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a. How many dollars might Theresa expect to need one year hence to pay for her 30-day vacation?
b. By what percent has the dollar cost gone up? Why?
Assumptions Value
Charge for suite plus meals in Malaysian ringgit (RM) 1,045.00
Spot exchange rate (RM/$) 3.1350
US$ cost today for a 30 day stay $10,000.00
Malaysian ringgit inflation rate expected to be 2.750%
U.S. dollar inflation rate expected to be 1.250%
a. How many dollars might you expecte to need one year hence for your 30-day vacation?
Spot exchange rate (ringgit per US$) 3.1350
Malaysian ringgit inflation rate expected to be 2.750%
U.S. dollar inflation rate expected to be 1.250%
Spot (expected in 1 year) = Spot x ( 1 + RM inflation) / ( 1 + US inflation)
Expected spot rate one year from now based on PPP (RM/$) 3.181444
Hotel charges expected to be paid one year from now for a 30-day stay (RM) 32,212.13
US dollars needed on the basis of these two expectations: $10,125.00
b. By what percent has the dollar cost gone up? Why?
New dollar cost $10,125.00
Original dollar cost $10,000.00
Percent change in US$ cost 1.250%
Problem 6.1 Pulau Penang Island Resort
The dollar cost has risen by the US dollar inflation rate. This is a result of Theresa's estimation of the future
suite costs and the exchange rate changing in proportion to inflation (relative purchasing power parity).
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 $10,000. The hotel
informed her that any increase in its room charges will be limited to any increase in the Malaysian cost of living.
Malaysian inflation is expected to be 2.75% per annum, while U.S. inflation is expected to be only 1.25%.
a. What should have been the exchange rate in January 2003 if PPP held?
b. By what percentage was the Argentine peso undervalued on an annualized basis?
c. What were the probable causes of undervaluation?
Assumptions Value
Spot exchange rate, fixed peg, early January 2002 (Ps/$) 1.0000
Spot exchange rate, January 29, 2003 (Ps/$) 3.2000
US inflation for year (per annum) 2.20%
Argentine inflation for year (per annum) 20.00%
a. What should have been the exchange rate in January 2003 if PPP held?
Beginning spot rate (Ps/$) 1.00
Argentine inflation 20.00%
US inflation 2.20%
PPP exchange rate 1.17
b. By what percentage was the Argentine peso undervalued on an annulized basis?
Actual exchange rate (Ps/$) 3.20
PPP exchange rate (Ps/$) 1.17
Percentage overvaluation (positive) or undervaluation (negative) -63.307%
c. What were the probable causes of undervaluation?
The rapid decline in the value of the Argentine peso was a result of not only inflation,
but also a severe crisis in the balance of payments (see Chapter 4).
Problem 6.2 Argentine Tears
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/$.
During that one year period Argentina's inflation rate was 20% on an annualized basis. Inflation in
the United States during that same period was 2.2% annualized.
Assumptions Value
Forecast annual rate of inflation for Japan 1.100%
Forecast annual rate of inflation for United States 5.900%
One-year interest rate for Japan 4.700%
One-year interest rate for United States 9.500%
Spot exchange rate (¥/$) 89.00
One-year forward exchange rate (¥/$)
84.90
a.
Forecast change in
Forward rate as spot exchange rate Purchasing
an unbaised
↔ ↔ 4.8% ↔ ↔ power
predictor (E) (Dollar expected to weaken) parity (A)
↕ ↕
↕ ↕ ↕
↕ ↕ ↕
↕ ↕ ↕
↕
Forward premium ↕Forecast difference
on foreign currency International in rates of inflation
4.8% Fisher Effect (C) -4.8%
(Japanese yen at a premium) ↕(US higher than Japan)
↕
↕ ↕ ↕
↕ ↕ ↕
↕
Interest rate ↔ ↔ Difference in nominal ↔ ↔ Fisher
parity (D) interest rates effect (B)
-4.8%
(higher in United States)
b.
Spot exchange rate (¥/$) 89.00
One-year forward exchange rate (¥/$)
84.90
4.8%
(Current Spot Rate - Forward Exchange Rate) / (Forward Exchange Rate)
As is the always the case with parity conditions, the future spot rate is implicitly forecast to be equal to the forward rate, the implied rate
from the international Fisher effect, and the rate implied by purchasing power parity. According to Yazzie's calculations, the markets are
indeed in equilibrium -- parity.
