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36. IRP and Changes in the Forward Rate. Assume that interest rate parity exists. As of this
morning, the 1-month interest rate in Canada was lower than the 1-month interest rate in the
U.S.. Assume that as a result of the Fed’s monetary policy this afternoon, the one-month
interest rate in the U.S. declined this afternoon, but was still higher than the Canadian
one-month interest rate. The one-month interest rate in Canada remained unchanged. Based on
the information, the forward rate of the Canadian dollar exhibited a ________ [discount or
premium] this morning that _________[increased or decreased] this afternoon. Explain.
ANSWER: The premium decreased. For all situations in which the foreign interest is less than
37. Deriving the Forward Rate Premium. Assume that the spot rate of the Brazilian real is $.30
today. Assume that interest rate parity exists. Obtain the interest rate data you need from
Bloomberg.com to derive the one-year forward rate premium (or discount), and then determine the
one-year forward rate of the Brazilian real.
ANSWER: Obtain the one-year U.S. interest rate and one-year Brazilian interest rate. Plug the
38. Change in the Forward Premium Over Time. Assume that interest rate parity exists and
will continue to exist. As of today, the one-year interest rate of Singapore is 4% versus 7% in
the U.S. The Singapore central bank is expected to decrease interest rates in the future so that
as of December 1, you expect that the one-year interest rate in Singapore will be 2%. The U.S.
interest rate is not expected to change over time. Based on the information, explain how the
forward premium (or discount) is expected to change by December 1.
ANSWER: The forward premium will become larger. For all situations in which the foreign
39. Forward Rates for Different Time Horizons. Assume that interest rate parity (IRP) exists.
Assume this information provided by today’s Wall Street Journal.
Spot rate of British pound = $1.80
6-month forward rate of pound=$1.82
12-month forward rate of pound=$1.78
a. Is the annualized 6-month U.S. risk-free interest rate above, below, or equal to the British risk-free
interest rate?
b. Is the 12-month U.S. risk-free interest rate above, below, or equal to the British risk-free interest
rate?
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International Arbitrage and Interest Rate Parity 2
ANSWER:
a. The 6-month U.S. risk-free interest rate must be above the 6-month British risk-free interest rate,
b. The 12-month U.S. risk-free interest rate must be below the 12-month British risk-free interest rate,
40. Interpreting Forward Rate Information. Assume that interest rate parity exists. The 6-month
forward rate of the Swiss franc has a premium while the 12-month forward rate of the Swiss franc has
a discount. What does this tell you about the relative level of Swiss interest rates versus U.S. interest
rates?
ANSWER: The 6-month Swiss interest rate must be lower than the 6-month U.S. interest rate. The
41. IRP and Speculation in Currency Futures. Assume that interest rate parity exists. The spot rate
of the Argentine peso is $.40. The one-year interest rate in the U.S. is 7% versus 12% in Argentina.
Assume the futures price is equal to the forward rate. An investor purchased futures contracts on
Argentine pesos, representing a total of 1,000,000 pesos. Determine the total dollar amount of profit
or loss from this futures contract based on the expectation that the Argentine peso will be worth $.42
in one year.
ANSWER:
Forward premium = (1 + .07)/ (1 + .12) -1 = -.04464
42. Profit from Covered Interest Arbitrage. Today, the one-year U.S. interest rate is 4%,
while the one-year interest rate in Argentina is 17%. The spot rate of the Argentine peso (AP) is
$.44. The one-year forward rate of the AP exhibits a 14% discount. Determine the yield
(percentage retrun on investment) to an investor from Argentina who engages in covered
interest arbitrage.
ANSWER:
Forward rate of Argentine peso = $.44 x (1 - .14) = $.3784.
Assume Argentine investors invest AP100,000. [You can start with any assumed amount.]
43. Assessing Whether IRP Exists. Assume zero transactions costs. As of now, the Japanese one-year
interest rate is 3 percent, and the U.S. one-year interest rate is 9 percent. The spot rate of the Japanese
yen is $.0090 and the one-year forward rate of the Japanese yen is $.0097.
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International Arbitrage and Interest Rate Parity 3
a. Determine whether interest rate parity exists, or whether the quoted forward rate is quoted too high
or too low.
b. Based on the information provided in (a), is covered interest arbitrage feasible for U.S. investors,
for Japanese investors, for both types of investors, or for neither type of investor?
ANSWER:
a. (1 + .09)/(1 + .03) -1 = ..05825 if IRP exists.
b. U.S. investors could engage in covered interest arbitrage by exchanging dollars for yen today and
44. Change in Forward Rate Due to Arbitrage. Earlier this morning, the annual U.S. interest rate
was 6 percent and Mexico’s annual interest rate was 8 percent. The spot rate of the Mexican peso was
$.16. The one-year forward rate of the peso was $.15. Assume that as covered interest arbitrage
occurred this morning, the interest rates were not affected, and the spot rate was not affected, but the
forward rate was affected, and consequently interest rate parity now exists. Explain which type of
investor (Mexican or U.S.) engaged in covered interest arbitrage, whether they were buying or selling
pesos forward, and how that affected the forward rate of the peso.
