimating future spot exchange rates?
Problems
1.Pulau Penang Island Resort. Theresa Nunn is planning a 30-day vacation on Pulau Penang, Malaysia, one
year from now. The present charge for a luxury suite
plus meals in Malaysian ringgit (RM) is RM1,045/day.
The Malaysian ringgit presently trades at RM3.1350/$.
She determines that the dollar cost today for a 30-day
stay would be $10,000. The hotel informs her that any
increase in its room charges will be limited to any
increase in the Malaysian cost of living. Malaysian
inflation is expected to be 2.75% per annum, while
U.S. inflation is expected to be 1.25%.
a. How many dollars might Theresa expect to need
one year hence to pay for her 30-day vacation?
b. By what percent will the dollar cost have gone up?
Why?
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PART 2 Foreign Exchange Theory and Markets
2.Crisis at the Heart of Carnaval. The Argentine peso
was fixed through a currency board at Ps1.00/$ throughout the 1990s. In January 2002, the Argentine peso was
floated. On January 29, 2003, it was trading at Ps3.20/$.
During that one-year period, Argentina’s inflation rate
was 20% on an annualized basis. Inflation in the United
States during that same period was 2.2% annualized.
a. What should have been the exchange rate in
January 2003 if PPP held?
b. By what percentage was the Argentine peso undervalued on an annualized basis?
c. What were the probable causes of undervaluation?
3.Japanese/United States Parity Conditions. Derek
Tosh is attempting to determine whether U.S./
Japanese financial conditions are at parity. The current spot rate is a flat ¥89.00/$, while the 360-day
forward rate is ¥84.90/$. Forecast inflation is 1.100%
for Japan, and 5.900% for the United States. The 360day euroyen deposit rate is 4.700%, and the 360-day
eurodollar deposit rate is 9.500%.
a. Diagram and calculate whether international parity
conditions hold between Japan and the United
States.
b. Find the forecasted change in the Japanese yen/
U.S. dollar (¥/$) exchange rate one year from now.
4.Traveling Down Under. Terry Lamoreaux owns
homes in Sydney, Australia, and Phoenix, Arizona.
He travels between the two cities at least twice a year.
Because of his frequent trips, he wants to buy some
new high-quality luggage. He has done his research
and has decided to purchase a Briggs and Riley threepiece luggage set. There are retail stores in Phoenix
and Sydney. Terry was a finance major and wants to
use purchasing power parity to determine if he is paying the same price regardless of where he makes his
purchase.
a. If the price of the three-piece luggage set in Phoenix is $850 and the price of the same three-piece set
in Sydney is A$930, using purchasing power parity,
is the price of the luggage truly equal if the spot
rate is A$1.0941/$?
b. If the price of the luggage remains the same in
Phoenix one year from now, determine the price
of the luggage in Sydney in one year’s time if PPP
holds true. The U.S. inflation rate is 1.15% and the
Australian inflation rate is 3.13%.
5.Starbucks in Croatia. Starbucks opened its first store in
Zagreb, Croatia in October 2010. In Zagreb, the price
of a tall vanilla latte is 25.70kn. In New York City,
the price of a tall vanilla latte is $2.65. The exchange
rate between Croatian kunas (kn) and U.S. dollars is
kn5.6288/$. According to purchasing power parity, is
the Croatian kuna overvalued or undervalued?
6.Corolla Exports and Pass-Through. Assume that the
export price of a Toyota Corolla from Osaka, Japan is
¥2,150,000. The exchange rate is ¥87.60/$. The forecast
rate of inflation in the United States is 2.2% per year
and in Japan it is 0.0% per year. Use this data to answer
the following questions on exchange rate pass-through.
a. What was the export price for the Corolla at the
beginning of the year expressed in U.S. dollars?
b. Assuming purchasing power parity holds, what
should be the exchange rate at the end of the year?
c. Assuming 100% exchange rate pass-through, what will
be the dollar price of a Corolla at the end of the year?
d. Assuming 75% exchange rate pass-through, what
will be the dollar price of a Corolla at the end of
the year?
7.Takeshi Kamada—CIA Japan (A). Takeshi Kamada,
a foreign exchange trader at Credit Suisse (Tokyo), is
exploring covered interest arbitrage possibilities. He
wants to invest $5,000,000 or its yen equivalent, in a
covered interest arbitrage between U.S. dollars and
Japanese yen. He faced the following exchange rate and
interest rate quotes. Is CIA profit possible? If so, how?
