Chapter 7
International Arbitrage and Interest Rate Parity
Lecture Outline
International Arbitrage
Locational Arbitrage
Triangular Arbitrage
Covered Interest Arbitrage
Comparison of Arbitrage Effects
Interest Rate Parity
Derivation of Interest Rate Parity
Variation in Forward Rate Premiums
Forward Premiums Across Maturities
Changes in Forward Premiums Over Time
2 International Arbitrage and Interest Rate Parity
Chapter Theme
This chapter illustrates how three types of arbitrage (locational, triangular, and covered interest) are
executed. Emphasize that the key to arbitrage from an MNC’s perspective is not the potential profits, but
the relationships that should exist due to arbitrage. The linkage between covered interest arbitrage and
interest rate parity is critical.
Topics to Stimulate Class Discussion
1. Why are quoted spot rates very similar across all banks?
POINT/COUNTER-POINT:
Does Arbitrage Destabilize Foreign Exchange Markets?
POINT: Yes. Large financial institutions have the technology to recognize when one participant in the
foreign exchange market is trying to sell a currency for a higher price than another participant. They also
COUNTER-POINT: No. When financial institutions engage in arbitrage, they create pressure on the
price of a currency that will remove any pricing discrepancy. If arbitrage did not occur, pricing
WHO IS CORRECT? Use the Internet to learn more about this issue. Which argument do you support?
Offer your own opinion on this issue.
International Arbitrage and Interest Rate Parity 3
ANSWER: The counter-point is correct. The type of arbitrage mentioned in this chapter is necessary to
Answers to End of Chapter Questions
1. Locational Arbitrage. Explain the concept of locational arbitrage and the scenario necessary for it
to be plausible.
ANSWER: Locational arbitrage can occur when the spot rate of a given currency varies among
2. Locational Arbitrage. Assume the following information:
Beal Bank Yardley Bank
Bid price of New Zealand dollar $.401 $.398
Ask price of New Zealand dollar $.404 $.400
Given this information, is locational arbitrage possible? If so, explain the steps involved in
locational arbitrage, and compute the profit from this arbitrage if you had $1,000,000 to use. What
market forces would occur to eliminate any further possibilities of locational arbitrage?
ANSWER: Yes! One could purchase New Zealand dollars at Yardley Bank for $.40 and sell them to
3. Triangular Arbitrage. Explain the concept of triangular arbitrage and the scenario necessary for it
to be plausible.
ANSWER: Triangular arbitrage is possible when the actual cross exchange rate between two
4 International Arbitrage and Interest Rate Parity
4. Triangular Arbitrage. Assume the following information:
Quoted Price
Value of Canadian dollar in U.S. dollars $.90
Value of New Zealand dollar in U.S. dollars $.30
Value of Canadian dollar in New Zealand dollars NZ$3.02
Given this information, is triangular arbitrage possible? If so, explain the steps that would reflect
triangular arbitrage, and compute the profit from this strategy if you had $1,000,000 to use. What
market forces would occur to eliminate any further possibilities of triangular arbitrage?
ANSWER: Yes. The appropriate cross exchange rate should be 1 Canadian dollar = 3 New Zealand
5. Covered Interest Arbitrage. Explain the concept of covered interest arbitrage and the scenario
necessary for it to be plausible.
ANSWER: Covered interest arbitrage involves the short-term investment in a foreign currency that
6. Covered Interest Arbitrage. Assume the following information:
Quoted Price
Spot rate of Canadian dollar $.80
90-day forward rate of Canadian dollar $.79
90-day Canadian interest rate 4%
90-day U.S. interest rate 2.5%
Given this information, what would be the yield (percentage return) to a U.S. investor who used
covered interest arbitrage? (Assume the investor invests $1,000,000.) What market forces would
occur to eliminate any further possibilities of covered interest arbitrage?
International Arbitrage and Interest Rate Parity 5
ANSWER:
7. Covered Interest Arbitrage. Assume the following information:
Spot rate of Mexican peso = $.100
180-day forward rate of Mexican peso = $.098
180-day Mexican interest rate = 6%
180-day U.S. interest rate = 5%
Given this information, is covered interest arbitrage worthwhile for Mexican investors who have
pesos to invest? Explain your answer.
ANSWER: To answer this question, begin with an assumed amount of pesos and determine the yield
8. Effects of September 11. The terrorist attack on the U.S. on September 11, 2001 caused
expectations of a weaker U.S. economy. Explain how such expectations could have affected U.S.
interest rates, and therefore have affected the forward rate premium (or discount) on various foreign
currencies.
ANSWER: The expectations of a weaker U.S. economy resulted in a decline of short-term interest
9. Interest Rate Parity. Explain the concept of interest rate parity. Provide the rationale for its
possible existence.