ANSWER:
Forward rate premium should = (1 + .06)/(1 + .08) -1 = -.01852 if IRP existed.
45. IRP Relationship. Assume that interest rate parity (IRP) exists. Assume this information is
provided by today’s Wall Street Journal.
Spot rate of Swiss franc = $.80
6-month forward rate of Swiss franc = $.78
12-month forward rate of Swiss franc = $.81
Assume that the annualized U.S. interest rate is 7% for a six-month maturity and a 12-month maturity.
Do you think the Swiss interest rate for a 6-month maturity is greater than, equal to, or less than the
U.S. interest rate for a 6-month maturity? Explain.
ANSWER: Since the 6-month forward rate contains a discount, the Swiss 6-month interest rate must
46. Impact of Arbitrage on Forward Rate. Assume that the annual U.S. interest rate is currently
8 percent and Japan’s annual interest rate is currently 7 percent. The spot rate of the Japanese yen is
$.01. The one-year forward rate of the Japanese yen is $.01. Assume that as covered interest arbitrage
occurs, the interest rates are not affected, and the spot rate is not affected. Explain how the one-year
forward rate of the yen will change in order to restore interest rate parity, and why it will change
[your explanation should specify which type of investor (Japanese or U.S.) would be engaging in
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International Arbitrage and Interest Rate Parity 4
covered interest arbitrage and whether these investors are buying or selling yen forward, and how that
affects the forward rate of the yen.]
ANSWER: Japanese investors will be able to engage in covered interest rate arbitrage and take
advantage of higher interest rates that exist in US. They will exchange yen for dollars in the spot
47. Profit from Triangular Arbitrage. The bank is willing to buy dollars for 0.9 euros per dollar.
It is willing to sell dollars for .91 euros per dollar.
You can sell Australian dollars (A$) to the bank for $.72.
You can buy Australian dollars from the bank for $.74.
The bank is willing to buy Australian dollars (A$) for 0.68 euros per A$.
The bank is willing to sell Australian dollars (A$) for 0.70 euros per A$.
You have $100,000. Estimate your profit or loss if you were to attempt triangular arbitrage by
converting your dollars to Australian dollars, and then convertubg Australian dollars to euros, and
then converting euros to U.S. dollars.
ANSWER:
$100,000/$.74=A$135,135
48. Profit from Triangular Arbitrage. Alabama Bank is willing to buy or sell British pounds for $1.98.
The bank is willing to buy or sell Mexican pesos at an exchange rate of 10 pesos per dollar. The bank
is willing to purchase British pounds at an exchange rate of 1 peso = .05 British pounds. Show how
you can make a profit from triangular arbitrage and what your profit would be if you had $100,000.
ANSWER:
1 pound = 20 pesos
49. Cross-rate and Forward Rate. Biscayne Co. will be receiving Mexican pesos and today and will
need to convert them into Australian dollars. Today, a U.S. dollar can be exchanged for 10 Mexican
pesos. Also, an Australian dollar is worth one-half of a U.S. dollar.
a. What is the spot rate of a Mexican peso in Australian dollars?
b. Assume that interest rate parity exists and that the annual risk-free interest rate in the U.S.,
Australia, and Mexico is 7 percent. What is the one-year forward rate of a Mexican peso in Australian
dollars?
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International Arbitrage and Interest Rate Parity 5
ANSWER:
a. peso = $.10
b. Since interest rates are the same, the forward rate is the same as the prevailing spot rate for all three
currencies. Thus, the peso's one-year forward rate is A$0.20.
50. Changes in the Forward Rate. Assume that interest rate parity exists and will continue to exist. As
of this morning, the 1-month interest rate in the U.S. was higer than the 1-month interest rate in the
eurozone. Assume that as a result of the European Central Bank’s monetary policy this afternoon, the
one-month interest rate of the euro increased, and is now higher than the U.S. one-month interest rate.
The one-month interest rate in the U.S. remained unchanged.
a. Based on the information, do you think the one-month forward rate of the euro exhibited a discount
or premium this morning?
b. How did the forward premium change this afternoon?
ANSWER:
a. Under conditions of interest rate parity, the forward rate exhibited a premium in the morning
b. In the afternoon, the foreign interest rate is below the US interest rate, so the forward rate
51. Forces of Triangular Arbitrage. You obtain the following quotes from different banks. One bank is
willing to buy or sell Japanese yen at an exchange rate of 110 yen per dollar. A second bank is willing
to buy or sell the Argentine peso at an exchange rate of $.37 per peso. A third bank is willing to
exchange Japanese yen at an exchange rate of 1 Argentine peso = 40 yen.
a. Show how you can make a profit from triangular arbitrage and what your profit would be if you
had $1,000,000.
b. As investors engage in triangular arbitrage, explain the effect on each of the exchange rates until
triangular arbitrage would no longer be possible.