Arbitrage funds available
$5,000,000
Spot rate (¥/$)
118.60
180-day forward rate (¥/$)
117.80
180-day U.S. dollar interest rate
4.800%
180-day Japanese yen interest rate
3.400%
8.Takeshi Kamada—UIA Japan (B). Takeshi Kamada,
Credit Suisse (Tokyo), observes that the ¥/$ spot rate
has been holding steady, and that both dollar and
yen interest rates have remained relatively fixed over
the past week. Takeshi wonders if he should try an
uncovered interest arbitrage (UIA) and thereby save
the cost of forward cover. Many of Takeshi’s research
associates—and their computer models—are predicting the spot rate to remain close to ¥118.00/$ for the
coming 180 days. Using the same data as in Problem
7, analyze the UIA potential.
9.Copenhagen Covered (A). Heidi Høi Jensen, a foreign exchange trader at JPMorgan Chase, can invest
$5 million, or the foreign currency equivalent of the
bank’s short-term funds, in a covered interest arbitrage with Denmark. Using the following quotes, can
Heidi make a covered interest arbitrage (CIA) profit?
Arbitrage funds available
$5,000,000
Spot exchange rate (kr/$)
6.1720
3-month forward rate (kr/$)
6.1980
U.S. dollar 3-month interest rate
3.000%
Danish kroner 3-month interest rate
5.000%
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161
Chapter 6 International Parity Conditions
10. Copenhagen Covered (B). Heidi Høi Jensen is now
evaluating the arbitrage profit potential in the same
market after interest rates change. (Note that any time
the difference in interest rates does not exactly equal
the forward premium, it must be possible to make a
CIA profit one way or another.)
Arbitrage funds available
Arbitrage funds available
$5,000,000
Spot exchange rate (kr/$)
6.1720
15. Statoil of Norway’s Arbitrage. Statoil, the national oil
company of Norway, is a large, sophisticated, and active
participant in both the currency and petrochemical markets. Although it is a Norwegian company, because it
operates within the global oil market, it considers the
U.S. dollar, rather than the Norwegian krone, as its
functional currency. Ari Karlsen is a currency trader
for Statoil and has immediate use of either $3 million
(or the Norwegian krone equivalent). He is faced with
the following market rates and wonders whether he can
make some arbitrage profits in the coming 90 days.
3-month forward rate (kr/$)
6.1980
U.S. dollar 3-month interest rate
4.000%
Danish kroner 3-month interest rate
5.000%
11. Copenhagen Covered (C). Heidi Høi Jensen is again
evaluating the arbitrage profit potential in the same
market after another change in interest rates. (Remember that any time the difference in interest rates does
not exactly equal the forward premium, it must be possible to make a CIA profit one way or another.)
Arbitrage funds available
$5,000,000
Spot exchange rate (kr/$)
6.1720
3-month forward rate (kr/$)
6.1980
U.S. dollar 3-month interest rate
3.000%
Danish kroner 3-month interest rate
6.000%
12. Casper Landsten—CIA (A). Casper Landsten is a foreign exchange trader for a bank in New York. He has
$1 million (or its Swiss franc equivalent) for a shortterm money market investment and wonders whether
he should invest in U.S. dollars for three months or
make a CIA investment in the Swiss franc. He faces
the following quotes:
Arbitrage funds available
Spot exchange rate (SFr/$)
3-month forward rate (SFr/$)
1.2740
Swiss franc 3-month interest rate
3.200%
13. Casper Landsten—UIA (B). Casper Landsten, using
the same values and assumptions as in Problem 12,
decides to seek the full 4.800% return available in U.S.
dollars by not covering his forward dollar receipts—
an uncovered interest arbitrage (UIA) transaction.
Assess this decision.
14. Casper Landsten—Thirty Days Later. One month
after the events described in Problems 12 and 13,
Casper Landsten once again has $1 million (or its
Swiss franc equivalent) to invest for three months. He
now faces the following rates. Should he again enter
into a covered interest arbitrage (CIA) investment?