ANSWER: Interest rate parity states that the forward rate premium (or discount) of a currency
6 International Arbitrage and Interest Rate Parity
10. Inflation Effects on the Forward Rate. Why do you think currencies of countries with high
inflation rates tend to have forward discounts?
11. Covered Interest Arbitrage in Both Directions. Assume that the existing U.S. one-year interest
rate is 10 percent and the Canadian one-year interest rate is 11 percent. Also assume that interest rate
parity exists. Should the forward rate of the Canadian dollar exhibit a discount or a premium? If
U.S. investors attempt covered interest arbitrage, what will be their return? If Canadian investors
attempt covered interest arbitrage, what will be their return?
ANSWER: The Canadian dollar’s forward rate should exhibit a discount because its interest rate
12. Interest Rate Parity. Why would U.S. investors consider covered interest arbitrage in France when
the interest rate on euros in France is lower than the U.S. interest rate?
13. Interest Rate Parity. Consider investors who invest in either U.S. or British one-year Treasury
bills. Assume zero transaction costs and no taxes.
a. If interest rate parity exists, then the return for U.S. investors who use covered interest arbitrage
will be the same as the return for U.S. investors who invest in U.S. Treasury bills. Is this
statement true or false? If false, correct the statement.
b. If interest rate parity exists, then the return for British investors who use covered interest
arbitrage will be the same as the return for British investors who invest in British Treasury bills.
Is this statement true or false? If false, correct the statement.
International Arbitrage and Interest Rate Parity 7
14. Changes in Forward Premiums. Assume that the Japanese yen’s forward rate currently exhibits a
premium of 6 percent and that interest rate parity exists. If U.S. interest rates decrease, how must
this premium change to maintain interest rate parity? Why might we expect the premium to change?
ANSWER: The premium will decrease in order to maintain IRP, because the difference between the
15. Changes in Forward Premiums. Assume that the forward rate premium of the euro was higher last
month than it is today. What does this imply about interest rate differentials between the United
States and Europe today compared to those last month?
16. Interest Rate Parity. If the relationship that is specified by interest rate parity does not exist at any
period but does exist on average, then covered interest arbitrage should not be considered by U.S.
firms. Do you agree or disagree with this statement? Explain.
ANSWER: Disagree. If at any point in time, interest rate parity does not exist, covered interest
17. Covered Interest Arbitrage in Both Directions. The one-year interest rate in New Zealand is 6
percent. The one-year U.S. interest rate is 10 percent. The spot rate of the New Zealand dollar
(NZ$) is $.50. The forward rate of the New Zealand dollar is $.54. Is covered interest arbitrage
feasible for U.S. investors? Is it feasible for New Zealand investors? In each case, explain why
covered interest arbitrage is or is not feasible.
ANSWER:
To determine the yield from covered interest arbitrage by U.S. investors, start with an assumed initial
8 International Arbitrage and Interest Rate Parity
18. Limitations of Covered Interest Arbitrage. Assume that the one-year U.S. interest rate is 11
percent, while the one-year interest rate in Malaysia is 40 percent. Assume that a U.S. bank is
willing to purchase the currency of that country from you one year from now at a discount of 13
percent. Would covered interest arbitrage be worth considering? Is there any reason why you should
not attempt covered interest arbitrage in this situation? (Ignore tax effects.)
ANSWER: Covered interest arbitrage would be worth considering since the return would be 21.8
19. Covered Interest Arbitrage in Both Directions. Assume that the annual U.S. interest rate is
currently 8 percent and Germany’s annual interest rate is currently 9 percent. The euro’s one-year
forward rate currently exhibits a discount of 2 percent.
a. Does interest rate parity exist?
b. Can a U.S. firm benefit from investing funds in Germany using covered interest arbitrage?
c. Can a German subsidiary of a U.S. firm benefit by investing funds in the United States through
covered interest arbitrage?
20. Covered Interest Arbitrage. The South African rand has a one-year forward premium of 2 percent.
One-year interest rates in the U.S. are 3 percentage points higher than in South Africa. Based on this
information, is covered interest arbitrage possible for a U.S. investor if interest rate parity holds?
ANSWER:
International Arbitrage and Interest Rate Parity 9
21. Deriving the Forward Rate. Assume that annual interest rates in the U.S. are 4 percent, while
interest rates in France are 6 percent.
a. According to IRP, what should the forward rate premium or discount of the euro be?
b. If the euro’s spot rate is $1.10, what should the one-year forward rate of the euro be?
ANSWER:
22. Covered Interest Arbitrage in Both Directions. The following information is available:
You have $500,000 to invest
The current spot rate of the Moroccan dirham is $.110.
The 60-day forward rate of the Moroccan dirham is $.108.
The 60-day interest rate in the U.S. is 1 percent.
The 60-day interest rate in Morocco is 2 percent.
a. What is the yield to a U.S. investor who conducts covered interest arbitrage? Did covered
interest arbitrage work for the investor in this case?
b. Would covered interest arbitrage be possible for a Moroccan investor in this case?