ANSWER:
a. Direct rate of peso =$.37
b. As dollars are converted to yen, the yen's value should appreciate against the dollar. As yen are
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International Arbitrage and Interest Rate Parity 6
52. Return Due to Covered Interest Arbitrage. Interest rate parity exists between the U.S. and Poland
(its currency is the zloty). The one-year risk-free CD (deposit) rate in the U.S. is 7%. The one-year
risk-free CD rate in Poland is 5% and denominated in zloty. Assume that there is zero probability of
any financial or political problem in either country such as a bank default or government restrictions
on bank deposits or currencies. Myron is from Poland and plans to invest in the U.S. What is Myron’s
return if he invests in the U.S. and covers the risk of his investment with a forward contract?
ANSWER: His return is 5%. The forward premium on the zloty will be about 2%. He will earn 7% on
53. Forces of Covered Interest Arbitrage. As of now, the nominal interest rate is 6% in the U.S. and 6%
in Australia. The spot rate of the Australian dollar is $.58, while the one-year forward rate of the
Australian dollar exhibits a discount of 2%. Assume that as covered interest arbitrage occurred this
morning, the interest rates were not affected, and the spot rate of the Australian dollar was not
affected, but the forward rate of the Australian dollar was affected, and consequently interest rate
parity now exists. Explain the forces that caused the forward rate of the Australian dollar to change by
completing this sentence: The ___________ [Australian or U.S.?] investors could benefit from
engaging in covered interest arbitrage; their arbitrage would involve ___________ [buying or
selling?] Australia dollars forward, which would cause the forward rate of the Australian dollar to
____________ [increase or decrease?].]
ANSWER: If IRP exists, the forward rate should be the same as the spot rate, since interest rates are
54. Change in Forward Premium Over Time. Assume that the one-year interest rate in the U.K.. is 9
percent, while the one-year interest in the U.S is 4%. The spot rate of the pound is $1.50. Assume that
interest rate parity exists. The quoted one-year interest in the U.K. is expected to rise consistently
over the next month. Meanwhile, the quoted one-year interest rate in the U.S. is expected to decline
consistently over the next month. Assume that the spot rate does not change over the month. Based on
this information, how will the quoted one-year forward rate change over the next month?
55. Forward Rate Premiums Among Maturities. Today, the annualized interest rate in the U.S. is 4%
for any debt maturity. The annualized interest rate in Australia is 4% for debt maturities of 3 months
or less, is 5% for debt maturities between 3 months and 6 months, and is 6% for debt maturities more
than 6 months. Assume that interest rate parity exists. Does the forward rate quoted today for the
Australian dollar exhibit a premium, or a discount, or does your answer vary with specific conditions?
Briefly explain.
ANSWER: The forward rate of the Australian dollar exhibits no discount or premium for maturities
56. Explaining Movements in Forward Premiums. Assume that interest rate parity holds and will
continue to hold in the future. At the beginning of the month, the spot rate of the British pound is
$1.60, while the one-year forward rate is $1.50. Assume that U.S. annual interest rate remains steady
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International Arbitrage and Interest Rate Parity 7
over the month. At the end of the month, the one-year forward rate of the British pound exhibits a
discount of 1 percent. Explain how the British annual interest rate changed over the month, and
whether it is higher, lower, or equal to the U.S. rate at the end of the month.
ANSWER: For interest parity to hold, the forward premium at the beginning of the month implies
that the U.S. interest rate is much higher than the British interest rate. During the month, the British
57. Forces of Covered Interest Arbitrage. Assume that the one-year interest rate in Canada is 4 percent.
The one-year U.S. interest rate is 8 percent. The spot rate of the Canadian dollar (C$) is $.94. The
forward rate of the Canadian dollar is $.98.
a. Is covered interest arbitrage feasible for U.S. investors? Show the results if a U.S. firm engages in
b. Assume that the spot rate and interest rates remain unchanged as coverage interest arbitrage is
ANSWER:
a. To determine the yield from covered interest arbitrage by U.S. investors, start with an assumed
initial investment, such as $1,000,000.
b. The forward rate of the Canadian dollar should decrease due to the heavy forward sales of the
Solution to Continuing Case Problem: Blades, Inc.