1.3286
U.S. dollar 3-month interest rate
4.750%
Swiss franc 3-month interest rate
3.625%
Arbitrage funds available
$3,000,000
Spot exchange rate (Nok/$)
6.0312
3-month forward rate (Nok/$)
6.0186
U.S. dollar 3-month interest rate
5.000%
Norwegian krone 3-month interest rate
4.450%
16. Separated by the Atlantic. Separated by more than
3,000 nautical miles and five time zones, money and
foreign exchange markets in both London and New
York are very efficient. The following information has
been collected from the respective areas:
1.2810
4.800%
1.3392
3-month forward rate (SFr/$)
$1,000,000
U.S. dollar 3-month interest rate
$1,000,000
Spot exchange rate (SFr/$)
Assumptions
London
New York
Spot exchange rate ($/€)
1.3264
1.3264
1-year Treasury bill rate
3.900%
4.500%
Expected inflation rate
Unknown
1.250%
a. What do the financial markets suggest for inflation
in Europe next year?
b. Estimate today’s 1-year forward exchange rate
between the dollar and the euro?
17. Chamonix Chateau Rentals. You are planning a ski
vacation to Mt. Blanc in Chamonix, France, one
year from now. You are negotiating the rental of a
chateau. The chateau’s owner wishes to preserve his
real income against both inflation and exchange rate
changes, and so the present weekly rent of €9,800
(Christmas season) will be adjusted upward or downward for any change in the French cost of living
between now and then. You are basing your budgeting on purchasing power parity (PPP). French inflation is expected to average 3.5% for the coming year,
while U.S. dollar inflation is expected to be 2.5%.
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PART 2 Foreign Exchange Theory and Markets
The current spot rate is $1.3620/€. What should you
budget as the U.S. dollar cost of the 1-week rental?
U.S. dollar, would he be better off receiving Maltese
lira in one year (assuming purchasing power parity)
or receiving a guaranteed dollar payment (assuming a
Spot exchange rate ($/€)$1.3620
gold price of $420 per ounce one year from now).
Expected U.S. inflation for coming year
2.500%
Expected French inflation for coming year
3.500%
20. Malaysian Risk. Clayton Moore is the manager of an
international money market fund managed out of
London. Unlike many money funds that guarantee their
Current chateau nominal weekly rent (€)9,800.00
investors a near risk-free investment with variable interest earnings, Clayton Moore’s fund is a very aggressive
18. East Asiatic Company—Thailand. The East Asiatic
fund that searches out relatively high interest earnings
Company (EAC), a Danish company with subsidiararound the globe, but at some risk. The fund is poundies throughout Asia, has been funding its Bangkok
denominated. Clayton is currently evaluating a rather
subsidiary primarily with U.S. dollar debt because of
interesting opportunity in Malaysia. Since the Asian
the cost and availability of dollar capital as opposed
Crisis of 1997, the Malaysian government enforced a
to Thai baht-denominated (B) debt. The treasurer of
number of currency and capital restrictions to protect
EAC-Thailand is considering a 1-year bank loan for
and preserve the value of the Malaysian ringgit. The
$250,000. The current spot rate is B32.06/$, and the
ringgit was fixed to the U.S. dollar at RM3.80/$ for seven
dollar-based interest is 6.75% for the 1-year period.
years. In 2005, the Malaysian government allowed the
1-year loans are 12.00% in baht.
currency to float against several major currencies. The
a. Assuming expected inflation rates for the comcurrent spot rate today is RM3.13485/$. Local currency
ing year of 4.3% and 1.25% in Thailand and the
time deposits of 180-day maturities are earning 8.900%
United States, respectively, according to purchase
per annum. The London eurocurrency market for
power parity, what would be the effective cost of
pounds is yielding 4.200% per annum on similar 180-day
funds in Thai baht terms?
maturities. The current spot rate on the British pound is
b.If EAC’s foreign exchange advisers believe
$1.5820/£, and the 180-day forward rate is $1.5561/£.
strongly that the Thai government wants to push
the value of the baht down against the dollar by
5% over the coming year (to promote its export
competitiveness in dollar markets), what might be
the effective cost of funds in baht terms?
c. If EAC could borrow Thai baht at 13% per annum,
would this be cheaper than either part (a) or part (b)?
19. Maltese Falcon. Imagine that the mythical solid gold
falcon, initially intended as a tribute by the Knights of
Malta to the King of Spain in appreciation for his gift
of the island of Malta to the order in 1530, has recently
been recovered. The falcon is 14 inches high and solid
gold, weighing approximately 48 pounds. Assume that
gold prices have risen to $440/ounce, primarily as a
result of increasing political tensions. The falcon is
currently held by a private investor in Istanbul, who is
actively negotiating with the Maltese government on
its purchase and prospective return to its island home.