Forcasted change in exchange rates
Problem 6.3 Derek Tosh and Yen-Dollar Parity
Approximate Form
Derek Tosh is attempting to determine whether US/Japanese financial conditions are at parity. The current spot rate is a flat ¥89.00/$, while
the 360-day forward rate is ¥84.90/$. Forecast inflation is 1.100% for Japan, and 5.900% for the US. The 360-day euro-yen deposit rate is
4.700%, and the 360-day euro-dollar deposit rate is 9.500%.
a. Diagram and calculate whether international parity conditions hold between Japan and the United States.
b. Find the forecasted change in the Japanese yes/U.S. dollar (¥/$) exchange rate one year from now.
Assumptions Value
Price of 3-Piece Luggage set in US$ 850.00
Price of 3-Piece Luggage set in A$ 930.00
Spot exchange rate, (A$/$) 1.0941
US inflation for year (per annum) 1.15%
Australian inflation for year (per annum) 3.13%
a. Is the spot rate accurate given both luggage prices?
Price of 3-Piece Luggage set in US$ 850.00
Price of 3-Piece Luggage set in A$ 930.00
Spot rate as determined by PPP 1.0941
Spot rate = Price in A$ / Price in US$
b. What should be the price of the luggage set in A$ in 1-year if PPP holds?
Beginning spot rate (A$/$) 1.0941
Australian inflation 3.13%
US inflation 1.15%
PPP exchange rate 1.1155
Price of 3-Piece Luggage set in US$ 850.00
PPP exchange rate 1.1155
Price of 3-piece luggage set in Sydney (A$) 948.19
Problem 6.4 Sydney to Phoenix
Terry Lamoreaux has homes in both Sydney, Australia and Phoenix, United States. 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's done his research and has decided to go with a Briggs & Riley
brand three-piece luggage set. There are retails stores in both Phoenix and Sydney. Terry was a
finance major and wants to use purchasing power parity to determine if he is paying the same price
no matter where he makes his purcahse.
a. If the price of the 3-piece luggage set in Phoenix is $850 and the price of the same 3-piece set in
Sydney is $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 what the
price of the luggage should be in Sydney in one-year time if PPP holds true. The US Inflation rate
is 1.15% and the Australian inflation rate is 3.13%.
However, purchasing power parity is not always an accurate predictor of exchange rate
movements, particularly in the short-term.
Assumptions Value
Spot exchange rate (Kn/$) 5.6288
Price of vanilla latter in Zagreb (kn) 25.70
Price of vanilla latter in NYC ($) 2.65
Actual price of Croatian latte in USD 4.57
Implied PPP of Croatian latte in USD 9.70
Percentage overvaluation (positive) or undervaluation (negative) 112.408%
Problem 6.5 Starbucks in Croatia
Starbucks opened its first store in Zagreb, Croatia in October 2010. The price of a tall vanilla latte
in Zagreb is 25.70kn (kn or HRK). In New York City, the price of a tall vanilla latte is $2.65.
The exchange rate bewteen Croatian kunas (kn) and U.S. dollars is kn5.6288/$. According to
purchasing power parity, is the Croatian kuna overvalued or undervalued?
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 the exchange rate be at the end of the year?
c. Assuming 100% pass-through of exchange rate, what will the dollar price of a Corolla be at the end of the year?
d. Assuming 75% pass-through, what will the dollar price of a Corolla be at the end of the year?
Steps Value
Initial spot exchange rate (¥/$) 87.60
Initial price of a Toyota Corolla (¥) 2,150,000
Expected US dollar inflation rate for the coming year 2.200%
Expected Japanese yen inflation rate for the coming year 0.000%
Desired rate of pass through by Toyota 75.000%
a. What was the export price for the Corolla at the beginning of the year?
Year-beginning price of an Corolla (¥) 2,150,000
Spot exchange rate (¥/$) 87.60
Year-beginning price of a Corolla ($) 24,543.38$
b. What is the expected spot rate at the end of the year assuming PPP?
Initial spot rate (¥/$) 87.60
Expected US$ inflation 2.20%
Expected Japanese yen inflation 0.00%
Expected spot rate at end of year assuming PPP (¥/$) 85.71
c. Assuming complete pass through, what will the price be in US$ in one year?
Price of Corolla at beginning of year (¥) 2,150,000
Japanese yen inflation over the year 0.000%
Price of Corolla at end of year (¥) 2,150,000
Expected spot rate one year from now assuming PPP (¥/$) 85.71
Price of Corolla at end of year in ($) 25,083.33$
d. Assuming partial pass through, what will the price be in US$ in one year?