ANSWER:
a. Covered interest arbitrage would involve the following steps:
10 International Arbitrage and Interest Rate Parity
Advanced Questions
23. Economic Effects on the Forward Rate. Assume that Mexico’s economy has expanded
significantly, causing a high demand for loanable funds there by local firms. How might these
conditions affect the forward discount of the Mexican peso?
ANSWER: Expansion in Mexico creates a demand for loanable funds, which places upward
24. Differences among Forward Rates. Assume that the 30-day forward premium of the euro is -1
percent, while the 90-day forward premium of the euro is 2 percent. Explain the likely interest rate
conditions that would cause these premiums. Does this ensure that covered interest arbitrage is
worthwhile?
ANSWER: These premiums could occur when the euro’s 30-day interest rate is above the U.S. 30-
25. Testing Interest Rate Parity. Describe a method for testing whether interest rate parity exists. Why
are transactions costs, currency restrictions, and differential tax laws important when evaluating
whether covered interest arbitrage can be beneficial?
ANSWER: At any point in time, identify the interest rates of the U.S. versus some foreign country.
26. Deriving the Forward Rate. Before the Asian crisis began, Asian central banks were maintaining a
somewhat stable value for their respective currencies. Nevertheless, the forward rate of Southeast
Asian currencies exhibited a discount. Explain.
ANSWER: The forward rate for the Asian currencies exhibited a discount to reflect that differential
27. Interpreting Changes in the Forward Premium. Assume that interest rate parity holds. At the
beginning of the month, the spot rate of the Canadian dollar is $.70, while the one-year forward rate
is $.68. Assume that U.S. interest rates increase steadily over the month. At the end of the month, the
one-year forward rate is higher than it was at the beginning of the month. Yet, the one-year forward
International Arbitrage and Interest Rate Parity 11
discount is larger (the one-year premium is more negative) at the end of the month than it was at the
beginning of the month. Explain how the relationship between the U.S. interest rate and the
Canadian interest rate changed from the beginning of the month until the end of the month.
ANSWER: The forward discount at the beginning of the month implies that the U.S. interest rate is
28. Interpreting a Large Forward Discount. The interest rate in Indonesia is commonly higher than the
interest rate in the U.S., which reflects a higher expected rate of inflation there. Why should Nike
consider hedging its future remittances from Indonesia to the U.S. parent even when the forward
discount on the currency (rupiah) is so large?
ANSWER: Nike may still consider hedging under these conditions because the alternative is to be
29. Change in the Forward Premium. At the end of this month, you (owner of a U.S. firm) are meeting
with a Japanese firm to which you will try to sell supplies. If you receive an order from that firm,
you will obtain a forward contract to hedge the future receivables in yen. As of this morning, the
forward rate of the yen and spot rate are the same. You believe that interest rate parity holds.
This afternoon, news occurs that makes you believe that the U.S. interest rates will increase
substantially by the end of this month, and that the Japanese interest rate will not change. However,
your expectations of the spot rate of the Japanese yen are not affected at all in the future. How will
your expected dollar amount of receivables from the Japanese transaction be affected (if at all) by the
news that occurred this afternoon? Explain.
ANSWER: If U.S. interest rates increase, then the forward rate of the yen will exhibit a premium.
30. Testing IRP. The one-year interest rate in Singapore is 11 percent. The one-year interest rate in the
U.S. is 6 percent. The spot rate of the Singapore dollar (S$) is $.50 and the forward rate of the S$ is
$.46. Assume zero transactions costs.
a. Does interest rate parity exist?
b. Can a U.S. firm benefit from investing funds in Singapore using covered interest arbitrage?
12 International Arbitrage and Interest Rate Parity
31. Implications of IRP. Assume that interest rate parity exists. You expect that the one-year nominal
interest rate in the U.S. is 7%, while the one-year nominal interest rate in Australia is 11%. The spot
rate of the Australian dollar is $.60. You will need 10 million Australian dollars in one year. Today,
you purchase a one-year forward contract in Australian dollars. How many U.S. dollars will you need
in one year to fulfill your forward contract?
ANSWER:
32. Triangular Arbitrage. You go to a bank and are given these quotes:
You can buy a euro for 14 pesos.
The bank will pay you 13 pesos for a euro.
You can buy a U.S. dollar for .9 euros.
The bank will pay you .8 Euros for a U.S. dollar.
You can buy a U.S. dollar for 10 pesos.
The bank will pay you 9 pesos for a U.S. dollar.
You have $1,000. Can you use triangular arbitrage to generate a profit? If so, explain the order of the
transactions that you would execute, and the profit that you would earn. If you can not earn a profit
from triangular arbitrage, explain why.
ANSWER: Yes, you can generate a profit by converting dollars to euros, and then euros to pesos,
and then pesos to dollars.
First convert the information to direct quotes: