Chapter
1
Globalization and the Multinational
Corporation
QUESTIONS
1. Define globalization. How has it proceeded in trade in goods and services versus
capital markets?
Answer: Globalization refers to the increasing connectivity and integration of countries
and corporations and the people within them in terms of their economic, political, and
social activities. Because of globalization, multinational corporations dominate the
corporate landscape.
2. Describe fours ways that a company can supply its products to a foreign country.
How do they differ?
Answer: An MNC can supply a foreign market through exports, by licensing local firms
abroad to manufacture the company’s products, by setting up a joint venture with a
foreign company, or by foreign direct investment.
3. What is a greenfield investment?
Answer: MNCs engage in greenfield investments when they enter foreign markets by
simply establishing new operations in these countries without having a local partner and
without acquiring a local company.
4. What percentage ownership typically defines FDI?
Answer: Foreign direct investment (FDI) occurs when a company from one country
makes a significant investment that leads to at least a 10% ownership interest in a firm in
another country.
5. What is agency theory? How does corporate governance the issues raised by agency
theory?
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2 Chapter 1 Globalization and the Multinational Corporation
Answer: Agency theory explores the problems that arise because the owners of the firm
do not typically manage the firm, and it devises ways to resolve these problems. This is
often called the separation of owneship and control. A manager of a firm, in particular
the chief executive officer (CEO), is viewed as an agent who contracts with various
principals—most importantly the firm’s shareholders but also the firm’s creditors,
suppliers, clients, and employees. The principals must design contracts that motivate the
agent to perform actions and make decisions that are in the best interests of the principals.
6. Why is ownership more concentrated in developing countries than in developed
countries?
Answer: In many developed countries, the rule of law is strong enough to discipline
managers through legal means, for example by takeovers and proxy contests or through
contractual compensation plans. Concentrated ownership is one way in which agency
problems are mitigated in developing countries. A block of stock is held by either a
wealthy investor, a family, or a financial intermediary, which might be a bank, a holding
company, a hedge fund or a pension fund. The large shareholder clearly has a vested
interest in monitoring management and has the power to implement changes in
management. Negative aspects of this approach include possible collusion between the
large shareholder and the management to expropriate wealth from smaller shareholders
and the fact that the stock may be more difficult to trade on the stock market if a
substantial block of shares is withdrawn from the market but is still available to be sold
should the large shareholder want to sell.
7. What is the IMF? What is its role in the world economy?
Answer: The International Monetary Fund (IMF) is an international organization of 187
member countries, based in Washington, DC, which was conceived at a United Nations
conference convened in Bretton Woods, New Hampshire, in 1944. The main goal of the
IMF is to ensure the stability of the international monetary and financial system—the
system of international payments and exchange rates among national currencies that
enables trade to take place between countries, to help resolve crises when they occur, and
to promote growth and alleviate poverty. To meet these objectives, the IMF offers
surveillance and technical assistance. Surveillance is the regular dialogue about a
country’s economic condition and policy advice that the IMF offers to each of its
members. Technical assistance and training are offered to help member countries
strengthen their capacity to design and implement effective policies, including fiscal
policy, monetary and exchange rate policies, banking and financial system supervision
and regulation, and statistics.
8. What is the World Bank? What is its role in the world economy?
Answer: The World Bank is an international institution created in 1944, as the
©2012 Pearson Education, Inc.
Chapter 1 Globalization and the Multinational Corporation 3
International Bank for Reconstruction and Development (IBRD) to facilitate postwar
reconstruction and development. Over time, the IBRD’s focus shifted toward poverty
reduction, and in 1960, the International Development Association (IDA) was established
as an integral part of the World Bank. Whereas the IBRD focuses on middle-income
countries, the IDA focuses on the poorest countries in the world. Together they provide
low-interest loans, interest-free credits, and grants to developing countries for
investments in education, health, infrastructure, communications, and other activities.
The World Bank also provides advisory services to developing countries and is actively
involved with efforts to reduce and cancel the international debt of the poorest countries.
9. What are the major multilateral development banks?
Answer: The term typically refers to the World Bank Group and four regional
development banks: the African Development Bank, the Asian Development Bank, the
European Bank for Reconstruction and Development, and the Inter-American
Development Bank. These banks have a broad membership that includes both developing
countries (borrowers) and developed countries (donors), and their membership is not
limited to countries from the region of the regional development bank. While each bank
has its own independent legal and operational status, their similar mandates and a
considerable number of joint owners lead to a high level of cooperation among MDBs.
The MDBs provide financing for development in three ways. First, they provide longterm loans at market interest rates. To fund these loans, the MDBs borrow on the
international capital markets and re-lend to borrowing governments in developing
countries. Second, the MDBs offer long-term loans (often termed credits) with interest
rates set well below market rates. These credits are funded through direct contributions of
governments in donor countries. Finally, grants are sometimes offered mostly for
technical assistance, advisory services, or project preparation.
10. What is the WTO? What is its role in the world economy?
Answer: The World Trade Organization (WTO) was founded in 1995. It is headquartered
in Geneva, Switzerland, and had 153 member countries in 2010. Whereas GATT was a
set of rules, the WTO is an institutional body. The WTO expanded its scope from traded
goods to trade within the service sector and intellectual property rights. Various WTO
agreements set the legal ground rules for international commerce to hopefully ensure that
the multilateral trading system operates smoothly. They are negotiated and signed by a
large majority of the world’s trading nations, and the agreements are ratified in the
parliaments of the member countries. If there is a trade dispute between countries, the
WTO’s dispute settlement process helps interpret the agreements and commitments, and
it ensures that countries’ trade policies conform to them.
11. What is an institutional investor? Along with individual investors, what do they
detemine?
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4 Chapter 1 Globalization and the Multinational Corporation
Answer: Institutional Investors are organizations that invest pools of money on behalf of
individual investors or other organizations. Examples include banks, insurance
companies, pension funds, mutual funds, and university endowments. Institutional
investors, together with individual investors, determine the prices of bonds and stocks
implicitly determining the expected rates of return on these assets thereby setting the
MNC’s cost of capital. The cost of capital, in turn, affects project valuations, which
determines a company’s investments.
12. What are anti-globalists?
Answer: Anti-globalization is an umbrella term encompassing separate social
movements, united in their opposition to the globalization of corporate economic activity
and the free trade with developing nations that results from such activity. Anti-globalists
generally believe that global laissez-faire capitalism is detrimental to poor countries and
to disadvantaged people in rich countries. Anti-globalists also criticize global financial
institutions such as the World Bank, the IMF, and the WTO. Especially under attack is
the so-called Washington consensus model of development, which, as promoted by
international financial institutions (especially the IMF), is interpreted as requiring
macroeconomic austerity, privatization, and a relatively laissez-faire approach to
economic management. Anti-globalists believe that these policies exacerbate
unemployment and poverty.
13. Who are Ante and Freedy Handel? How do their views on the world economy
differ?
Answer: Ante and Freedy Handel are two brothers who discuss various international
financial management problems and controversial issues in international finance in
Point–Counterpoint features. The brothers are enrolled in an international finance class.
Ante typically rails against free trade and free markets as he believes financial markets
are inefficient and that prices do not necessarily correctly reflect information about a
firm’s prospects. Freedy believes more in the power of the capitalist system to allocate
resources efficiently, and he consequently believes that financial markets by and large get
things right.
PROBLEMS
1. Go to the Web site of your favorite multinational firm and determine where it
operates thoughout the world. How many employees does it have worldwide? Has
it done any interesting cross-border mergers and acquisitions during the last year?
Answer: As an example, Siemens, http://www.siemens.com/investor/en/index.htm, has an
investor relations section in which you can find the current annual and quarterly reports.
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Chapter 1 Globalization and the Multinational Corporation 5
Doing a Google search for acquisition will allow you to find the most current acquisitions
that the company has done. The company operates in over 190 countries around the
world listed on its Web site. There are over 340,000 employees.
2. Go to UNCTADstat at http://unctadstat.unctad.org. Update the data in Exhibit 1.6
on cross-border mergers and acquisitions for the most recent years.
Answer: UNCTAD provides lots of interesting data on FDI. As of publication of the
book in 2011, Exhibit 1.6 was as current as we could get.
3. Go to the IMF’s Web site at www.imf.org and download the 2011 World Economic
Outlook. Pick your favorite country and determine if this is a good time to invest in
it or not.
Answer: On the IMF’s Web site, click on Data and Statistics to find the WEO.
4. Go to the WTO’s Web site at www.wto.org and determine which goods or services
are the sources of trade disputes between countries this year.
Answer: In May 2011, China was appealing the resolution of a dispute with the United
States over passenger vehicle and light truck tires, and the Ukraine accused Moldova of
protectionism because of certain environmental regulations.
©2012 Pearson Education, Inc.
Chapter
2
The Foreign Exchange Market
QUESTIONS
1. What is an exchange rate?
Answer: An exchange rate is the relative price of two currencies, like the U.S. dollar price of
the euro, the Thai baht price of the Malaysian ringgit, or the Mexican peso price of the
Canadian dollar.
2. What is the structure of the foreign exchange market? Is it like the New York Stock
Exchange?
Answer: The interbank foreign exchange market is a very large, diverse, over-the-counter
market, not a physical trading place where buyers and sellers gather to agree on a price to
exchange currencies. Traders, who are employees of financial institutions in the major
financial cities around the world, deal with each other primarily over the phone or via
computer, with written or formal electronic confirmations of transactions occurring only
later.
3. What is a spot exchange rate contract? When does delivery occur on a spot contract?
Answer: When currencies in the interbank spot market are traded, certain business
conventions are followed. For example, when the trade involves the U.S. dollar, business
convention dictates that spot contracts are settled in 2 business days—that is, the payment of
one currency and receipt of the other currency occurs in 2 business days. One business day is
necessary because of the back-office paperwork involved in any financial transaction. The
second day is needed because of the time zone differences around the world.
Several exceptions to the 2-business-day rule are noteworthy. First, for exchanges
between the U.S. dollar and the Canadian dollar or the Mexican peso, the rule is 1 business
day. Second, if the transaction involves the dollar and the first of the 2 days is a holiday in
the United States but not in the other settlement center, the first day is counted as a business
day for settlement purposes. Third, Fridays are not part of the business week in most Middle
Eastern countries, although Saturdays and Sundays are. Hence, non–Middle Eastern
currencies settle on Fridays, and Middle Eastern currencies settle on Saturdays.
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2 Chapter 2 The Foreign Exchange Market
4. What was the Japanese yen spot price of the U.S. dollar on December 21, 2010?
Answer: Examining Exhibit 2.5 for December 21, 2010 we find that the Japanese yen spot
price of the U.S. dollar was ¥84.12/$.
5. What was the U.S. dollar spot price of the Swiss franc on December 21, 2010?
Answer: Examining Exhibit 2.5 for December 21, 2010, we find that the U.S. dollar spot
price of the Swiss franc was $1.0289/CHF.
6. How large are the bid–ask spreads in the interbank spot market? What is their
purpose?
Answer: The purpose of the bid-ask spread is to allow traders to profit by buying a currency
at a low bid price and selling that currency at a higher ask price. Bid–ask spreads in the spot
foreign exchange market are quite small, often only two or three basis points. For example, a
yen–dollar trader might quote a bid price of yen per dollar at which she is willing to buy
dollars in exchange for yen of, say, ¥83.74/$. The trader would then quote a higher ask price
at which she is willing to sell dollars for yen, say, at an exchange rate of ¥83.76/$. This
percentage bid-ask spread is
¥83.76/$ - ¥83.74/$
100  0.02%
 ¥83.76/$ + ¥83.74/$  / 2
7. What was the euro price of the British pound on December 21, 2010? Why?
Answer: We can find this information two ways. The cross-rate quote from Exhibit 2.6 is
€1.1818/£. The exchange rates of euros per dollar and dollars per pound from Exhibit 2.5 are
€0.7636/$ and $1.5477/£. We know that there would be a triangular arbitrage possibility if
the cross-rate differs from the indirect rate using the dollar as an intermediary. Thus, we find
the same value if we calculate
€0.7636/$  $1.5477/£ = €1.1818/£
8. If the direct euro price of the British pound is higher than the indirect euro price of the
British pound using the dollar as a vehicle currency, how could you make a profit by
trading these currencies?