Price of Corolla at end of year (¥) 2,150,000
Amount of expected exchange rate change, in percent (from PPP) 2.200%
Proportion of exchange rate change passed through by Toyota 75.000%
Proportional percentage change 1.650%
Effective exchange rate used by Toyota to price in US$ for end of year 86.178
Price of Toyota at end of year ($) 24,948.34$
Problem 6.6 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 is 0.0% per year in Japan. Use this data to answer the
following questions on exchange rate pass through.
Value Yen Equivalent
Arbitrage funds available $5,000,000 593,000,000
Spot rate (¥/$) 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%
Difference in interest rates ( i ¥ - i $) -1.400%
Forward premium on the yen 1.358%
CIA profit potential -0.042%
U.S. dollar interest rate (180 days)
4.800%
5,000,000$ → → 1.0240 → → 5,120,000$
↑ ↓
↑ ↓
↑ ↓
↑ ↓
↑ ↓
Spot (¥/$) ---------------> 180 days ----------------> Forward-180 (¥/$)
118.60 117.80
↑ ↓
↑ ↓
↑603,136,000
593,000,000.00 → → 1.0170 → → 603,081,000
Japanese yen 55,000
3.400%
START Japanese yen interest rate (180 days) END
Problem 6.7 Takeshi Kamada -- CIA Japan (A)
Assumptions
Takeshi Kamada generates a CIA profit by investing in the higher interest rate currency, the dollar, and
simultaneously selling the dollar proceeds forward into yen at a forward premium which does not completely negate
This tells Takeshi Kamada that he should borrow yen and invest in the higher yielding currency, the U.S. dollar, to
lock-in a covered interest arbitrage (CIA) profit.
Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium/discount, or
expected change in the spot rate for UIA, invest in the higher interest yielding currency. If the difference in interest
rates is less than the forward premium (or expected change in the spot rate), invest in the lower yielding currency.
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?
the interest differential.
Value Yen Equivalent
Arbitrage funds available $5,000,000 593,000,000
Spot rate (¥/$) 118.60
180-day forward rate (¥/$) 117.80
Expected spot rate in 180 days (¥/$) 118.00
180-day U.S. dollar interest rate 4.800%
180-day Japanese yen interest rate 3.400%
Difference in interest rates ( i ¥ - i $) -1.400%
Expected gain (loss) on the spot rate 1.017%
UIA profit potential -0.383%
U.S. dollar interest rate (180 days)
4.800%
$5,000,000 → → 1.0240 → → $5,120,000
↑ ↓
↑ ↓
↑ ↓
↑ ↓
↑Expected Spot Rate
Spot (¥/$) ---------------> 180 days ----------------> in 180 days (¥/$)
118.60 118.00
↑ ↓
↑ ↓
↑604,160,000
593,000,000.00 → → 1.0170 → → 603,081,000
Japanese yen 1,079,000
3.400%
START Japanese yen interest rate (180 days) END
This tells Takeshi Kamada that he should borrow yen and invest in the higher yielding currency, the U.S. dollar, to
potentially gain on an uncovered basis (UIA).
Problem 6.8 Takeshi Kamada -- UIA Japan (B)
Assumptions
Takeshi Kamada, Credit Suisse (Tokyo), observes that the ¥/$ spot rate has been holding steady, and 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 the previous problem, analyze the UIA potential.
Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium/discount, or
expected change in the spot rate for UIA, invest in the higher interest yielding currency. If the difference in interest
rates is less than the forward premium (or expected change in the spot rate), invest in the lower yielding currency.
b) The risk Takeshi is taking is that the actual spot rate at the end of the period can theoretically be anything, better
or worse for his speculative position. He in fact has very little "wiggle room," as they say. A small movement will
cost him a lot of money. If the spot rate ends up any stronger than about 117.79/$ (a smaller number), he will lose
money. (Verify by inputting ¥117.70/$ in the expected spot rate cell under assumptions.)
a) Takeshi Kamada generates an uncovered interest arbitrage (UIA) profit of ¥1,079,000 if his expectations about the
future spot rate, the one in effect in 180 days, prove correct.
Value
Arbitrage funds available $5,000,000
Spot exchange rate (kr/$) 6.1720
3-month forward rate (kr/$) 6.1980
US dollar 3-month interest rate 3.000%
Danish kroner 3-month interest rate 5.000%
Difference in interest rates (ikr - i$) 2.000%
Forward discount on the krone -1.678%
CIA profit potential 0.322%
U.S. dollar interest rate (3-month)
START 3.000% END
5,000,000.00$ → → 1.0075 → → 5,037,500.00$
↓5,041,263.31
↓3,763.31$
↓ ↑
↓ ↑
↓ ↑
Spot (kr/$) ---------------> 90 days ----------------> Forward-90 (kr/$)
6.1720 6.1980
↓ ↑
↓ ↑
↓ ↑
kr 30,860,000.00 → → 1.0125 → → kr 31,245,750.00
5.000%
Danish kroner interest (3-month)
Heidi Høi Jensen generates a covered interest arbitrage (CIA) profit because she is able to generate an even higher
interest return in Danish kroner than she "gives up" by selling the proceeds forward at the forward rate.