The sale and payment are to take place one year from
now, and the parties are negotiating over the price and
currency of payment. The investor has decided, in a
show of goodwill, to base the sales price only on the
falcon’s specie value—its gold value.
The current spot exchange rate is 0.39 Maltese lira (ML)
per 1.00 U.S. dollar. Maltese inflation is expected to be
about 8.5% for the coming year, while U.S. inflation,
on the heels of a double-dip recession, is expected to
come in at only 1.5%. If the investor bases value in the
21. The Beer Standard. In 1999, The Economist reported
the creation of an index, or standard, for the evaluation of African currency values using the local prices
of beer. Beer, instead of Big Macs, was chosen as the
product for comparison because McDonald’s had not
penetrated the African continent beyond South Africa,
and beer met most of the same product and market
characteristics required for the construction of a proper
currency index. Investec, a South African investment
banking firm, has replicated the process of creating a
measure of purchasing power parity (PPP) like that of
the Big Mac Index of The Economist, for Africa.
The index compares the cost of a 375 milliliter bottle
of clear lager beer across Sub-Saharan Africa. As a
measure of PPP, the beer needs to be relatively homogeneous in quality across countries, and must possess
substantial elements of local manufacturing, inputs,
distribution, and service in order to actually provide a
measure of relative purchasing power. The beer is first
priced in local currency (purchased in the taverns of the
locals, and not in the high-priced tourist centers). The
price is then converted to South African rand and the
rand-price compared to the local currency price as one
measure of whether the local currency is undervalued or
overvalued versus the South African rand. Use the data
in the table and complete the calculation of whether the
individual currencies are undervalued or overvalued.
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Chapter 6 International Parity Conditions
163
Beer Prices
Country
Beer
Local
Currency
Price in
Currency
Price in
Rand
Implied
PPP Rate
Spot Rate
South Africa
Castle
Rand
2.30
—
—
—
Botswana
Castle
Pula
2.20
2.94
0.96
0.75
Ghana
Star
Kenya
Tusker
Malawi
Carlsberg
Mauritius
Phoenix
Namibia
Windhoek
Zambia
Castle
Zimbabwe
Castle
Z$
Cedi
1,200.00
3.17
521.74
379.10
Shilling
41.25
4.02
17.93
10.27
Kwacha
18.50
2.66
8.04
6.96
Rupee
15.00
3.72
6.52
4.03
N$
2.50
2.50
1.09
1.00
Kwacha
1,200.00
3.52
521.74
340.68
9.00
1.46
3.91
6.15
Internet Exercises
Data Listed by the Financial Times:
■
International money rates (bank call rates for
major currency deposits)
■
Money rates (LIBOR and CD rates, etc.)
■
10-year spreads (individual country spreads versus
the euro and U.S. 10-year treasuries). Note: Which
countries actually have lower 10-year government
bond rates than the United States and the euro?
Probably Switzerland and Japan. Check.
The Economistwww.economist.com/markets-data
■
2.Purchasing Power Parity Statistics. The Organization for Economic Cooperation and Development
(OECD) publishes detailed measures of prices and
purchasing power for its member countries. Go to the
OECD’s Web site and download the spreadsheet file
with the historical data for purchasing power for the
member countries.
Benchmark government bonds (sampling of representative government issuances by major countries
and recent price movements). Note which countries are showing longer maturity benchmark rates.
■
Emerging market bonds (government issuances,
Brady bonds, etc.)
■
Eurozone rates (miscellaneous bond rates for
assorted European-based companies; includes
debt ratings by Moodys and S&P)
1.Big Mac Index Updated. Use The Economist’s Web
site to find the latest edition of the Big Mac Index
of currency overvaluation and undervaluation. (You
will need to do a search for “Big Mac Currencies.”)
Create a worksheet to compare how the British
pound, the euro, the Swiss franc, and the Canadian
dollar have changed from the version presented in
this chapter.
OECDwww.oecd.org/std/prices-ppp/
3.International Interest Rates. A number of Web sites
publish current interest rates by currency and maturity. Use the Financial Times Web site listed here to
isolate the interest rate differentials between the U.S.
dollar, the British pound, and the euro for all maturities up to and including one year.