Answer: If the direct euro price of the British pound is higher than the indirect euro price of
the British pound using the dollar as a vehicle currency, there would be a triangular arbitrage.
We would want to buy pounds at the indirect low price and sell pounds at the direct high
price. Suppose in Question 7 that the direct price euros per pound were €1.2115/£ and the
exchange rates versus the dollar are €0.7636/$ and $1.5477/£. The indirect euro price of the
pound is therefore
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Chapter 2: The Foreign Exchange Market 3
€0.7636/$  $1.5477/£ = €1.1818/£
If we start with €10,000,000, we can convert euros to dollars and get
€10,000,000 / €0.7636/$ = $13,095,862
Converting these dollars into pounds gives
$13,095,862 / $1.5477/£ = £8,461,499
Converting these pounds into euros gives
€1.2115/£  £8,461,499 = €10,251,106
Thus, we make a profit of €251,106 or 2.51%.
9. What is an appreciation of the dollar relative to the pound? What happens to the dollar
price of the pound in this situation?
Answer: An appreciation of the dollar relative to the pound means that it takes fewer dollars
to buy a pound, so the dollar price of the pound falls. This situation is also described as the
dollar is stronger in the foreign exchange market, the pound has depreciated versus the dollar,
and the pound is weaker in the foreign exchange market.
10. What is a depreciation of the Thai baht relative to the Malaysian ringgit? What
happens to the baht price of the ringgit in this situation?
Answer: A depreciation of the Thai baht relative to the Malaysian ringgit means that it will
take more baht to buy one ringgit. Thus, the baht price of the ringgit is now higher after the
depreciation of the baht.
PROBLEMS
1. Mississippi Mud Pies, Inc. needs to buy 1,000,000 Swiss francs (CHF) to pay its Swiss
chocolate supplier. Its banker quotes bid–ask rates of CHF1.3990–1.4000/USD. What
will be the dollar cost of the CHF1,000,000?
Answer: The bank’s bid rate is CHF1.3990/$. That is the price at which the bank is willing to
buy $1 in return for CHF1.3990. The bank sells dollars at its ask price CHF1.4000/$.
Mississippi Mud Pies must sell dollars to the bank to buy CHF. Therefore Mississippi Mud
Pies will receive the bank’s bid rate of CHF1.3990/$. The dollar cost of CHF1,000,000 is
consequently
CHF 1,000,000 / CHF1.399/$ = $714,796
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4 Chapter 2 The Foreign Exchange Market
2. If the Japanese yen–U.S. dollar exchange rate is ¥104.30/$, and it takes 25.15 Thai bahts
to purchase 1 dollar, what is the yen price of the baht?
Answer: To prevent triangular arbitrage, the direct quote of the yen price of the baht (¥/THB)
must equal the yen price of the dollar times the dollar price of the baht (which is the
reciprocal of the baht price of the dollar):
¥104.30/$  1/(THB25.15/$) = ¥104.30/$  $0.03976/THB = ¥ 4.1471/THB
3. As a foreign exchange trader, you see the following quotes for Canadian dollars (CAD),
U.S. dollars (USD), and Mexican pesos (MXN):
USD0.7047/CAD
MXN6.4390/CAD MXN8.7535/USD
Is there an arbitrage opportunity, and if so, how would you exploit it?
Answer: The direct quote for the cross-rate of MXN6.4390/CAD should equal the implied
cross-rate using the dollar as an intermediary currency; otherwise there exists a triangular
arbitrage opportunity. The indirect cross rate is
MXN8.7535/USD  USD0.7047/CAD = MXN6.1686/CAD
This indirect cross rate is less than the direct quote so there is an arbitrage opportunity to
exploit between the three currencies. In this situation, buying the CAD with MXN by first
buying USD with MXN and then buying the CAD with the USD and finally selling that
amount of CAD directly for MXN would make a profit because we would be buying the
CAD at a low MXN price and selling the CAD at a high MXN price.
4. The Mexican peso has weakened considerably relative to the dollar, and you are trying
to decide whether this is a good time to invest in Mexico. Suppose the current exchange
rate of the Mexican peso relative to the U.S. dollar is MXN9.5/USD. Your investment
advisor at Goldman Sachs argues that the peso will lose 15% of its value relative to the
dollar over the next year. What is Goldman Sachs’s forecast of the exchange rate in 1
year?
Answer: One way to think of this is to say that the investment advisor is referring to the fact
that the Mexican peso price of the dollar will be 15% higher next year. In this case, the
forecast of the MXN/USD exchange rate in year 1
MXN9.5/USD  1.15 = MXN 10.925/USD
A 15% loss of value of the Mexican peso versus the U.S. dollar technically means that dollar
price of the peso is 15% lower. We know that the current USD price of the peso is
1 / (MXN9.5/USD) = USD0.105263/MXN
If this exchange rate falls by 15%, the new exchange rate will be
0.85  USD0.105263/MXN = USD0.089474/MNX
In this case the forecast for the future exchange rate measured in pesos per dollar is
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Chapter 2: The Foreign Exchange Market 5
1 / (USD0.089474/MXN) = MXN11.1765/USD
The difference arises because the simple percentage change in the exchange rate depends on
how the exchange rate is quoted.
5. Deutsche Bank quotes bid–ask rates of $1.3005/€ - $1.3007/€ and ¥104.30 - 104.40/$.
What would be Deutsche Bank’s direct asking price of yen per euro?
Answer: The direct asking price of yen per euro (¥/€) is the amount of yen that the bank
charges someone who is buying euros with yen. The bank would want this to be the same as
the price at which it sells dollars for yen (the bank’s ask price) times the price at which it
sells euros for dollars (also the bank’s ask price). Thus, the asking price of yen per euro
should be
(¥104.40/$)  ($1.3007/€) = ¥135.79/€
6. Alumina Limited of Australia has called Mitsubishi UFJ Financial Group to get its
opinion about the Japanese yen–Australian dollar exchange rate. The current rate is
¥67.72/A$, and Mitsubishi thinks the Australian dollar will weaken by 5% over the next
year. What is Mitsubishi UFJ’s forecast of the future exchange rate?
Answer: If the Australian dollar weakens by 5% over the next year, it will take 5% fewer
Japanese yen to purchase the Australian dollar. Thus, the forecast is
¥67.72/A$  (1 – 0.05) = ¥64.334/A$
7. Go to www.fxstreet.com, find the “Live Charts Window,” and plot the exchange rate of
the dollar vs. the euro with a “candle stick” high-low chart at 5 minute intervals for one
day, daily intervals for one month, and weekly intervals for one year. Now, cover the
units and ask a classmate to identify the different graphs. Are you surprised?
Answer: The Web site, fxstreet.com, provides some interesting ways to look at the data. The
point of this exercise is that the dynamics of exchange rates look quite similar at the different
intervals. The eye easily sees “trends” and other “reversals.” These are often quite difficult
to detect with statistical analysis, and in real time one never knows when the “trend” will
stop.
8. Pick 3 currencies, and go to www.oanda.com to get their current bilateral exchange
rates. Is there an arbitrage opportunity?
Answer: Oanda is an excellent source of high quality data. When we checked prices, they all
satisfied the no arbitrage requirement.
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6 Chapter 2 The Foreign Exchange Market
9. Go to the CLS Bank web site, www.cls-group.com, and read about In/Out Swaps. How
do they help participants manage their risks?
Answer: Here is the quote from the Web site:
An In/Out Swap comprises two equal and opposite FX transactions that are
agreed as an intraday swap. One of the two FX transactions is input to CLS,
in order to reduce each Member's net position in the two currencies. The
other is settled outside CLS.
The combined effect of these two FX transactions is a reduction in the
intraday funding requirements of the two Members, whilst leaving the
institutions’ overall FX position unchanged. In/Out Swaps exploit the
likelihood that an institution with a large short position in CLS will almost
certainly have one or more large long positions in CLS.
As In/Out Swaps reduce these “in-CLS” cash positions as well as the
corresponding liquidity positions outside of CLS, banks can more easily
manage liquidity flows for their non-CLS needs, as well as in the CLS Bank
system.
CLS offers a full In/Out Swap service that identifies potential In/Out Swaps,
notifies participants and implements In/Out Swaps efficiently through the
CLS Bank system.
The multilateral netting effect together with the In/Out Swap process has
proved to be extremely efficient, resulting in a pay in requirement from
Settlement Members of less than 2% of the gross value of instructions being
settled through CLS Bank.
©2012 Pearson Education, Inc.
Chapter
3
Forward Markets and Transaction
Exchange Risk
QUESTIONS
1. What is a forward exchange rate? When does delivery occur on a 90-day forward
contract?
Answer: The forward exchange rate is a price quoted today for the exchange of currencies
at the maturity of the forward contract. To find the delivery date for a 90-day forward
contract, one first finds the spot value date, which is typically two business days in the
future relative to the day that the contract is made. Then, to find the forward value date, one
goes to the calendar date in three months corresponding to the calendar date of the spot
value date. If that calendar date in three months is a legitimate business day in both
countries, that date is the forward value date. If the banks in one of the countries are closed
on that date, because it is a weekend or holiday, the forward value date is the next available
business day without going out of the month. If going forward in time would take you out
of the month, you go backward in time. This rule is followed except when the spot value
day is the last business day of the current month, in which case the forward value day is the
last business day in both countries in three months (this is referred to as the end-end rule).
2. If the yen is selling at a premium relative to the euro in the forward market, is the
forward price of EUR per JPY larger or smaller than the spot price of EUR per JPY?
Answer: When the yen is selling at a premium in the forward market, the euro price of the
yen in the forward market, EUR per JPY, would be larger than the spot price of EUR per
JPY.
3. What do we mean by the expected future spot rate?
Answer: The expected future spot rate is the conditional mean of the probability
distribution of future spot rates. The probability distribution describes all of the possible
realizations (or ranges of realizations) of the future spot rate and assigns probabilities to
those values (or ranges of values). The conditional mean of the probability distribution of
future spot rates takes a probability weighted average of those possible realizations (or
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Chapter 3: Forward Markets and Transaction Exchange Risk
ranges of realizations). We say that the expectation is conditional because we use all
available information at the time when we are describing the probability distribution.
4. How much of the probability distribution of future spot rates is between plus or
minus 2 standard deviations?
Answer: For a normal distribution, when we go from 2 standard deviations below the
conditional mean to 2 standard deviations above the conditional mean, we encompass
95.44% of the probability distribution.
5. If you are a U.S. firm and owe someone ¥10,000,000 in 180 days, what is your
transaction exchange risk?
Answer: Because you owe ¥10,000,000 in 180 days, you have a transaction exchange risk
because if you do nothing to hedge and the yen strengthens, it will take more dollars to
eliminate your yen liability.
6. What is a spot–forward swap?
Answer: A spot-forward swap involves either the purchase of foreign currency spot against
the sale of the same amount of foreign currency forward, or the sale of foreign currency
spot against the purchase of the same amount of foreign currency forward.
7. What is a forward–forward swap?
Answer: A forward-forward swap involves either the purchase of foreign currency at a
short maturity forward against the sale of the same amount of foreign currency at a longer
maturity forward, or the sale of foreign currency at the short maturity forward against the
purchase of the same amount of foreign currency at a longer maturity forward.
PROBLEMS
1. If the spot exchange rate of the yen relative to the dollar is ¥105.75, and the 90-day
forward rate is ¥103.25/$, is the dollar at a forward premium or discount? Express
the premium or discount as a percentage per annum for a 360-day year?