Problem 6.9 Copenhagen Covered (A)
Heidi Høi Jensen, a foreign exchange trader at J.P. Morgan 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 covered interest arbitrage (CIA) profit?
Assumptions
This tells Heidi Høi Jensen that he should borrow dollars and invest in the higher yielding currency the Danish
kroner, for CIA profit.
Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium/discount, or
expected change in the spot rate for UIA, invest in the higher interest yielding currency. If the difference in interest
rates is less than the forward premium (or expected change in the spot rate), invest in the lower yielding currency.
Value kr Equivalent
Arbitrage funds available $5,000,000 kr 30,860,000
Spot exchange rate (kr/$) 6.1720
3-month forward rate (kr/$) 6.1980
US dollar 3-month interest rate 4.000% a)
Danish kroner 3-month interest rate 5.000% a)
Difference in interest rates (ikr - i$) 1.000%
Forward discount on the krone -1.678%
CIA profit potential -0.678%
U.S. dollar interest rate (3-month)
4.000%
5,000,000.00$ → → 1.0100 → → 5,050,000.00$
↑ ↓
↑ ↓
↑ ↓
↑ ↓
↑ ↓
Spot (kr/$) ---------------> 90 days ----------------> F-90 (kr/$)
6.1720 6.1980
↑ ↓
↑ ↓
↑kr 31,299,900.00
kr 30,860,000.00 → → 1.0125 → → kr 31,245,750.00
kr 54,150.00
5.000%
START Danish kroner interest (3-month) END
a) Heidi Høi Jensen generates a covered interest arbitrage profit of kr54,150 because, although U.S. dollar interest
rates are lower, the U.S. dollar is selling forward at a premium against the Danish krone.
Problem 6.10 Copenhagen Covered (B)
Heidi Høi Jensen is now evaluating the arbitrage profit potential in the same market after interest rates change. (Note
that anytime the difference in interest rates does not exactly equal the forward premium, it must be possible to make
CIA profit one way or another.)
Assumptions
This tells Heidi that she should borrow Danish kroner and invest in the LOWER interest rate currency, the dollar,
gaining on the re-exchange of dollars for kroner at the end of the period.
Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium/discount, or
expected change in the spot rate for UIA, invest in the higher interest yielding currency. If the difference in interest
rates is less than the forward premium (or expected change in the spot rate), invest in the lower yielding currency.
Value kr Equivalent
Arbitrage funds available $5,000,000 kr 30,860,000
Spot exchange rate (kr/$) 6.1720
3-month forward rate (kr/$) 6.1980
US dollar 3-month interest rate 3.000% b)
Danish kroner 3-month interest rate 6.000% b)
Difference in interest rates (ikr - i$) 3.000%
Forward discount on the krone -1.678%
CIA profit potential 1.322%
U.S. dollar interest rate (3-month)
3.000%
START END
$5,000,000 → → 1.0075 → → 5,037,500.00$
↓5,053,710.87$
↓16,210.87$
↓ ↑
↓ ↑
↓ ↑
Spot (kr/$) ---------------> 90 days ----------------> F-90 (kr/$)
6.1720 6.1980
↓ ↑
↓ ↑
↓ ↑
kr 30,860,000.00 → → 1.0150 → → kr 31,322,900.00
6.000%
Danish kroner interest (3-month)
This tells Heidi Høi Jensen that she should borrow US dollars and invest in the HIGHER interest rate currency, the
kroner, gaining on the re-exchange of kroner for dollars at the end of the period.
b) If the Danish kroner interest rate increases to 6.00%, while the U.S. dollar interest rate stays at 3.00% and spot
and forward rates remain the same, Heidi Høi Jensen's CIA profit is $16,210.87.
Problem 6.11 Copenhagen Covered ( C )
Heidi Høi Jensen is now evaluating the arbitrage profit potential in the same market after interest rates change. (Note
that anytime the difference in interest rates does not exactly equal the forward premium, it must be possible to make
CIA profit one way or another.)
Assumptions
Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium/discount, or
expected change in the spot rate for UIA, invest in the higher interest yielding currency. If the difference in interest
rates is less than the forward premium (or expected change in the spot rate), invest in the lower yielding currency.