Financial Timesmarkets.ft.com/RESEARCH/
Markets/Interest-Rates
4.World Bank’s International Comparison Program. The
World Bank has an ongoing research program that
focuses on the relative purchasing power of 107 different
economies globally, specifically in terms of household consumption. Download the latest data tables and highlight
which economies seem to be showing the greatest growth
in recent years in relative purchasing power. Search the
Internet for the World Bank’s ICP program site.
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CHAPTER 6 APPENDIX
An Algebraic Primer to International
Parity Conditions
The following is a purely algebraic presentation of the parity conditions explained in this
chapter. It is offered to provide those students who desire additional theoretical detail and
definition ready access to the step-by-step derivation of the various conditions.
The Law of One Price
The law of one price refers to the state in which—in the presence of free trade, perfect substitutability of goods, and costless transactions—the equilibrium exchange rate between two
currencies is determined by the ratio of the price of any commodity i denominated in two
different currencies. For example,
St =
P$i,t
PSF
i,t
where P$i and PSF
i refer to the prices of the same commodity i, at time t, denominated in U.S.
dollars and Swiss francs, respectively. The spot exchange rate, St, is simply the ratio of the
two currency prices.
Purchasing Power Parity
The more general form in which the exchange rate is determined by the ratio of two price
indexes is termed the absolute version of purchasing power parity (PPP). Each price index
reflects the currency cost of the identical “basket” of goods across countries. The exchange
rate that equates purchasing power for the identical collection of goods is then stated as
follows:
St =
P$t
PSF
t
where P$t and PSF
t are the price index values in U.S. dollars and Swiss francs at time t, respectively. If p$ and pSF represent the rates of inflation in each currency respectively, then the
spot exchange rate at time t + 1 would be
St + 1 =
164
P$t (1 + p$)
SF
PSF
t (1 + p )
= St J
(1 + p$)
(1 + pSF)
R
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APPENDIX An Algebraic Primer to International Parity Conditions
165
The change from period t to t + 1 is then
P$t (1 + p$)
St J
SF
PSF
St + 1
t (1 + p )
=
=
St
P$t
(1 + p$)
(1 + pSF)
St
R
=
(1 + p$)
(1 + pSF)
PSF
t
Isolating the percentage change in the spot exchange rate between periods t and t + 1 is then
St + 1 - St
=
St
St J
(1 + p$)
(1 + pSF)
St
R - St
=
(1 + p$) - (1 + pSF)
(1 + pSF)
This equation is often approximated by dropping the denominator of the right-hand side if it
is considered to be relatively small. It is then stated as
St + 1 - St
= (1 + p$) - (1 + pSF) = p$ - pSF
St
Forward Rates
The forward exchange rate is the contractual rate that is available to private agents through
banking institutions and other financial intermediaries who deal in foreign currencies and debt
instruments. The annualized percentage difference between the forward rate and the spot rate
is termed the forward premium,
f SF = J
Ft, t + 1 - St
St
R * J
360
R
nt,t + 1
where f SF is the forward premium on the Swiss franc, Ft, t + 1 is the forward rate contracted at
time t for delivery at time t + 1, St is the current spot rate, and nt, t + 1 is the number of days
between the contract date (t) and the delivery date (t + 1).
Covered Interest Arbitrage (CIA)
and Interest Rate Parity (IRP)
The process of covered interest arbitrage is when an investor exchanges domestic currency for
foreign currency in the spot market, invests that currency in an interest-bearing instrument,
and signs a forward contract to “lock in” a future exchange rate at which to convert the foreign
currency proceeds (gross) back to domestic currency. The net return on CIA is
Net Return = J
(1 + iSF)Ft,t + 1
St
R - (1 + i$)
where St and Ft, t + 1 are the spot and forward rates ($/SF), iSF is the nominal interest rate (or
yield) on a Swiss franc-denominated monetary instrument, and i$ is the nominal return on a
similar dollar-denominated instrument.
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APPENDIX An Algebraic Primer to International Parity Conditions
If they possess exactly equal rates of return—that is, if CIA results in zero riskless profit—
interest rate parity (IRP) holds, and appears as
(1 + i$) = J
(1 + iSF)Ft,t + 1
St
R
or alternatively as
(1 + i$)
SF
(1 + i )
=
Ft,t + 1
St
If the percent difference of both sides of this equation is found (the percentage difference
between the spot and forward rate is the forward premium), then the relationship between the
forward premium and relative interest rate differentials is
Ft, t + 1 - St
St
= f SF =
i$ - iSF
1 + iSF
If these values are not equal (thus, the markets are not in equilibrium), there exists a
potential for riskless profit. The market will then be driven back to equilibrium through
CIA by agents attempting to exploit such arbitrage potential—until CIA yields no positive return.
Fisher Effect
The Fisher effect states that all nominal interest rates can be decomposed into an implied real
rate of interest (return) and an expected rate of inflation:
i$ = [(1 + r $)(1 + p$)] - 1
where r $ is the real rate of return and p$ is the expected rate of inflation for dollar-denominated
assets. The subcomponents are then identifiable:
i $ = r $ + p $ + r $p $
As with PPP, there is an approximation of this function that has gained wide acceptance. The
cross-product term of r $p$ is often very small and therefore dropped altogether:
i $ = r $ + p$
International Fisher Effect
The international Fisher effect is the extension of this domestic interest rate relationship to
the international currency markets. If capital, by way of covered interest arbitrage (CIA),
attempts to find higher rates of return internationally resulting from current interest rate
differentials, the real rates of return between currencies are equalized (e.g., r $ = r SF):
(1 + i$) - (1 + iSF)
St + 1 - St
i$ - iSF
=
=
St
(1 + iSF)
(1 + iSF)
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APPENDIX An Algebraic Primer to International Parity Conditions
167
If the nominal interest rates are then decomposed into their respective real and expected
inflation components, the percentage change in the spot exchange rate is
(r $ + p$ + r $p$) - (r SF + pSF + r SFpSF)
St + 1 - St
=
St
1 + r SF + pSF + r SFpSF
The international Fisher effect has a number of additional implications if the following requirements are met: (1) capital markets can be freely entered and exited; (2) capital markets possess
investment opportunities that are acceptable substitutes; and (3) market agents have complete
and equal information regarding these possibilities.
Given these conditions, international arbitragers are capable of exploiting all potential
riskless profit opportunities until real rates of return between markets are equalized (r $ = r SF).
Thus, the expected rate of change in the spot exchange rate reduces to the differential in the
expected rates of inflation:
St + 1 - St
p$ + r $p$ - pSF - r SFpSF
=
St
1 + r SF + pSF + r SFpSF
If the approximation forms are combined (through the elimination of the denominator
and the elimination of the interactive terms of r and p), the change in the spot rate is simply
St + 1 - St
= p$ - pSF
St
Note the similarity (identical in equation form) of the approximate form of the international Fisher effect to purchasing power parity discussed previously—the only potential
difference is that between ex post and ex ante (expected) inflation.
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CHAPTER
7
Foreign Currency
Derivatives
and Swaps
Unless derivatives contracts are collateralized or guaranteed, their ultimate value also depends on the creditworthiness of the counterparties to them. In the meantime,
though, before a contract is settled, the counterparties
record profits and losses—often huge in amount—in their
current earnings statements without so much as a penny
changing hands. The range of derivatives contracts is
limited only by the imagination of man (or sometimes, so
it seems, madmen).
—Warren Buffett, Berkshire Hathaway Annual Report, 2002.
Learning Objectives
■
Explain how foreign currency futures are quoted, valued, and used for speculation
purposes
■
Illustrate how foreign currency futures differ from forward contracts
■
Analyze how foreign currency options are quoted and used for speculation purposes
■
Consider the distinction between buying options and writing options in terms of
whether profits and losses are limited or unlimited
■
Explain how foreign currency options are valued
■
Define interest rate risk and demonstrate how it can be managed
■
Explain interest rate swaps and how they can be used to manage interest rate risk
■
Analyze how interest rate swaps and cross-currency swaps can be used to manage both
foreign exchange risk and interest rate risk simultaneously
Financial management of the multinational enterprise in the twenty-first century will certainly
include the use of financial derivatives. These derivatives, so named because their values are
derived from an underlying asset like a stock or a currency, are powerful tools used in business today for two very distinct management objectives, speculation and hedging. The financial manager of an MNE may purchase financial derivatives in order to take positions in the
expectation of profit—speculation—or may use these instruments to reduce the risks associated with the everyday management of corporate cash flow—hedging. Before these financial
instruments can be used effectively, however, the financial manager must understand certain
basics about their structure and pricing.
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