Answer: When the forward rate of yen per dollar is less than the spot rate of yen per dollar,
the dollar is said to be at a discount in the forward market. The magnitude of the discount is
expressed in percentage per annum by dividing the difference between the forward rate and
the spot rate by the spot rate and multiplying by reciprocal of the fraction of the year
corresponding to the maturity of the forward contract (360/N days) and by 100. Thus, the
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Chapter 3: Forward Markets and Transaction Exchange Risk 3
annualized forward discount is 9.46% because
¥103.25/$ - ¥105.75/$ 360

100  9.46%
¥105.75/$
90
Notice that the word “discount” implies that the forward rate is less than the spot rate.
2. Suppose today is Tuesday, January 18, 2011. If you enter into a 30-day forward
contract to purchase euros, when will you pay your dollars and receive your euros?
(Hints: February 18, 2011, is a Friday, and the following Monday is a holiday.)
Answer: To determine the value date of the forward contract, which is the day on which the
exchange of currencies happens, one must first find the spot value date. For dollar-euro
contracts, the spot value date is two business days in the future. Thus, for a spot contract on
Tuesday, January 18, 2011, the exchange of currencies would take place on Thursday,
January 20, 2011. The 30-day forward contract settles on the calendar day in the next
month corresponding to the date of spot settlement if that is a legitimate business day. The
forward contract would therefore settle on February, 20, 2011 if that is a legitimate
business day, but that date is a Sunday. Furthermore, Monday, February 21, 2011, is a
holiday, so the settlement of the forward contract would be on Tuesday, February 22, 2011.
3. As a foreign exchange trader for JPMorgan Chase, you have just called a trader at
UBS to get quotes for the British pound for the spot, 30-day, 60-day, and 90-day
forward rates. Your UBS counterpart stated, “We trade sterling at $1.7745-50, 47/44,
88/81, 125/115.” What cash flows would you pay and receive if you do a forward
foreign exchange swap in which you swap into £5,000,000 at the 30-day rate and out
of £5,000,000 at the 90-day rate? What must be the relationship between dollar
interest rates and pound sterling interest rates?
Answer: The fact that you are swapping into £5,000,000 at the 30-day rate forward rate
means that you are paying dollars and buying pounds. You would do this transaction at the
bank’s 30-day forward ask rate. To find the forward ask rate, you must realize that the 30day forward points of 47/44 indicate the amounts that must be subtracted from the spot bid
and ask quotes to get the forward rates. We know to subtract the points because the first
forward point is greater than the second. Hence, the first part of the swap would be done at
$1.7750/£ - $0.0044/£ = $1.7706/£. Therefore, to buy £5,000,000 you would pay
$1.7706/£  £5,000,000 = $8,853,000
In the second leg of the swap, you would sell £5,000,000 for dollars in the 90-day forward
market. Because you are selling pound for dollars, you transact at the 90-day forward bid
rate of $1.7745/£ - $0.0125/£ = $1.7620/£. Therefore, you would receive
$1.7620/£  £5,000,000 = $8,810,000
Notice that you get back fewer dollars than you paid, but you had use of £5,000,000 for 60
days. Thus, the pound must be the higher interest rate currency.
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Chapter 3: Forward Markets and Transaction Exchange Risk
4. Consider the following spot and forward rates for the yen–euro exchange rates:
Spot
30 days
60 days
90 days
180 days
360 days
146.30
145.75
145.15
144.75
143.37
137.85
Is the euro at a forward premium or discount? What are the magnitudes of the
forward premiums or discounts when quoted in percentage per annum for a 360-day
year?
Answer: The forward rates of yen per euro are lower than the spot rates. Therefore, the euro
is at a discount in the forward market. The annualized forward premium or discount for the
N day forward contract is
F-S
360
n
= 100
S
N days
If the value of this calculation is negative, say -2%, we say there is a 2% discount.
Therefore, the discounts are 4.51% for 30 days, 4.72% for 60 days, 4.24% for 90 days,
4.01% for 180 days, and 5.78% for 360 days.
5. As a currency trader, you see the following quotes on your computer screen:
Exch. Rate
Spot
1-month
2-month
3-month
6-month
USD/EUR
1.0435/45
20/25
52/62
75/90
97/115
JPY/USD
98.75/85
12/10
20/16
25/19
45/35
USD/GBP
1.6623/33
30/35
62/75
95/110
120/130
a. What are the outright forward bid and ask quotes for the USD/EUR at the 3-month
maturity?
Answer: The spot bid and ask quotes for USD/EUR are 1.0435/45. These quotes mean that the
bank buys euros with dollars spot at $1.0435/€, and the bank sells euros for dollars at
$1.0445/€. Because the forward points at the 3-month maturity are 75/90, we know that we
must add the points to get the outright forward bid and ask rates. Adding the points makes the
bid-ask spread in the forward market larger than the bid-ask spread in the spot market.
Consequently, the forward bid rate is $1.0435/€ + $0.0075/€ = $1.0510/€, and the forward ask
quote is $1.0445/€ + $0.0090/€ = $1.0535/€.
b. Suppose you want to swap out of $10,000,000 and into yen for 2 months. What are the
cash flows associated with the swap?
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Answer: When you swap out of $10,000,000 into yen in the spot market, you are selling
dollars to the bank. The bank buys dollars at its low bid rate of ¥98.75/$, so you get
¥98.75/$  $10,000,000 = ¥987,500,000
When you contract to buy the $10,000,000 back from the bank in the 2-month forward
market, you must pay the bank’s ask rate of
¥98.85/$ - ¥00.16/$ = ¥98.69/$
You subtract the points because the 2-month forward quote is 20/16. Subtracting the
points makes the bid-ask spread in the forward market larger than the bid-ask spread in
the spot market. Hence, the amount of yen you pay is
¥98.69/$  $10,000,000 = ¥986,900,000
c. If one of your corporate customers calls you and wants to buy pounds with
dollars in 6 months, what price would you quote?
Answer: If the customer wants to buy pounds with dollars, the customer must pay the
bank’s 6-month ask rate. The spot quotes are 1.6623/33 which means the spot ask rate is
$1.6633/£. The 6-month forward points are 120/130. We add the points because the first
one, 120, is less than the second, 130. Hence, the outright forward quote would be
$1.6633/£ + $0.0130/£ = $1.6763/£
6. Intel is scheduled to receive a payment of ¥100,000,000 in 90 days from Sony in
connection with a shipment of computer chips that Sony is purchasing from Intel.
Suppose that the current exchange rate is ¥103/$, that analysts are forecasting that the
dollar will weaken by 1% over the next 90 days, and that the standard deviation of 90day forecasts of the percentage rate of depreciation of the dollar relative to the yen is
4%.
a. Provide a qualitative description of Intel’s transaction exchange risk.
Answer: Intel is a U.S. company, and it is scheduled to receive yen in the future. A
weakening of the yen versus the dollar causes a given amount of yen to convert to fewer
dollars in the future. This loss of value could be severe if the yen depreciates by a
significant amount.
b. If Intel chooses not to hedge its transaction exchange risk, what is Intel’s expected
dollar revenue?
Answer: If Intel chooses not to hedge, the expected dollar revenue is the expected dollar
value of the ¥100,000,000. The expected spot rate incorporates a 1% weakening of the
dollar. This means that the expected yen price of the dollar is 1% less than the current
spot rate of ¥103/$ or
Et[S(t+90,¥/$)] = 0.99  ¥103/$ = ¥101.97/$
Hence, Intel expects to receive ¥100,000,000 / ¥101.97/$ = $980,681
c. If Intel does not hedge, what is the range of possible dollar revenues that
incorporates 95.45% of the possibilities?
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Chapter 3: Forward Markets and Transaction Exchange Risk
Answer: We are told that the standard deviation of the rate of depreciation of the dollar is 4%.
The standard deviation of the future spot rate is therefore 4% of the current spot rate or 0.04
 ¥103/$ = ¥4.12/$. Thus, plus or minus 2 standard deviations around the conditional expected
future spot rate is
¥101.97/$ + ¥8.24/$ = ¥110.21/$
¥101.97/$ - ¥8.24/$ = ¥93.73/$
The range that encompasses 95.45% of possible future values for Intel’s receivable is therefore
¥100,000,000 / ¥110.21/$ = $907,359
¥100,000,000 / ¥93.73/$ = $1,066,894
7. Go to the Wall Street Journal’s Market Data Center and find New York closing prices for
currencies. Calculate the 180-day forward premium or discount on the dollar in terms of the
yen.
Answer: The correct calculation is
F (t ,180)  S (t )
 200 .
S (t )
8. Go to the St. Louis Federal Reserve Bank’s data base, FRED, at
http://research.stlouisfed.org/fred2/ and download data for the exchange rate of the Brazilian
real vs. the U.S. dollar. Calculate the percentage changes over a one month interval. What loss
would you take if you owed BRL 1 million in one month and the dollar depreciated by two
standard deviations.
Answer: Data on FRED for the Brazilian real per dollar start in January 1995 until the present. Our
data ended with April 2011. Using the full sample available to us, the monthly standard deviation of
the rate of appreciation of the dollar relative to the real was 4.49%. Thus, a 2 standard deviation
move would be 8.98%. The spot rate was BRL1.5833/USD. Thus, the exchange rate could change
to (BRL1.5833 / USD)  (1  0.0898)  BRL1.4411/ USD if the dollar weakened by 2 standard
BRL1, 000, 000
deviations. The dollar cost of the BRL1 million could go from
 USD631,592
(BRL1.5833 / USD)
BRL1, 000, 000
to
 USD693,914 . This is a loss of USD62,322 . Of course, this calculation
(BRL1.4411/ USD)
assumes that the spot rate is not expected to change so that the expected spot rate is the current spot
rate.
©2012 Pearson Education, Inc.
Chapter
4
The Balance of Payments
QUESTIONS
1. What are the major accounts of the balance of payments, and what transactions are
recorded on each account?
Answer: The three major account of the balance of payments are the current account, the
capital account, and the official settlements account.
The current account records the following:
1. Imports, which are purchases of goods and services from foreign residents, and
exports, which are sales of goods and services to foreign residents.
2. Transactions associated with the income flows from the ownership of foreign assets
(dividends and interest paid to domestic residents who own foreign assets as well as
dividends and interest paid to foreign residents who own domestic assets).
3. Unilateral transfers of money between countries (foreign aid, gifts, and grants given
by the residents or governments of one country to those of another).
The capital account records the following:
Purchases and sales of foreign assets by domestic residents as well as the purchases and
sales of domestic assets by foreign residents.
The definition of an asset is all inclusive: It is any form in which wealth can be held. It
encompasses both financial assets (bank deposits and loans, corporate and government
bonds, and equities) and real assets (factories, real estate, antiques, and so forth). Hence, the
capital account records all changes in the domestic ownership of the assets of other nations as
well as changes in the foreign ownership of the assets of the domestic country.
The official settlements account records the following:
Transactions involving the purchase or sale of official international reserve assets by a
nation’s central bank.
International reserves are the assets of the central bank that are not denominated in the
domestic currency. Gold and assets denominated in foreign currency are the typical
international reserves.
2. Why is it important for an international manager to understand the balance of
payments?
Answer: The balance of payments provides information that is useful in understanding the
determination of exchange rates and the growth prospects of a country. For example,
persistent, large current account deficits, especially ones that are primarily consumer driven,
are often associated with currency crises in which the currency of the country with the deficit
depreciates substantially and the country suffers a severe recession. Knowledge of the
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Chapter 4: The Balance of Payments
official settlements account indicates whether the country is gaining or losing international
reserves, and sufficient losses of reserves indicate a loss of the ability to maintain a fixed
exchange rate. Massive increases in international reserves indicate that the central bank is
resisting pressure for the currency to appreciate in value. Large capital account surpluses that
are primarily driven by private sector investments indicate that foreigners find the assets of
the country to be attractive investment opportunities.
3. What are the rules that determine the residency requirements on the balance of
payments?
Answer: The rules for residency are that the entity has a primary economic interest in the
country. Thus, it is not citizenship that is being measured. These concepts are discussed in
detail in the IMF’s Balance of Payments manual available online at
http://www.imf.org/external/np/sta/bop/BOPman.pdf.