1. The first arbitrage opportunity relates to locational arbitrage. Holt has obtained spot rate quotations
from two banks in Thailand, Minzu Bank and Sobat Bank, both located in Bangkok. The bid and ask
prices of Thai baht for each bank are displayed in the table below:
Minzu Bank Sobat Bank
Bid $0.0224 $0.0228
Ask $0.0227 $0.0229
Determine whether the foreign exchange quotations are appropriate. If they are not appropriate,
determine the profit you could generate by withdrawing $100,000 from Blades’ checking account and
engaging in arbitrage before the rates are adjusted.
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International Arbitrage and Interest Rate Parity 8
ANSWER: Locational arbitrage is possible:
Locational Arbitrage
2. Besides the bid and ask quotes for the Thai baht provided in the previous question, Minzu Bank has
provided the following quotations for the U.S. dollar and the Japanese yen:
Quoted Bid Price Quoted Ask Price
Value of a Japanese yen in U.S. dollars $0.0085 $0.0086
Value of a Thai baht in Japanese yen ¥2.69 ¥2.70
Determine whether the cross exchange rate between the Thai baht and Japanese yen is appropriate. If
it is not appropriate, determine the profit you could generate for Blades Inc, by withdrawing $100,000
from Blades’ checking account and engaging in triangular arbitrage before the rates are adjusted.
ANSWER: Triangular arbitrage is possible.
Triangular Arbitrage
1. Exchange dollars for Thai baht ($100,000/$0.0227) 4,405,286.34
3. Ben Holt has obtained several forward contract quotations for the Thai baht to determine whether
covered interest arbitrage may be possible. He was quoted a forward rate of $0.0225 per Thai baht for
a 90-day forward contract. The current spot rate is $0.0227. Ninety-day interest rates available to
Blades in the U.S. are 2 percent, while 90-day interest rates in Thailand are 3.75 percent (these rates
are not annualized). Holt is aware that covered interest arbitrage, unlike locational and triangular
arbitrage, requires an investment of funds. Thus, he would like to be able to estimate the dollar profit
resulting from arbitrage over and above the dollar amount available on a 90-day U.S. deposit.
Determine whether the forward rate is priced appropriately. If it is not priced appropriately, determine
the profit you could generate for Blades by withdrawing $100,000 from Blades’ checking account and
engaging in covered interest arbitrage. Measure the profit as the excess amount above what you could
generate by investing in the U.S. money market.
ANSWER: Covered interest arbitrage is possible.
Covered Interest Arbitrage
1. On Day 1, convert U.S. dollars to Thai baht and set up a 90-day deposit
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International Arbitrage and Interest Rate Parity 9
4. Why are arbitrage opportunities likely to disappear soon after they have been discovered? To illustrate
your answer, assume that covered interest arbitrage involving the immediate purchase and forward
sale of baht is possible. Discuss how the baht’s spot and forward rates would adjust until covered
interest arbitrage is no longer possible. What is the resulting equilibrium state called?
ANSWER: Arbitrage opportunities are likely to disappear soon after they have been discovered
because of market forces. Due to the actions taken by arbitrageurs, supply and demand for the foreign
Solution to Supplemental Case: Zuber, Inc.
a. The expected value of the yield on investing funds in this country would be 14 percent, versus only 9
b. Covered interest arbitrage would involve exchanging dollars for the currency today, investing the
c. The risks of covered interest arbitrage are as follows:
The Treasury of the country could default on its securities issued.
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International Arbitrage and Interest Rate Parity 10
d. While covered interest arbitrage would be expected to achieve a yield of 11.15 percent (versus only 9
percent in the U.S.), the risks are significant, especially considering that the country is still
experimenting with cross-border transactions. Since some students will probably suggest going for
the higher returns, this question may allow for an interesting class discussion.
Small Business Dilemma
Assessment of Prevailing Spot and Forward Rates by the Sports Exports Company
1. Do you think Jim will be able to find a bank that provides him with a more favorable spot rate than
his local bank? Explain.
ANSWER: The quoted spot rate for British pounds will typically be similar among banks at a given
2. Do you think that Jim’s bank is likely to provide more reasonable quotations for the spot rate of the
British pound if it is the only bank in town that provides foreign exchange services? Explain.
ANSWER: The bank is likely to provide more reasonable quotations for the spot rate of the British
3. Jim is considering using a forward contract to hedge the anticipated receivables in pounds next
month. His local bank quoted him a spot rate of $1.65 and a one-month forward rate of $1.6435.
Before Jim decides to sell pounds one month forward, he wants to be sure that the forward rate is
reasonable, given the prevailing spot rate. A one-month Treasury security in the United States
currently offers a yield (not annualized) of 1 percent, while a one-month Treasury security in the
United Kingdom offers a yield of 1.4 percent. Do you believe that the one-month forward rate is
reasonable given the spot rate of $1.65?
ANSWER: Yes. According to interest rate parity, the forward rate premium should be based on the
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International Arbitrage and Interest Rate Parity 11
The actual premium is very close to what the premium should be according to interest rate parity.
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