Value SFr. Equivalent
Arbitrage funds available $1,000,000 SFr. 1,281,000
Spot exchange rate (SFr./$) 1.2810
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$
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3.200%
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.
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).
U.S. dollar 3-month interest rate 4.800%
Swiss franc3-month interest rate 3.200%
Value SFr. Equivalent
Arbitrage funds available $1,000,000 SFr. 1,339,200
Difference in interest rates ( i SFr. – i $) -1.125%
Forward premium on the Swiss france 3.191%
CIA profit 2.066%
U.S. dollar interest rate (3-month)
START 4.750% END
$1,000,000 → → 1.011875 → → 1,011,875.00$
↓1,017,113.13
↓5,238.13$
Swiss franc interest rate (3-month)
Problem 6.14 Casper Landsten — Thirty Days Later
Assumptions
This tells Casper Landsten he should borrow U.S. dollars and invest in the lower yielding currency, the Swiss franc,
and then sell the Swiss franc principal and interest forward three months locking in a CIA profit.
One month after the events described in the previous two questions, 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 ener into a
covered interest arbitrage (CIA) investment?
U.S. dollar 3-month interest rate 4.750%
Value Krone Equivalent
Arbitrage funds available $3,000,000 18,093,600
Difference in interest rates ( i Nok – i $) -0.550%
Forward premium on the krone 0.835%
CIA profit 0.285%
Norwegian krone interest rate (3-month)
4.450%
18,093,600.00 → → 1.0111250 → → 18,294,891.30
↑ ↓
↑ ↓
↑ ↓
↑ ↓
5.000%
Ari Karlsen can make $2,210.25 for Statoil on each $3 million he invests in this covered interest arbitrage (CIA)
This tells Ari Karlsen he should borrow U.S. dollars and invest in the lower yielding currency, the Norwegian krone,
selling the dollars forward 90 days, and therefore earn covered interest arbitrage (CIA) profits.
Problem 6.15 Statoil of Norway’s Arbitrage
Assumptions
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 as its functional currency, not the Norwegian krone. Ari Karlsen is a currency trader for Statoil, and has
immediate use of either $3 million (or the Norwegian krone equivalent). He is faced with the following market rates, and
wonders whether he can make some arbitrage profits in the coming 90 days.
U.S. dollar 3-month interest rate 5.000%
Norwegian krone 3-month interest rate 4.450%
Assumptions London New York
Spot exchange rate ($/€)
1.3264 1.3264
a. What do the financial markets suggest for inflation in Europe next year?
b. Estimate today’s one-year forward exchange rate between the dollar and the euro.
a. What do the financial markets suggest for inflation in Europe next year?
The expected rate of inflation in Europe is then: 0.669%
According to the Fisher effect, real interest rates should be the same in both Europe and the US.
b. Estimate today‘s one-year forward exchange rate between the dollar and the euro.
Spot exchange rate ($/€)
1.3264
Problem 6.16 Separated by the Atlantic
The separation of over 3,000 nautical miles and five time zones, money and foreign exchange markets in
both London and New York are very efficient. The following information has been collected from the
respective areas:
Assumptions Value
Spot exchange rate ($/€)
$1.3620
Forecasting the future rent amount and exchange rate: Value
Purchasing power parity exchange rate forecast ($/€) 1.3488
Nominal monthly rent, in euros, one year from now 10,143.00
Cost of rent one year from now in US dollars 13,681.29$
Problem 6.17 Chamonix Chateau Rentals
You are planning a ski vacation to Mt. Blanc in Chamonix, France, one year from now. You are
negotiating over 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 upwards or downwards 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%. The current spot rate is $1.3620/€. What should you budget as the U.S.
dollar cost of the one week rental?
2.500%
3.500%
Value
Current spot rate, Thai baht/$ 32.06
Expected Thai inflation 4.300%
First, it is necessary to forecast the future spot exchange rate for the baht/$.
PPP forecast of Thai baht/$ 33.0258
Different expectations of the future spot exchange rate, either PPP for part a), or an expected devaluation for
part b), allow the isolation of exactly how many Thai baht would be required to repay the dollar loan.
U.S. dollar borrowing rate (one year)
6.750%
250,000$ → → 1.06750 → → 266,875$
↓ ↓
↓ ↓
↓ ↓
↓ ↓
↓ ↓
↓ ↓
↓ ↓
b) Assuming a future spot rate for the baht which is 5% weaker than the current spot rate (B32.06/$ ÷ ( 1 – .05), or
Problem 6.18 East Asiatic Company — Thailand
Assumptions
a) Assuming a purchasing power parity forecast of the future spot rate, B33.0258/$, it will take 8,813,760 baht to
repay the U.S. dollar loan. The implied cost of funds, in baht terms, is 9.966%.
The East Asiatic Company (EAC), a Danish company with subsidiaries all over Asia, has been funding its Bangkok
subsidiary primarily with U.S. dollar debt because of the cost and availability of dollar capital as opposed to Thai
baht-denominated (B) debt. The treasuer of EAC-Thailand is considering a one-year bank loan for $250,000. The
current spot rate is B32.06/$, and the dollar-based interest is 6.75% for the one year period. One year loans are
12.00% in baht.
a. Assuming expected inflation rates of 4.3% and 1.25% in Thailand and the United States, repectively, for the
coming year, according to purchase power parity, what would the effective cost of funds be in Thai baht terms?
b. If EAC’s foreign exchange advisers believe strongly that the Thai government wants to push the value of the
Expected dollar inflation 1.250%
Loan principal in U.S. dollars $250,000
Thai baht interest rate, 1-year loan 12.000%
US dollar interest rate, 1-year loan 6.750%
Now In One Year
Weight of falcon, in pounds 48 48
The purchasing power parity forecast of the Maltese lira/dollar exchange rate:
Current spot rate, Maltese lira/$ 0.3900
Expected Maltese inflation 8.500%
PPP forecast of Maltese lira/$ 0.4169
Investor Receives
in March 2004
Current Value Assuming PPP
337,920$ 316,116$
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Problem 6.19 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 in March 2004, 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 U.S. dollar, would he be better off receiving Maltese lira in one year
(assuming purhcasing power parity), or receiving a guaranteed dollar payment (assuming a gold price of $420 per
ounce)?
Total number of ounces in weight 768 768
Price of gold, $/ounce 440.00$ 420.00$
Falcon value based on price of gold 337,920.00$ 322,560.00$
Assumptions Values
Principal investment, British pounds £1,000,000.00
Spot exchange rate ($/£) 1.5820$
180-day forward rate ($/£) 1.5561$
Malaysian ringgit 180-day yield 8.900%
Spot exchange rate, Malaysian ringgit/$ 3.1384
Return = (Proceeds/Initial investment) – 1 6.188%
Initial Investment Investment Proceeds
£1,000,000.00 £1,061,884.84
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If Clayton Moore invests in the Malaysian ringgit deposit, and accepts the uncovered risk associated with the RM/$
exchange rate (managed by the government), and sells the dollar proceeds forward, he should expect a return of
6.188% on his 180-day pound investment. This is better than the 4.200% he can earn in the euro-pound market.
Problem 6.20 Malaysian Risk
Clayton Moore is the manager of an international money market fund managed out of London. Unlike many money
funds that guarantee their investors a near risk-free investment with variable interest earnings, Clayton Moore’s fund
is a very aggressive fund that searches out relatively high interest earnings around the globe, but at some risk. The
fund is pound-denominated. Clayton is currently evaluating a rather interesting opportunity in Malaysia. Since the
Spot Under or
Local Local In Implied rate overvalued
Country Beer currency currency rand PPP rate (3/15/99) to rand (%)
South Africa Castle Rand 2.30 —- —- —- —-
Botswana Castle Pula 2.20 2.94 0.96 0.75 27.9%
Notes:
1. Beer price in South African rand = Price in local currency / spot rate on 3/15/99.
Beer Prices
In 1999 the Economist magazine reported the creation of an index or standard for the evaluation of African currency values using the local prices of beer.
Beer was chosen as the product for comparison because McDonald’s had not peneterated 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.
Problem 6.21 The Beer Standard
Borrowing principal 25,000,000$
U.S. dollar borrowing rate (one year)
6.800%
25,000,000$ → → 1.0680 → → 26,700,000$
↓ ↓
↓ ↓
↓ ↓
↓ ↓
↓ ↓
↓ ↓
↓ ↓
9.600%
a. If the ending spot rate was Ps11.01/$ as PPP would predict, the actual peso-based interest cost would be 8.894%.
b. The real peso-denominated interest cost (corrected for inflation) would be:
Nominal interest 8.8940%
Problem 6.22 Grupo Bimbo (Mexico)
Grupo Bimbo, headquartered in Mexico City, is one of the largest bakery companies in the world. On January 1st, when
the spot exchange rate is Ps10.80/$, the company borrows $25.0 million from a New York bank for one year at 6.80%
interest (Mexican banks had quoted 9.60% for an equivalent loan in pesos). During the year, U.S. inflation is 2% and
Mexican inflation is 4%. At the end of the year the firm repays the dollar loan.
a. If Bimbo expected the spot rate at the end of one year to be that equal to purchasing power parity, what would be the
cost to Bimbo of its dollar loan in peso-denominated interest?
b. What is the real interest cost (adjusted for inflation) to Bimbo, in peso-denominated terms, of borrowing the dollars for
one year, again assuming purchasing power parity ?
c. If the actual spot rate at the end of the year turned out to be Ps9.60/$, what was the actual peso-denominated interest
cost of the loan?
Current spot rate, pesos/dollar (Ps/$) 10.800
Mexican inflation (actual) 4.00%
Actual spot rate end of year (Ps/$) 9.60
Actual spot rate end of year (Ps/$) 9.60
Calendar year 2001 2002 2003 2004 2005 2006
Kalina Price (rubles) 260,000
Russian inflation (forecast) 14.0% 12.0% 11.0% 8.0% 8.0%
U.S. inflation (forecast) 2.5% 3.0% 3.0% 3.0% 3.0%
Exchange rate (rubles = USD 1.00) 30.00
a. If the domestic price of the Kalina increases with the rate of inflation, what would its price be over the 2002-2006 period?
g. So what did the Russian ruble end up doing over the 2001-2006 period?
Calendar year 2001 2002 2003 2004 2005 2006
a. Kalina Price with Russian inflation (rubles) 260,000 296,400 331,968 368,484 397,963 429,800
Problem 6.23 AvtoVAZ of Russia’s Kalina Export Pricing Analysis
b. Assuming that the forecasts of US and Russian inflation prove accurate, what would the value of the ruble be over the coming years if its value versus
the dollar followed purchasing power parity?
c. If the export price of the Kalina were set using the purchasing power parity forecast of the ruble-dollar exchange rate, what would the export price be
over the 2002-2006 period?
AvtoVAZ OAO, a leading auto manufacturer in Russia, was launching a new automobile model in 2001, and is in the midst of completing a complete
pricing analysis of the car for sales in Russia and export. The new car, the Kalina, would be initially priced at Rubles 260,000 in Russia, and if exported,
$8,666.67 in U.S. dollars at the current spot rate of Rubles 30 = $1.00. AvtoVAZ intends to raise the price domestically with the rate of Russian inflation
over time, but is worried about how that compares to the export price given U.S. dollar inflation and the future exchange rate. Use the following data table
to answer the pricing analysis questions.
d. How would the Kalina’s export price evolve over time if it followed Russian inflation and the exchange rate of the ruble versus the dollar remained
relatively constant over this period of time?
e. Vlad, one of the newly hired pricing strategists, believes that prices of automobiles in both domestic and export markets will both increase with the rate
of inflation, and that the ruble/dollar exchange rate will remain fixed. What would this imply or forecast for the future export price of the Kalina?
f. If you were AvtoVAZ, what would you hope would happen to the ruble’s value versus the dollar over time given your desire to export the Kalina? Now if
you combined that ‘hope’ with some assumptions about the competition — other automobile sales prices in dollar markets over time — how might your
strategy evolve?
c. Export price if using PPP (dollars) 8,666.67$ 8,883.33$ 9,149.83$ 9,424.33$ 9,707.06$ 9,998.27$
d. Export price at fixed exchange rate (dollars) 8,666.67$ 9,880.00$ 11,065.60$ 12,282.82$ 13,265.44$ 14,326.68$
An added note is to recognize that if this was the case, PPP is definitely not ‘holding’ in the academic sense.
If export price rises at dollar inflation 8,666.67$ 8,883.33$ 9,149.83$ 9,424.33$ 9,707.06$ 9,998.27$
b. Exchange rate (rubles=$1.00) if purchasing
power parity (PPP) holds