4. Which items on the balance of payments are recorded as credits, and which items are
recorded as debits? Why?
Answer: The balance of payments uses a double-entry system. Each transaction gives rise to
two entries: One entry is a credit, and the other entry is a debit of equal value. Any
transaction resulting in a payment to foreigners is entered in the BOP accounts as a debit.
Any transaction resulting in a receipt of funds from foreigners is entered as a credit. In the
double entry system, the flow of money from a domestic resident to a foreign resident is a
credit and the item that gives rise to the flow (either an import of a good or service or the
purchase of a foreign asset) is a debit.
5. How are gifts and grants handled in the balance of payments?
Answer: Gifts and grants are handled as imports and exports of goodwill. If a domestic
resident gives a gift to a foreign resident, the value of the gift is a debit (an import of
goodwill) and the value of the gift is a credit on the domestic balance of payments because it
results in payment of funds to foreigners.
6. What does it mean for a country to experience a capital inflow? Is this associated with a
surplus or a deficit on the country’s capital account?
Answer: When a country experiences a capital inflow, foreign residents are investing in
domestic assets and domestic residents are selling foreign assets. These transactions are
credits on the balance of payments because the country is effectively exporting assets. If
capital inflows exceed capital outflows, there is a surplus on the country’s capital account.
This surplus would be offsetting a combined deficit on the current account and the official
settlements account.
7. If you add up all the current accounts of all countries in the world, the sum should be
zero. Yet this is not so. Why?
©2012 Pearson Education, Inc.
Chapter 4: The Balance of Payments 3
Answer: There is a large, consistently negative sign for the global balance of payments which
suggests that the discrepancy cannot simply be due to measurement errors because if it were,
the balance would be positive about as often as it is negative. One reason why there is a
consistent negative sign in the aggregate errors has to do with tax evasion. Many individuals
try to escape taxes on the income from their investments. Hence, they may fail to report the
interest income they earn on their foreign securities, which would constitute a credit for their
home country’s current account balance. Unrecorded earnings in the international shipping
business may also account for a large part of the missing surplus. Once again, these would be
credits on the service account of the balance of payments. Countries that receive foreign aid
may fail to fully account for official aid disbursements. Freer trade has made it more difficult
for governments to measure sales accurately, and sales over the Internet may also escape
detection.
8. What is the investment income account of the balance of payments?
Answer: The investment income account of the balance of payments is a sub-account of the
current account. It records the dividend and interest receipts that domestic residents receive
as income from their ownership of foreign assets. These flows are credits. The dividend and
interest payments that domestic residents make to foreigners who own domestic assets are
recorded as debits on the investment income account.
9. What is the official settlements account of the balance of payments? How are official
settlements deficits and surpluses associated with movements in the international
reserves of the balance of payments?
Answer: The official settlements account records the purchases and sales of the country’s
international reserves. Just as on the private sector’s capital account, if the central bank
increases its ownership of international reserves, this is recorded as a debit, whereas a sale of
international reserves is a credit. Thus, if the official settlements account is in surplus, the
country is losing international reserves.
10. What is the meaning of an account labeled “statistical discrepancy” or “errors and
omissions”? If this account is a credit, what does that imply about the measurement of
other items in the balance of payments?
Answer: The “statistical discrepancy” or “errors and omissions” account is the value of the
measured items on all other accounts with the sign reversed. Thus, if the sum of all other
accounts is a negative number, indicating that the other accounts are in deficit, the statistical
discrepancy must be a credit (a positive number). The statistician missed some credit items
on the other accounts, because we know that the sum of all accounts should be zero due to
the double entry nature of the balance of payments.
11. Why must the national income of a closed economy equal the national expenditures of
that economy? What separates the two concepts in an open economy?
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Chapter 4: The Balance of Payments
Answer: In a closed economy, the value of the final expenditures on all goods and services
must be the income of the factors of production in the economy. In an open economy, final
expenditures can fall on foreign goods and factors of production can earn income abroad.
Net factor income from abroad plus net unilateral transfers from abroad provide flows of
resources that separate the income of the country from the value of final goods and services
produced in a country.
12. Explain why private national saving plus government saving equals the current
account of the balance of payments.
Answer: Saving is the difference between the income of an entity and what that entity
consumes. In a closed economy, the value of what is produced, the country’s gross domestic
product or GDP, must equal its expenditures and its income. Thus, investment expenditures
must be financed by national savings. In the case of an open economy, this does not have to
be the case. By definition, national savings are equal to national income minus the
consumption of the private (C) and public sectors (G):
National savings = Gross national income – Consumption of the private and public sectors
Symbolically,
S = GNI – C – G
We know that gross national income is GDP plus net foreign income, so
S = GDP + NFI – C – G
Substituting the components of GDP gives
S = C + I + G + NX + NFI – C – G
Upon canceling out the consumption terms and rearranging terms, we find
S – I = NX + NFI = CA
National saving – National investment = Current account
If a country’s purchases of investment goods are more than its savings, the country must
run a current account deficit; that is, the country’s investment spending must be financed
from abroad with a capital account surplus.
13. It has been argued that the high correlation between national saving and national
investment that Feldstein and Horioka first measured in 1980 is not evidence of
imperfect capital mobility. What arguments can you offer for why they might have
misinterpreted the data, and what do recent investigations of this issue imply about the
degree of capital mobility throughout the world?
Answer: There are several important caveats to the Feldstein and Horioka interpretation that
have been noted in the literature. One line of argument asserts that the high correlation
between savings and investment could be produced by common forces that move both
variables even though the international capital market is open and competitive. For example,
Baxter and Crucini (1993) and Mendoza (1991) argue that economic shocks affecting
productivity can increase both saving and investment over the business cycle. The argument
©2012 Pearson Education, Inc.
Chapter 4: The Balance of Payments 5
goes like this: An increase in productivity causes output and income to increase. Some of the
increase in income is consumed, but some of it is saved because the shock is not expected to
be permanent. But because productivity is temporarily high and is expected to be high for
awhile, it is also a good time to invest. Hence, investment and saving both increase. Bai and
Zhang (2010) argue that financial frictions, such as default risk, prevent people in different
countries from sharing risk adequately, leading to the positive correlation between savings
and investment.
Finally, Jeffrey Frankel (1991) has argued that high correlations between national
investment rates and national saving rates should not really be surprising because the world
economy during the 1960s, 1970s, and even much of the 1980s and 1990s was not
characterized by perfect capital mobility. That is, capital markets were not completely open
around the world. For example, there were significant barriers to international investment in
many European countries and Japan that persisted well into the 1980s. (See also Chapter 1.)
Hence, it would stand to reason that in countries in which saving rates are high, investment
rates would be high as well because there is nowhere else for the capital to go. Frankel argues
that to assess how integrated the world’s capital markets are, we must look at the various
rates of return offered around the world and not merely the flows of saving and investment
stressed by Feldstein and Horioka.
More recent investigations of this issue, such as Bai and Zhang (2010) find that the
correlations between savings and investment are going down, which implies that capital
mobility is increasing.
PROBLEMS
1. Suppose that the following transactions take place on the U.S. balance of payments
during a given year. Analyze the effects on the merchandise trade balance, the
international investment income account, the current account, the capital account, and
the official settlements account.
a. Boeing, a U.S. aerospace company, sells $3 billion of its 747 airplanes to the People’s
Republic of China, which pays with proceeds from a loan from a consortium of
international banks.
Answer: Boeing’s sale of planes is an export on the U.S. balance of payments, which is a
credit. The fact that China borrows from international banks is difficult to assess but
ultimately, it means that U.S. ownership of foreign assets is going up. The Chinese must
ultimately be borrowing from U.S. residents. This is a debit on the U.S. balance of
payments.
U.S. BOP
Sale of airplanes by a U.S. exporter to China
(Current account; U.S. goods export, trade balance)
Reduction of Ownership of U.S. assets by the
Consortium of International Banks
(Capital account; U.S. Capital outflow)
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Credit
$3 billion
Debit
$3 billion
6
Chapter 4: The Balance of Payments
b. Mitsubishi UFJ Financial Group purchases $70 million of 30-year U.S. Treasury
bonds for one of its Japanese clients. Mitsubishi draws down its dollar account with
Bank of America to pay for the bonds.
Answer: The purchase of Treasury bonds by a foreign company is a credit on the U.S.
balance of payments just like an export of goods is a credit. The reduction in Mitsubishi’s
bank account is a reduction in foreign ownership of U.S. assets and is a corresponding
debit.
U.S. BOP
Mitsubishi draws down its account with Bank of
America
(Capital account; U.S. Capital outflow)
Mitsubishi purchases U.S. Treasury bonds
(Capital account; U.S. Capital inflow)
Credit
Debit
$70 million
$70 million
c. Eli Lilly, a U.S. pharmaceutical company, sends a dividend check for $25,255 to a
Canadian investor in Toronto. The Canadian investor deposits the check in a U.S. dollardenominated bank account at the Bank of Montreal.
Answer: The dividend check is a debit on the U.S. balance of payments because it is a payment to
a foreigner. The corresponding credit is the increase in foreign ownership of U.S. assets that
occurs when the dollars are deposited in the bank and not spent on goods or services in the U.S.
U.S. BOP
Dividend check to a Canadian investor
(Current account; dividend payout in international
investment account)
Canadian investor deposits the check in a U.S. dollardenominated foreign bank account
(Capital account; U.S. Capital inflow)
Credit
Debit
$25,255
$25,255
d. The U.S. Treasury authorizes the New York Federal Reserve Bank to intervene in the
foreign exchange market. The New York Fed purchases $5 billion with Japanese yen and
euros that it holds as international reserves.
Answer: When the New York Fed purchases $5 billion in the foreign exchange market and thus
sells international reserves, this is a credit on the official settlements account of the U.S. balance
of payments just as if the private sector were selling goods or assets. The corresponding debit is a
decrease in the foreign ownership of U.S. assets because the New York Fed bought dollars.
U.S. BOP
$5 billion increase in foreign holdings of U.S. assets
(Capital account; U.S. Capital inflow)
The New York Fed sells $5 billion worth of international
reserves
(Official Settlements Account; decrease in international
reserves)
Credit
Debit
$5 billion
$5 billion
e. The president of the United States sends troops into a Latin American country to establish a
democratic government. The total operation costs U.S. taxpayers $8.5 billion. To show their
©2012 Pearson Education, Inc.
Chapter 4: The Balance of Payments 7
support for the operation, the governments of Mexico and Brazil each donate $1 billion to
the United States, which they raise by selling U.S. Treasury bonds that they were holding as
international reserves.
Answer: It is not entirely clear how much, if any, of the $8.5 billion of military expenditures
would be part of the balance of payments. Any expenditures on soldiers would not be, as the
soldiers are considered U.S. residents for balance of payments purposes. Any equipment that was
damaged or destroyed would also be U.S. equipment, and would not be part of the U.S. balance
of payments. Only purchases made in the Latin American country would be imports. We assume
these expenditures are zero, as we know how to deal with imports from previous questions.
The $2 billion donations by Mexico and Brazil are unilateral transfers from foreigners, which
corresponds to an export of goodwill. The transfers are thus credits on the U.S. balance of
payments. The reduction in the ownership of U.S. assets by Mexico and Brazil are the
corresponding debits.
U.S. BOP
The governments of Mexico and Brazil each donate $1
billion to the United States (U.S. export of goodwill)
(Current account; Brazilian & Mexican donations)
Mexico & Brazil Sale of U.S. Treasury bonds
(Capital account, U.S. Capital outflow)
f.
Credit
$2 billion
Debit
$2 billion
Honda of America, the U.S. subsidiary of the Japanese automobile manufacturer, obtains
$275 million from its parent company in Japan in the form of a loan to enable it to
construct a new state-of-art manufacturing facility in Ohio.
Answer: The loan is considered a credit on the U.S. balance of payments because foreigners are
increasing their ownership of U.S. assets. The reduction in the parent company’s ownership of
U.S. assets is a corresponding debit.
U.S. BOP
Honda’s American Subsidiary obtains a foreign loan
(Capital account; U.S. Capital inflow)
Reduction in Honda Japan’s ownership of U.S. assets
(Capital account; U.S. Capital outflow)
Credit
$275 million
Debit
$275 million
2. Consider the situation of La Nación, a hypothetical Latin American country. In 2010, La
Nación was a net debtor to the rest of the world. Assume that all of La Nación’s foreign debt
was dollar denominated, and at the end of 2010, its net private foreign debt was $75 billion and
the official foreign debt of La Nación’s treasury was $55 billion. Suppose that the interest rate
on these debts was 2.5% per annum (p.a.) over the London Interbank Offering Rate (LIBOR),
and no principal payments were due in 2011. International reserves of the Banco de Nación, La
Nación’s central bank, were equal to $18 billion at the end of 2010 and earn interest at LIBOR.
There were no other net foreign assets in the country. Because La Nación is growing very
rapidly, there is great demand for investment goods in La Nación. Suppose that residents of La
Nación would like to import $37 billion of goods during 2011. Economists indicate that the
value of La Nación’s exports is forecast to be $29 billion of goods during 2011. Suppose that the
Banco de Nación is prepared to see its international reserves fall to $5 billion during 2011. The
LIBOR rate for 2011 is 4% p.a.
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Chapter 4: The Balance of Payments
a. What is the minimum net capital inflow during 2011 that La Nación must have if it wants to
see the desired imports and exports occur and wants to avoid having its international
reserves fall below the desired level?
Answer: We know that the balance of payments always sums to zero:
Current account + Regular capital account + Official settlements account = 0
The current account records exports minus imports plus interest inflows minus interest outflows.
Interest outflows are required to service the $75 billion of private debt and $55 billion of public
debt. The interest payments will be at a rate of 6.5% (LIBOR of 4% plus a spread of 2.5%), or
total interest payments of 0.065  ($75 billion + $55 billion) = $8.45 billion. There will be
interest income on the $18 billion of interest reserves which earn interest at 4%. Thus, interest
income is 0.04  ($18 billion) = $0.72 billion. Hence, the deficit on the interest income account
will be $8.45 billion - $0.72 billion = $7.73 billion. Because La Nación wants to import more
than it exports, it will have a trade deficit of $37 billion - $29 billion = $8 billion. The current
account deficit will be the sum of the trade account deficit and the interest income deficit or $8
billion + $7.73 billion = $15.73 billion. This deficit must be balanced by a surplus on the official
settlements account and a private sector capital account surplus. If the central bank draws down
its international reserves from $18 billion to the minimum of $5 billion, they can provide $13
billion of the $15.73 billion that must be financed. Thus, the private sector would need to have a
capital inflow of $2.73 billion.
b.
If this capital inflow occurs, what will La Nación’s total net foreign debt be at the end of
2011?
Answer: The total net foreign debt is the sum of private and public foreign debts minus public
assets. At the end of 2010, net foreign debt was
$75 billion + $55 billion - $18 billion = $112 billion
At the end of 2011, the new net foreign debt is
$75 billion + $55 billion + $2.73 billion - $5 billion = $127.73
The increase in net foreign debt is the current account deficit of $15.73 billion.
3. True or false: If a country is a net debtor to the rest of the world, its international investment
service account is in deficit. Explain your answer.
Answer: The statement is false. The situation of the U.S. in the late 1990s is a good counter example.
As long as the income that a country receives on its foreign assets is providing a higher rate of return
than the payments that country is making to foreigners who own domestic assets, the country can be a
net debtor (that is, have a negative net international investment position) but still have a surplus on its
international investment service account.
4. Choose a country and analyze its balance of payments for the past 10 years. Good sources of
data include official bulletins of the statistical authority of a country or its central banks;
International Financial Statistics, which is a publication of the IMF (www.imf.org), and the
Main Economic Indicators, which is a publication of the Organization for Economic Cooperation and Development (www.oecd.org).
©2012 Pearson Education, Inc.
Chapter 4: The Balance of Payments 9
a. Examine how trade in goods and services has evolved over time. Is the country becoming
more or less competitive in world markets?
b. Consider the relationship between the country’s net foreign asset position and its
international investment income account.
c. If the country has run a current account deficit, what capital inflows have financed the
deficit? If the country has run a current account surplus, how have the capital outflows
been invested?
5. Pick a country and search the internet for newspaper or magazine articles that contain
information related to the balance of payments of the country and corresponding movements in
the foreign exchange value of the country’s currency. Does an unexpectedly large current
account deficit cause the country’s currency to strengthen or weaken on the foreign exchange
market?
6. What are the effects on the British balance of payments of the following set of transactions?
U.K. Videos imports £24 million of movies from the U.S. firm Twenty-First Century Wolf
(TFCW). The payment is denominated in pounds, is drawn on a British bank, and is deposited
in the London branch of a U.S. bank by TFCW because TFCW anticipates purchasing a film
studio in the United Kingdom in the near future.
Answer: The import of movies is a debit of £24 million on the British balance of payments. The
offsetting credit is the increase in foreign ownership of British assets – the increase in the TFCW
bank account in London of £24 million.
7. What are the effects on the French balance of payments of the following set of transactions? Les
Fleurs de France, the French subsidiary of a British company, The Flowers of Britain, has just
received €4.4 million of additional investment from its British parent. Part of the investment is
a €0.9 million computer system that was shipped from Britain directly. The €3.5 million
remainder was financed by the parent by issuing euro denominated Eurobonds to investors
outside of France. Les Fleurs de France is holding these euros in its Paris bank account.
Answer: The €4.4 million of additional investment from the British parent to the French subsidiary is
an increase in the foreign ownership of French assets, which is a credit on the French balance of
payments. There is an import of €0.9 million for the computer system that is a debit on the French
balance of payments. The remaining €3.5 million, corresponding to the funds that were borrowed
abroad by Flowers of Britain and are now being held by Fleur de France, represents a decrease in
foreign ownership of French assets.
French BOP
Increase in the direct foreign ownership of French assets
by Flowers of Britain
(Capital account; French Capital inflow)
Computer system that was shipped from Britain to France
(Current account; French import)
Decrease in Foreign ownership of French assets by
Flowers of Britain
(Capital account; French Capital outflow)
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Credit
€4.4 million
Debit
€0.9 million
€3.5 million
10 Chapter 4: The Balance of Payments
8. In December 1994, a major earthquake rocked Kobe, Japan, destroying the housing stock of
more than 300,000 people and ruining bridges, highways, and railroad tracks. What impact, if
any, do you think this event had on the Japanese current account deficit? Why?
Answer: This major disaster destroys capital and infrastructure and causes an increase in desired
investment spending relative to income. It is likely that the earthquake reduces the economy’s ability
to produce income and that wealth falls leading to a reduction in consumption spending. Private
savings will likely fall as people try to maintain their standard of living. It is also likely that the
government reacts by increases spending on infrastructure without increasing taxes. Thus, overall
investment should rise relative to savings, and there should be less of a current account surplus.
9.
After running high current account surpluses in the second half of the 1980s, Germany ran
sizable deficits in the early 1990s. The most important reason for the current account deficit
was the surge in demand from eastern Germany after reunification, causing imports to rise
sharply. At the same time, Germany went from being a net creditor country to being a net
debtor. Explain why this is a logical implication of the current account deficits. Interest rates in
Germany were historically high during this period. Why might that have been the case? Could
East Germany have been developed without running a current account deficit? How?
Answer: The reunification of Germany caused a surge in demand because the public and private
capital stock of East Germany was well below western standards. To equip the whole country with
better capital required massive investment spending. The country could have cut its consumption and
shifted its purchases to investment goods, but this would not have been logical. Instead, the country
maintained its consumption level and borrowed from abroad to finance the increased investment
spending. The high interest rates attract foreign capital and serve to ration the investment projects.
The current account deficits also implied that Germany increased its debts to the rest of the world,
eventually moving from a net creditor position to a net debtor position. (Recall that the change in net
foreign assets equals the current account balance.)
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Chapter
5
Exchange Rate Systems
QUESTIONS
1. How can you quantify currency risk in a floating exchange rate system?
Answer: To characterize the risk of a currency position, you must try to characterize the
conditional distribution of the future exchange rate changes. With floating exchange rates,
historical information provides useful information about this distribution. For example, you
can use data to measure the average historical dispersion (standard deviation or volatility) of
the distribution. The higher this volatility, the riskier are positions in this currency. It is also
possible to rely on more forward-looking information using the options markets (see Chapter
20). Finally, we should point out that volatility is an adequate indicator of risk when
exchange rate changes are approximately normally distributed. In reality, the distribution of
exchange rate changes displays fat tails, even in floating exchange rate systems, and this
increases the risk of currency positions.
2. Why might it be hard to quantify currency risk in a target zone system or a pegged
exchange rate system?
Answer: If the peg or target zone holds for a long time, historical volatility appears to be zero
or very limited, but this may not accurately reflect underlying tensions that may ultimately
result in a devaluation or revaluation of the currency. Hence, the true currency risk does not
show up in day-to-day fluctuations of the exchange rate. It is hard to quantify this “latent
volatility.”
3. What is likely to be the most credible exchange rate system?
Answer: Among fixed exchange rate systems, a monetary union with a common currency is
likely the most credible exchange rate system. But even here, we see tensions within the
Economic and Monetary Union in Europe that could lead to a breakup of the euro. The
inability of Greece and the other peripheral countries to devalue their currencies is leading to
a protracted period of high unemployment with associated fiscal deficits and an inability to
regenerate growth. Ultimately, one of the problem countries might withdraw from the EMU
or the strong countries, like Germany and Finland, might withdraw rather than subsidize their
inefficient neighbors.
4. How can a central bank create money?
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Chapter 5: Exchange Rate Systems
Answer: First, because the central bank operates the only authorized printing press in the
country, it can actually print money to pay its bills or to acquire assets, thereby increasing the
money supply. Second, the central bank can create money by increasing the reserve accounts
financial institutions hold with it. For example, if the central bank buys an asset (a
government bond say) from a financial institution, it credits the financial institution’s reserve
account at the central bank for the purchase price of the bond. Because this financial
institution can now use this credit to its account to lend money to individuals and businesses,
the central bank has, essentially, created money.
5. What are official international reserves of the central bank?
Answer: Official reserves consist of three major components: foreign exchange reserves, gold
reserves, and IMF-related reserve assets, with the first being by far the most important
component. Foreign exchange reserves are all the foreign currency denominated assets the
central bank holds, and mostly consist of foreign government bonds.
6. What is likely to happen if a central bank suddenly prints a large amount of new
money?
Answer: Whereas there are theories that predict that changes in the supply of money have
real effects on the economy in the short run, it is likely that if the central bank showers the
economy suddenly with money, the only result will be higher inflation. This is because the
demand for money ultimately depends on the amount of real transactions in the economy and
how much money is needed to facilitate these transactions. Additional supply of money is
unlikely to make people consume more or work harder.
7. What is the effect of a foreign exchange intervention on the money supply? How can a
central bank offset this effect and still hope to influence the exchange rate?
Answer: When a central bank buys (sells) foreign currency, its international reserves increase
(decrease), and the money supply increases (decreases) simultaneously. To offset the effect
on the money supply, the foreign exchange intervention can be sterilized; that is, the central
bank can perform an open market operation that counteracts the effect on the money supply
of the original foreign exchange intervention. The direct effects of a sterilized intervention
are two-fold. First, it forces a portfolio shift on private investors, by replacing foreign bonds
with domestic bonds (or vice versa). This may affect expectations and prices. Second, the
actions of the central bank in the foreign exchange markets, while very small relative to the
nominal trading volumes, may still manage to squeeze foreign exchange inventories at dealer
banks and generate pricing effects. Indirectly, the central bank can signal its opinion on the
fundamental value of the exchange rate through an intervention that consequently affects
market expectations. There is no consensus on how effective sterilized interventions are in
affecting the level and volatility of exchange rates.
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Chapter 5: Exchange Rate Systems
3
8. How can a central bank peg the value of its currency relative to another currency?
Answer: To peg the value of its currency to another currency, the government must make a
market in the two currencies. If there is excess supply of the foreign currency (which is
equivalent to excess demand for the domestic currency) that would drive down the domestic
currency price of the foreign currency, the government must buy the private excess supply of
foreign currency and deliver domestic currency to those demanding it. On the contrary, if
there is excess demand for foreign currency (which is equivalent to excess supply of
domestic currency) that would drive up the domestic currency price of the foreign currency,
the government must supply the foreign currency and demand the domestic currency to
prevent the foreign currency from appreciating in value.
9. Describe two channels through which foreign exchange interventions may affect the
value of the exchange rate.
Answer: There is a direct and an indirect channel. As indicated in question 7, the direct effect
of forex purchases or sales is likely small, because trading volumes are so large in the forex
market, but there may be some short-term effects if the inventories of dealer banks are
adversely affected by the intervention. If not sterilized, interventions affect the money
supply, but that effect too, is likely to be small relative to the size of the money supply. The
indirect channel refers to the fact that an intervention can alter peoples’ expectations and
affect their investments, thus helping to push the exchange rate in the direction the central
bank desires. For example, the intervention may be a signal to the public of the central bank’s
monetary policy intentions, or it may signal the central banks inside information about future
market fundamentals, or it may signal to investors that a currency’s exchange rate is
deviating too far from its long-run equilibrium value. The signal is costly and therefore
potentially more credible, because if the central bank is wrong and, for example, buys an
“undervalued” currency, which keeps depreciating, the intervention will lose money.
10. What was the Bretton Woods currency system?
Answer: In the Bretton Woods System, in place between 1944 and 1971, the participating
countries agreed to an exchange rate regime that linked their exchange rates to the dollar.
They could fluctuate in a 1% band around a fixed parity. The dollar itself had a fixed gold
parity ($35 per ounce). When a country ran into a temporary balance of payments problem (a
current account deficit) that threatened the currency peg, it could draw on the lending
facilities of the IMF, also established at Bretton Woods in 1944, to help it defend the
currency. Countries were also allowed to change their parities when their balances of
payments were considered to be in “fundamental disequilibrium.” The system broke down
when President Nixon abandoned the U.S. commitment to exchange dollars for gold in
August 1971.
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Chapter 5: Exchange Rate Systems
11. How do developing countries typically manage to keep currencies pegged at values that
are too high? Who benefits from such an overvalued currency? Who is hurt by an
overvalued currency?
Answer: Such a situation is difficult to maintain, because if the exchange rate overvalues the
local currency on the foreign exchange markets, there will be an excess supply of the local
currency—everybody will want to turn in local currency to the central bank, receive foreign
currencies, and invest them abroad. If this situation persists, the central bank’s foreign
reserves will dwindle quite fast. The only way to sustain such a system is to impose exchange
controls. The central bank of the developing country must ration the use of foreign exchange,
manage who gets access to it, and restrict capital flows; in short, it must strictly control
financial transactions involving foreign currencies. That currencies of developing countries
are primarily traded by the central bank of the country or by a number of financial
institutions with strict controls on their use of foreign currency (i.e. the currencies are
inconvertible), is helpful to maintain such a system.
It is clear who benefits and who loses from this situation. The fixed exchange rate
undervalues the foreign currency and overvalues the domestic currency, thereby subsidizing
buyers of foreign currency (such as importers and those investing abroad) and taxing sellers
of foreign exchange (such as exporters and foreign buyers of domestic assets). Not
surprisingly, one main reason for the popularity of over-valued exchange rates is that such
situations increase the external purchasing power of the political elite.
12. What are the potential benefits of a pegged currency system?
Answer: Some believe that fixed exchange rate systems bring with it policy discipline and
stability. A fixed exchange rate should discourage over-expansionary fiscal or monetary
policies, which would cause inflation and a loss of competitiveness under a fixed exchange
rate system. Hence, fixed exchange rates should induce the kind of policies that help control
inflation. The absence of day-to-day exchange rate volatility in such a system should
eliminate the uncertainty that comes with floating exchange rates and which might hamper
international trade. Note that the argument that exchange rate volatility hampers international
trade is far from generally accepted. For example, it ignores the possibility to hedge currency
fluctuations. Moreover, pegged exchange rate systems are not without risks, and may show
considerable “latent variability,” see Question 2. Such devaluation risk also complicates
international trade.
13. Describe two different currency systems that have been introduced in countries such as
Hong Kong and Ecuador to improve the credibility of pegged exchange rate systems.
Answer: Hong Kong has a currency board system. A currency board is a monetary institution
that issues base money (notes and coins, and required reserves of financial institutions) that is
fully backed by a foreign reserve currency and fully convertible into the reserve currency at a
fixed rate and on demand. Hence, the domestic currency monetary base is 100% backed by
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Chapter 5: Exchange Rate Systems
5
assets payable in the reserve currency. In practical terms, this requirement bars the currency
board from extending credit to either the government or the banking sector. Ecuador instead
has officially adopted the U.S. dollar as its currency. This is an example of (“Official”)
dollarization, which occurs when a foreign currency has exclusive or predominant status as
full legal tender in a particular country.
14. What is the difference between a target zone and a crawling peg?
Answer: In a target zone, the currency is allowed to fluctuate in a percentage band around a
“central value.” One can view a pegged system as a target zone system with a very narrow
band. In a crawling peg system, the fixed rate or band is adjusted over time, typically in a
pre-determined way as a function of the inflation differential between the crawling peg
country and the country to whose currency the peg is set. Such a system is often used in
developing countries, where the “crawl” of the band prevents the country from losing too
much competitiveness when its inflation rate is higher than that of the benchmark country.
15. How can central banks defend their currency—for example, if the currency is within a
target zone or pegged at a particular value?
Answer: The monetary authorities in the countries with weaker currencies have three basic
defense mechanisms available: interventions, interest rate increases, and capital controls.
Interventions (see Questions 7 and 9) to support the local currency may result (when not
sterilized) in a lower money supply, reduced liquidity in the money market, and therefore
higher interest rates. Central banks can also directly raise the interest rates they control
(typically, the rate at which banks can borrow from the central bank), both to make currency
speculation more costly and to signal commitment to the central rate. Finally, the authorities
can limit foreign exchange transactions through capital controls, which may include taxes on
(or outright prohibition of) the purchases of most foreign securities by the country’s
residents.
16. What was the EMS?
Answer: EMS stands for European Monetary System, a target zone system that operated in
Europe between 1979 and 1999. Exchange rates were, for most of the time, maintained
between bands of 2.25% around central rates. The countries participating in the EMS were a
gradually increasing number of European Union countries.
17. What is a basket currency?
Answer: A basket of currencies is a composite currency consisting of various units of other
currencies. Examples include the ECU (European Currency Unit) in the EMS and the SDR
(Special Drawing Right) of the IMF.
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Chapter 5: Exchange Rate Systems
18. What did the Maastricht Treaty try to accomplish?
Answer: The 1991 Maastricht Treaty mapped out the road to economic and monetary union
within the European Union to be finalized by 1999. The Treaty called for eliminating all
remaining restrictions on the movement of capital and payments between member states and
between member states and third countries; the creation of a European central bank, and the
introduction of a new currency, the euro, in 1999. The monetary union was indeed
established (but not all EU countries participate).
19. What is an optimum currency area?
Answer: An optimum currency area is an area that balances the microeconomic benefits of
perfect exchange rate certainty against the costs of macroeconomic adjustment problems. The
area is therefore suitable for the introduction of a single currency and monetary union.
Sharing a currency across a border enhances price transparency (that is, makes prices easier
to understand and compare across countries), lowers transactions costs, removes exchange
rate uncertainty for investors and firms, and enhances competition. The potential cost of a
single currency is the loss of independent monetary policies for the participating countries. If
countries experience adverse shocks, such as a sudden fall in demand for a country’s main
export product or a sudden increase in the price of one of the main inputs for a country’s
manufacturing sector, it can no longer stave off a recession or unemployment through
monetary policy actions when it has a common currency. It also cannot devalue its currency
to try to regain competitiveness.
20. Do you believe its monetary union will be beneficial for Europe?
Answer: The gains are already being realized throughout Europe—for example, car prices
have decreased and converged across Europe. Academic research documents sizable
economic benefits following the introduction of the euro in terms of price convergence,
lower costs of capital, and increased trade. For example, the European Commission has
estimated the microeconomic gains of monetary union to amount to 0.5% of GDP of the
entire EU—a substantial sum. On the other hand, the sovereign debt crises in Greece, Ireland,
and Portugal, and potentially in Spain, and the persistent high unemployment rates in these
countries while Germany thrives suggest that asymmetric macroeconomic adjustment costs
are present and are causing strain within Europe.
21. Do you think the euro will survive?
The survival of the euro will depend on the political will of the strong countries to bail out
the weaker countries. It is difficult to image that a weak country will abandon the euro and
reissue its own money. This would surely be quite inflationary and could not be done without
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Chapter 5: Exchange Rate Systems
7
also adopting severe capital controls. A more likely scenario is that strong countries decide
that they can no longer afford to bailout the weaker countries, which causes a crisis of
confidence in the European banking system and a call for the reissuance of the Deutsche
mark. Things would have to get very bad before the political process would lead to the
breakdown of the euro.
PROBLEMS
1. Toward the end of 1999, the central bank (Reserve Bank) in Zimbabwe stabilized the
Zimbabwe dollar, the Zim for short, at Z$38/USD and privately instructed the banks to
maintain that rate. In response, at the end of 1999, an illegal market developed wherein
the Zim traded at Z$44/USD. Are you surprised at rumors that claim corporations in
Zimbabwe were “hoarding” USD200 million? Explain.
Answer: The existence of an illegal exchange market indicates that the Zim is incorrectly
valued at Z$38/USD. Clearly, the Zim is over-valued at the official rate (See Exhibit 5.10 for
an example of such a situation). At this “artificial” exchange rate everybody wants to turn in
Zim to the central bank, receive foreign currency and invest them abroad. To maintain the
overvalued rate without losing all its international reserves, the government must control the
use of foreign exchange (impose exchange controls). It likely forces exporters to convert
their foreign exchange at the official rate, which is too low. Given this situation, hoarding
foreign exchange is a rational response. Anyone who earns foreign exchange has an incentive
to hold on to the foreign exchange until the Zim is valued correctly, i.e. after it is devalued.
Moreover, given high inflation in Zimbabwe and a highly unstable political regime, U.S.
dollars are a better store of value than Zimbabwe dollars. The situation in Zimbabwe
subsequently deteriorated into hyperinflation, and the abandonment of the Zim.
2. In Chapter 3, we described how exchange rate risk could be hedged using forward
contracts. In pegged or limited-flexibility exchange rate systems, countries imposing
capital controls sometimes force their importers and exporters to hedge. First,
assuming that forward contracts are to be used, and an exporter has future foreign
currency receivables, what will the government force him to do? Second, how does this
help the government in defending their exchange rate peg?
Answer: Exporters, who have foreign currency receivables, have an incentive to lag the
foreign currency payments (e.g. by giving generous trade credit), if they think their domestic
currency is under pressure and may be devalued. Doing so allows them to potentially profit
from an impending devaluation of the local currency. Of course, extending trade credit
involves an opportunity cost, but the interest rates reflect some probability that the peg will
hold. Hence, if the currency is actually devalued, lagging the payment is beneficial ex-post.
Lagging foreign currency payments causes further pressure on the local currency as
the exporter’s demand for local currency is postponed. A forced hedge would require the
exporter to sell the foreign currency forward for the local currency. Hence, there is
immediate positive demand for the local currency. That the demand is in the forward market
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Chapter 5: Exchange Rate Systems
is inconsequential. Because of covered interest rate parity, if the forward rate decreases (in
local currency per foreign currency) it would result in lower local interest rates. This is
because the spot rate is fixed and the foreign interest rate is not likely affected. Hence, this
relieves the speculative pressure.
3. In years past, Belgium, a participant of the former EMS, and South Africa operated a
two-tier, or dual, exchange rate market. The two-tier market was abolished in March
1990 in Belgium and in March 1995 in South Africa. Import and export transactions
were handled on the official market, and capital transactions were handled on the
financial market, where the “financial” exchange rate was freely floating. Discuss why
such a system may prevent speculators from profiting when betting on devaluation.
Answer: Speculators will try to profit by buying foreign exchange forward, deposit money in
foreign accounts or buy foreign securities, hoping to repatriate capital after the devaluation
happens. All these transactions imply selling local currencies in the foreign exchange market.
With the double tier market, the “financial” exchange rate immediately reacts to the selling
pressure and the local currency instantly depreciates so that the speculators cannot profit
from their actions. Of course, exporters and importers can still engage in leading and lagging
operations, and they massively did so.
4. The Kuna is the currency of Croatia. Find the web site of Croatia’s central bank, and
determine the exchange rate system Croatia runs? Suppose the Kuna weakens
substantially relative to the euro. Which action can the central bank take to keep its
currency system functioning properly?
Answer: The web site of Croatia’s central bank, called the Croatian National Bank, is at
http://www.hnb.hr/eindex.htm. Under the Tab entitled Exchange Rate List, there is another
Tab entitled About the Exchange Rate. Here is what was written on June 2, 2011:
HOW IS THE KUNA EXCHANGE RATE SET?
Croatia implements the exchange rate regime of managed floating, where the
exchange rate of the domestic currency is not fixed against another foreign
currency or basket of currencies, but is rather freely determined by the foreign
exchange market. The exchange rate thus floats depending on the foreign
exchange supply and demand on the foreign exchange market. However, the
Croatian National Bank prevents too excessive exchange rate fluctuations by
occasional market interventions in an attempt to maintain relative stability of the
exchange rate.
Hence, if the currency weakens substantially, the central bank can intervene directly on the
foreign exchange market. It may also increase the domestic interest rate.
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Chapter 5: Exchange Rate Systems
9
5. Type “People’s Bank of China” into your favorite search engine and go to the English
versions of the web site. Under “Statistics” find the Balance Sheet of the Monetary
Authority. Calculate the growth rate of base money and the growth rate of
international assets for the last few years. How much foreign exchange intervention is
China doing? Are they sterilizing it?
Answer: The URL for the English version of the People’s Bank of China is
http://www.pbc.gov.cn/publish/english/963/index.html where you will find a Tab entitled
“The Balance Sheet of the Monetary Authority.” The base money supply corresponds to the
row entitled Reserve Money, which is the sum of Currency and Deposits of Financial
Corporations. During 2010, Reserve Money grew by 29.75% from 142,815.58 to 185,311.08
or by 42,491.50, where the units are 100 million yuan. The line labeled Foreign Assets grew
by 14.59% from 188,021.75 to 215,419.60 or by 27,397.85, also in units of 100 million yuan.
The fact that Reserve Money grew by more than Foreign Assets indicates that the foreign
exchange intervention is likely not sterilized.
©2012 Pearson Education, Inc
Chapter
6
Interest Rate Parity
QUESTIONS
1. Explain the concepts of present value and future value.
Answer: These concepts relate to the time value of money. Because interest rates are positive,
a given amount of money in the future is not worth as much today. If you want to know how
much a future amount of money is worth, you take the present value. This is the amount that
you could borrow against the future amount while using the future amount to pay the interest
plus principal on the loan. Analogously, the future value of an amount of money available
today is the value that would be available in the future if you invested today and received the
principal plus interest on the investment in the future.
2. If the dollar interest rate is positive, explain why the value of $1,000,000 received every
year for 10 years is not $10,000,000 today.
Answer: If you were to borrow against each of the annual $1,000,000 payments, the bank
would lend you progressively smaller amounts. The present value of the 10 payments could
be found by using the spot interest rates, i(t,k), at time t for year t+k in the future. The present
value would be
10
$1,000,000
PV = 
k
k=1 1 + i(t,k) 
3. Describe how you would calculate a 5-year forward exchange rate of yen per dollar if
you knew the current spot exchange rate and the prices of 5-year pure discount bonds
denominated in yen and dollars. Explain why this has to be the market price.
Answer: The 5-year forward rate would be equal to the spot rate of yen per dollar times the
ratio of the future value in 5 years of one yen to the future value in 5 years of one dollar. The
logic is the following. If you can invest directly in yen for 5 years, you can convert one yen
into the future value of one yen in 5 years. Alternatively, you can convert the one yen into
dollars in the spot foreign exchange market, invest that dollar principal for 5 years to get the
future value of dollars, and contract today to sell those dollars in the forward market to get
back to future yen in 5 years. If the two amounts of future yen differ, there would be an
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Chapter 6: Interest Rate Parity
arbitrage available in which you would borrow future yen where they are cheap and invest in
future yen where they are expensive. Hence, the 5 year forward rate should satisfy
1 + i(t,5,¥) 
5
1 + i(t,5,$) 
5
F(t,5,¥/$) = S(t,¥/$) ×
4. If interest rate parity is satisfied, there are no opportunities for covered interest
arbitrage. What does this imply about the relationship between spot and forward
exchange rates when the foreign currency money market investment offers a higher
return than the domestic money market investment?
Answer: If the foreign currency money market investment offers a higher return (in the
foreign currency) than the domestic money market investment, the foreign currency must be
at a discount in terms of the domestic currency in the forward market. The forward discount
locks in a capital loss when the transaction exchange risk is offset, which reduces the higher
return of the foreign currency back to the lower return offered in the domestic money market.
5. It is often said that interest rate parity is satisfied when the differential between the
interest rates denominated in two currencies equals the forward premium or discount
between the two currencies. Explain why this is an imprecise statement when the
interest rates are not continuously compounded.
Answer: Interest rate parity requires the equality of returns from investing directly in the
domestic money market versus converting domestic currency into foreign currency, investing
the foreign currency, and selling the foreign currency forward. Symbolically, we have
1
× 1 + i(t,FC)  × F(t,DC/FC)
1 + i(t,DC)  =
S(t,DC/FC)
If we divide by 1 + i(t,FC)  on both sides and subtract one from both sides, we get
i(t,DC) - i(t,FC)
F(t,DC/FC) - S(t,DC/FC)
=
S(t,DC/FC)
1 + i(t,FC) 
The left-hand side is the interest differential between the domestic and foreign rates adjusted
for the denominator term and the right-hand side is the forward premium or discount on the
foreign currency in terms of the domestic currency.
6. What do economists mean by the external currency market?
Answer: The external currency market is an interbank market for deposits and loans that are
denominated in currencies that are not the currency of the country in which the bank is
operating. Its settlement procedures are identical to those of the foreign exchange market.
The first currency for which these deposits and loans began to trade was the dollar, and the
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Chapter 6: Interest Rate Parity
3
deposits were called Eurodollars because they were dollar-denominated deposits at European
banks. The market for other currencies came to be called the Eurocurrency market, even
though the trading might be done in Asia or the Americas. With the advent of the euro as a
currency, the term external currency market seems less confusing.
7. What determines the bid–ask spread in the external currency market? Why is it usually
so small?
Answer: The bid-ask spread in the external currency market is the difference between the bid
rate, which is the interest rate that the bank pays on its deposits and the ask rate, which is the
interest rate that the bank charges on its loans. The market is very competitive, and the bidask spreads are small. The reason is because the banks accepting the deposits and making the
loans are subject only to the regulations of the government of the country in which the bank
is operating, not the government of the country that issues the money in which the deposits
and loans are denominated. These regulations include how much banks must keep on reserve
with their nation’s central bank. Because reserve requirements are often lower for foreign
currency deposits than for domestic currency deposits, banks can lend out a larger part of
these deposits. Thus, the foreign currency deposits are potentially more profitable.
8. Explain why the absence of covered interest arbitrage possibilities can be characterized
by two inequalities in the presence of bid–ask spreads in the foreign exchange and
external currency markets.
Answer: Because there are bid-ask spreads in the foreign exchange market and in the external
currency market, we do not convert from one currency to another at the same spot or forward
exchange rates, and we do not borrow at the same rate at which we lend. The absence of
covered interest arbitrage therefore is characterized by two inequalities. We cannot profit by
borrowing the domestic currency (at the ask domestic interest rate), converting to the foreign
currency (at the ask spot rate of domestic currency per unit of foreign currency), lending the
foreign currency (at the foreign bid interest rate), and converting to the domestic currency in
the forward market (at the bid forward rate of domestic currency per unit of foreign
currency). Similarly, we cannot profit by borrowing the foreign currency (at the ask foreign
interest rate), converting to domestic currency (at the bid spot rate of domestic currency per
unit of foreign currency), lending the domestic currency (at the domestic bid interest rate),
and converting to the foreign currency forward (at the ask forward rate of domestic currency
per unit of foreign currency).
9. Describe the sequence of transactions required to do a covered interest arbitrage out of
Japanese yen and into U.S. dollars.
Answer: To do a covered interest arbitrage out of Japanese yen and into U.S. dollars, one
would borrow yen from the bank at the bank’s ask interest rate. You would owe interest on
the yen and would have to return the yen principal at the end of the investment horizon. You
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Chapter 6: Interest Rate Parity
would then convert the yen principal into dollars at the ask spot exchange rate of yen per
dollar. You would pay the ask rate because you are buying dollars from the bank with yen.
You would then invest the dollar principal at the bank’s bid dollar interest rate. Because you
would know how much the dollar interest plus principal would be at the end of the
investment horizon, you would contract to sell that amount of dollars forward for yen. This
forward contract would be made at the bank’s forward bid rate of yen per dollar. If the
amount of yen that you get from the forward contract exceeds the amount of yen that you
owe the bank from the initial borrowing, you have successfully done a covered interest
arbitrage.
10. Suppose you saw a set of quoted prices from a U.S. bank and a French bank such that
you could borrow dollars, sell the dollars in the spot foreign exchange market for euros,
deposit the euros for 90 days, and make a forward contract to sell euros for dollars and
make a guaranteed profit. Would this be an arbitrage opportunity? Why or why not?
Answer: It could be an arbitrage opportunity, but it could also reflect the fact that
counterparty risk differs across banks. It may be that the market knows that the default risk of
the French bank is higher than other banks, which has induced the French bank to increase its
promised deposit rates above rates charged by other banks with lower default risk. The
perceived arbitrage opportunity would be illusory in this case.
11. The interest rates on U.S. dollar–denominated bank accounts in Mexican banks are
often higher than the interest rates on bank accounts in the United States. Can you
explain this phenomenon?
Answer: Mexico has periodically gotten into balance of payments difficulties and suffered
severe depreciations of the peso. During these periods of crisis, the Mexican government
converted dollar-denominated bank deposits into peso-denominated accounts at exchange
rates that were unfavorable to the depositor, effectively expropriating some of an investor’s
principal. If there is a possibility of this type of risk or just higher default risk by the Mexican
banks than at U.S. banks, the higher dollar-denominated Mexican deposit rates would be
required to induce depositors to invest in Mexican banks.
12. What is a money market hedge? How is it constructed?
Answer: In a money market hedge you offset the underlying transaction exchange risk with
borrowing or lending in the foreign money market rather than with a forward market
transaction. For example, if the underlying business transaction gives you a liability in
foreign currency, you can borrow domestic currency, convert the principal from the
borrowing into foreign currency, and invest the foreign currency thereby acquiring a foreign
currency asset that is equivalent in value to the underlying foreign currency liability. You
would want to borrow an amount of domestic currency equal to the present value of the
foreign currency liability when converted at the spot exchange rate.
©2012 Pearson Education, Inc.
Chapter 6: Interest Rate Parity
5
13. Suppose you are the French representative of a company selling soap in Canada.
Describe your foreign exchange risk and how you might hedge it with a money market
hedge.