Value SFr. Equivalent
Arbitrage funds available $1,000,000 SFr. 1,281,000
Spot exchange rate (SFr./$) 1.2810
3-month forward rate (SFr./$) 1.2740
U.S. dollar 3-month interest rate 4.800%
Swiss franc3-month interest rate 3.200%
Difference in interest rates ( i SFr. - i $) -1.600%
Forward premium on the Swiss franc 2.198%
CIA profit potential 0.598%
U.S. dollar interest rate (3-month)
START 4.800% END
1,000,000.00$ → → 1.0120 → → 1,012,000.00$
↓1,013,538.46
↓1,538.46$
↓ ↑
↓ ↑
↓ ↑
Spot (SFr./$) ---------------> 90 days ----------------> Forward-90 (SFr./$)
1.2810 1.2740
↓ ↑
↓ ↑
↓ ↑
SFr. 1,281,000.00 → → 1.0080 → → SFr. 1,291,248.00
3.200%
Swiss franc interest rate (3-month)
Problem 6.12 Casper Landsten -- CIA (A)
Assumptions
Casper Landsten is a foreign exchange trader for a bank in New York. He has $1 million (or its Swiss franc
equivalent) for a short term money market investment and wonders if he should invest in U.S. dollars for three
months, or make a covered interest arbitrage investment in the Swiss franc. He faces the following quotes:
This tells Casper Landsten he should borrow U.S. dollars and invest in the LOWER yielding currency, the Swiss
franc, in order to earn covered interest arbitrage (CIA) profits.
Arbitrage Rule of Thumb: If the difference in interest rates is greater than the forward premium/discount, or
expected change in the spot rate for UIA, invest in the higher interest yielding currency. If the difference in interest
rates is less than the forward premium (or expected change in the spot rate), invest in the lower yielding currency.
a) Casper Landsten makes a net profit, a covered interest arbitrage profit, of $1,538.46 on each million he invests in
the Swiss franc market (by going around the box). He should therefore take advantage of it and perform covered
0.62%
b) Assuming a $1 million investment for the 90-day period, the annual rate of return
on this near risk-less investment is:
interest arbitrage.
Value SFr. Equivalent
Arbitrage funds available $1,000,000 SFr. 1,281,000
Spot exchange rate (SFr./$) 1.2810
3-month forward rate (SFr./$) 1.2740
Expected spot rate in 90 days (SFr./$) 1.2700
U.S. dollar 3-month interest rate 4.800%
Swiss franc3-month interest rate 3.200%
START U.S. dollar interest rate (3-month) END
4.800%
1,000,000$ → → 1.0120 → → 1,012,000.00$
1,012,029.16$
↓29.16$
↓ ↑
↓ ↑
↓ ↑
Spot (SFr/$) ---------------> 90 days ----------------> Expected Spot (SFr/$)
1.2810 1.2759
↓ ↑
↓ ↑
↓
SFr. 1,281,000 → → 1.0080 → → SFr. 1,291,248
3.200%
Swiss franc interest rate (3-month)
Since Casper is in the US market (starting point), if he were to undertake uncovered interest arbitrage he would be
first exchange dollars for Swiss francs, investing the Swiss francs for 90 days, and then exchanging the Swiss franc
proceeds (principle and interest) back into US dollars at whatever the spot rate of exchange is at that time. In this
case Casper will have to -- at least in his mind -- make some assumption as to what the exchange rate will be at the
end of the 90 day period.
Problem 6.13 Casper Landsten -- UIA (B)
Assumptions
Casper Landsten, using the same values and assumptions as in the previous question, now decides to seek the full
4.800% return available in US dollars by not covering his forward dollar receipts -- an uncovered interest arbitrage
(UIA) transaction. Assess this decision.
For an UIA transaction to result in higher dollar proceeds at the end of the 90 day period, the ending spot rate of
exchange would have to be SF1.2759/$ or less (a stronger and stronger Swiss franc resulting in more and more US
dollars when exchanged).
If Casper assumed the spot rate at the end of 90 days were the same as the current spot rate (SFr1.2810/$), the UIA
transaction would not make much sense. The lower Swiss franc interest rate would yield final dollar proceeds of only
$1,008,000, a full $4,000 less than simply investing in the US (straight across the top of the box).
Should Casper do it? Well, depends on his bank's policies on uncovered transactions, and his beliefs on the future
spot exchange rate. But, given that he is invested in a foreign currency with a lower interest rate, not a higher one, so
he is placing all of his 'bets' on the exchange rate, it is not a speculation for the weak of heart.