Answer: As a French company, you are interested in euro profits. Selling soap in Canada will
give you Canadian dollar revenues. The euro value of these Canadian dollar revenues will
fall in value if the Canadian dollar weakens relative to the euro. To offset this loss in value,
your company should borrow in Canadian dollars.
14. What is a pure discount bond?
Answer: A pure discount bond only has one cash flow at the maturity of the bond. Hence, the
bond’s price is less than its face value, and this discount of the price from the face value
provides the return to holding the bond.
15. What is the term structure of interest rates? How are spot interest rates determined
from coupon bond prices?
Answer: The term structure of interest rates is the relation between the maturities of bonds
and the pure discount bond yields, which are the spot interest rates for the various maturities.
At the shortest maturities, one typically has spot interest rates from pure discount bond
prices. One can then begin to use coupon bonds at longer maturities, discounting the early
coupons at the known spot interest rates for those maturities and determining the final spot
interest rate by finding the discount rate such that discounting the final coupon and principal
payment provides a present value equal to the bond price minus the present value of the
intervening coupon payments.
16. How does a coupon bond’s yield to maturity differ from the spot interest rate that
applies to cash flows occurring at the maturity of the bond? When are the two the
same?
Answer: A coupon bond’s yield to maturity is the internal rate of return that sets the present
value of the promised coupon payments and principal payment equal to the bond price. The
yield to maturity is therefore a kind of average of the spot interest rates at various maturities.
The yield to maturity equals the spot interest rates at various maturities only when the term
structure of interest rates is flat, that is, when the spot interest rates at various maturities are
all identical.
©2012 Pearson Education, Inc.
6
Chapter 6: Interest Rate Parity
PROBLEMS
1. In the entry forms for its contests, Publisher’s Clearing House states, “You may have
already won $10,000,000.” If the Prize Patrol visits your house to inform you that you
have won, it offers you $333,333.33 each and every year for 30 years. If the interest rate
is 8% p.a., what is the actual present value of the $10,000,000 prize?
Answer: The present value of 30 annual payments of $333,333.33 when discounted at 8% is
30
$333,333.33
 $3, 752,594.41

1.08k
k 1
This value can be found in Excel by using the function NPV(rate, cashflows), where rate =
8% and cashflows refers to a sequence of 30 cells that all have the value $333,333.33.
2. Suppose the 5-year interest rate on a dollar-denominated pure discount bond is 4.5%
p.a., whereas in France, the euro interest rate is 7.5% p.a. on a similar pure discount
bond denominated in euros. If the current spot rate is $1.08/€, what is the value of the
forward exchange rate that prevents covered interest arbitrage?
Answer: We know that the 5-year forward rate must satisfy
1+i(t,5,$) 
F(t,5,$/€) = S(t,$/€)×
5
1+i(t,5,€) 
5
= $1.08/€ ×
1.0455
= $0.9375/€
1.0755
3. Carla Heinz is a portfolio manager for Deutsche Bank. She is considering two
alternative investments of EUR10,000,000: 180-day euro deposits or 180-day Swiss
francs (CHF) deposits. She has decided not to bear transaction foreign exchange risk.
Suppose she has the following data: 180-day CHF interest rate, 8% p.a., 180-day EUR
interest rate, 10% p.a., spot rate EUR1.1960/CHF, 180-day forward rate,
EUR1.2024/CHF. Which of these deposits provides the higher euro return in 180 days?
If these were actually market prices, what would you expect to happen?


180 
Answer: The euro return to investing directly in euros is 5%  10% 
 , so the euros
360

available in 180 days is EUR10,000,000  1.05 = EUR10,500,000. Alternatively, the
EUR10,000,000 can be converted into Swiss francs at the spot rate of EUR1.1960/CHF. The
Swiss francs purchased would equal EUR10,000,000 / EUR1.1960/CHF = CHF8,361,204.


This amount of Swiss francs can be invested to provide a 4%   8% 
180 
 return over the
360 
next 180 days. Hence, interest plus principal on the Swiss francs is CHF8,361,204  1.04 =
CHF8,695,652. If we sell this amount of Swiss francs forward for euros at the 180-day
forward rate of EUR1.2024/CHF, we get a euro return of CHF8,695,652  EUR1.2024/CHF
= EUR10,455,652. This is less than the return from investing directly in euros.
©2012 Pearson Education, Inc.
Chapter 6: Interest Rate Parity
7
If these were the actual market prices, you should expect investors to do covered interest
arbitrages. Investors would borrow Swiss francs, which would tend to drive the CHF interest
rate up; they would sell the Swiss francs for euros in the spot foreign exchange market,
which would tend to lower the spot rate of EUR/CHF; they would deposit euros, which
would tend to drive the EUR interest rate down; and they would contract to buy CHF with
EUR in the 180-day forward market, which would put upward pressure on the forward rate of
EUR/CHF. Each of these actions would help bring the market back to equilibrium.
4. If the 30-day yen interest rate is 3% p.a., and the 30-day euro interest rate is 5% p.a., is
there a forward premium or discount on the euro in terms of the yen? What is the
magnitude of the forward premium or discount?
Answer: We know that the high interest rate currency must sell at a forward discount when
priced in the low interest rate currency to prevent a covered interest arbitrage. Therefore the
euro is at a discount in the forward market. To determine the magnitude of the discount,
recognize that interest rate parity requires equality of the return to investing in yen versus
converting the yen principal into euros, investing the euros, and selling the euro principal
plus interest in the forward market for yen:
1
× 1 + i(€)  × F(¥/€)
1 + i(¥)  =
S(¥/€)
Solving this expression for the forward premium, we find
F(¥/€) - S(¥/€)
i(¥) - i(€)
=
S(¥/€)
1 + i(€) 
The de-annualized interest rates are 0.0025 = (3/100)  (30/360) for the yen and
0.004167 = (5/100)  (30/360) for the euro. The right-hand side of the above expression is
therefore -0.00166. The annualized value is -0.00166  (100)  (360/30) = -1.99%. We
therefore say that the euro sells at an annualized discount of 1.99%.
5. Suppose the spot rate is CHF1.4706/$ in the spot market, and the 180-day forward rate
is CHF1.4295/$. If the 180-day dollar interest rate is 7% p.a., what is the annualized
180-day interest rate on Swiss francs that would prevent arbitrage?
Answer: Interest rate parity requires equality of the return to investing in CHF versus
converting the CHF principal into dollars, investing the dollars, and selling the dollar
principal plus interest in the forward market for CHF:
1
× 1 + i($)  × F(CHF/$)
1 + i(CHF)  =
S(CHF/$)
If we de-annualize the dollar interest rate, we find that the 180 day interest rate is 0.035.
Hence, the Swiss franc interest rate that prevents arbitrage is
1
i(CHF) =
× 1.035 × CHF1.4295/$ - 1 = 0.0061
CHF1.4706/$
©2012 Pearson Education, Inc.
8
Chapter 6: Interest Rate Parity
If we annualize this value, we find 0.0061  (100)  (360/180) = 1.21%.
6. As a trader for Goldman Sachs you see the following prices from two different banks:
1-year euro deposits/loans:
6.0% – 6.125% p.a.
1-year Malaysian ringgit deposits/loans: 10.5% – 10.625% p.a.
Spot exchange rates:
MYR 4.6602 / EUR – MYR 4.6622 / EUR
1-year forward exchange rates:
MYR 4.9500 / EUR – MYR 4.9650 / EUR
The interest rates are quoted on a 360-day year. Can you do a covered interest
arbitrage?
Answer: We need to check the two inequalities that characterize the absence of covered
interest arbitrage. In the first, we will borrow euros at 6.125%, convert to ringgits in the spot
market at MYR4.6602 / EUR, invest the ringgits at 10.5%, and sell the ringgit principal plus
interest forward for euros at MYR4.9650 / EUR. We find that
MYR4.6602
1
1.06125 >
× 1.105 ×
= 1.0372
EUR
MYR4.9650/EUR
Thus, it is not profitable to try to arbitrage in this direction as the amount that we would
owe is greater than the amount that we would gain.
Let’s try the other direction, arbitraging out of ringgits into euros and covering the
foreign exchange risk. We will borrow ringgits at 10.625%, convert to euros in the spot
market at MYR4.6622 / EUR, invest the euros at 6.0%, and sell the euro principal plus
interest forward for ringgits at MYR4.9500 / EUR. We find that
1
MYR4.9500
1.10625 <
× 1.06 ×
= 1.1254
MYR4.6622/EUR
EUR
Thus, there is a possible arbitrage opportunity because the amount that we owe from
borrowing ringgits is less than the amount that we gain by converting from ringgits to euros,
investing the euros, and covering the transaction exchange risk with a forward sale of euros
for ringgits.
7. As an importer of grain into Japan from the United States, you have agreed to pay
$377,287 in 90 days after you receive your grain. You face the following exchange rates
and interest rates: spot rate, ¥106.35/$, 90-day forward rate ¥106.02/$, 90-day USD
interest rate, 3.25% p.a., 90-day JPY interest rate, 1.9375% p.a.
a. Describe the nature and extent of your transaction foreign exchange risk.
Answer: As a Japanese grain importer, you are contractually obligated to pay $377,287 in
90 days. Any weakening of the yen versus the dollar will increase the yen cost of your
grain. The possible loss is unbounded.
©2012 Pearson Education, Inc.
Chapter 6: Interest Rate Parity
9
b. Explain two ways to hedge the risk.
Answer: You could hedge your risk by buying dollars forward at ¥106.02/$.
Alternatively, you could determine the present value of the dollars that you owe and buy
that amount of dollars today in the spot market. You could borrow that amount of yen to
avoid having to pay today.
c. Which of the alternatives in part b is superior?
Answer: If you do the forward hedge, you will have to pay
¥106.02/$  $377,287 = ¥39,999,967.74
in 90 days. If you do the money market hedge, you first need to find the present value of
$377,287 at 3.25%. The de-annualized interest rate is (3.25/100)  (90/360) = 0.008125.
Thus, the present value is
$377,287 / 1.008125 = $374,246.25
Purchasing this amount of dollars in the spot market costs
¥106.35/$  $374,246.25 = ¥39,801,088.69
To compare this value to the forward hedge, we must take its future value at 1.9375% p.a.
The de-annualized interest rate is (1.9375/100)  (90/360) = 0.00484375, and the future
value is
¥39,801,088.69  (1.00484375) = ¥39,993,875.21
The cost of the money market hedge is essentially the same as the cost of the forward
hedge because interest rate parity is satisfied.
8. You are a sales manager for Motorola and export cellular phones from the United
States to other countries. You have just signed a deal to ship phones to a British
distributor. The deal is denominated in pounds, and you will receive £700,000 when the
phones arrive in London in 180 days. Assume that you can borrow and lend at 7% p.a.
in U.S. dollars and at 10% p.a. in British pounds. Both interest rate quotes are for a
360-day year. The spot exchange rate is $1.4945/£, and the 180-day forward exchange
rate is $1.4802/£.
a. Describe the nature and extent of your transaction foreign exchange risk.
Answer: As a U.S. exporter, you have a contract to receive £700,000 in 180 days. Any
weakening of the pound versus the dollar will decrease the dollar value of your pounddenominated receivable. Large losses are possible as the dollar value could go to zero,
although that is highly unlikely.
©2012 Pearson Education, Inc.
10 Chapter 6: Interest Rate Parity
b. Describe two ways of eliminating the transaction foreign exchange risk.
Answer: You could hedge by selling pounds forward for dollars. Alternatively, you could
do a money market hedge in which you borrow the present value of the pounds, and
convert the loan principal to dollars in the spot market, and then use the pound receivable
to pay off the interest plus principal on the loan at maturity.
c. Which of the alternatives in part b is superior?
Answer: The forward hedge gives
$1.4802/£  £700,000 = $1,036,140
in 180 days. The money market hedge requires the present value of the £700,000. The
interest rate is (10/100)  (180/365) = 0.0493. Thus, the present value is
£700,000 / 1.0493 = £667,111.41
The dollar value of this is
$1.4945/£  £667,111.41 = $996,998
To compare this to the forward hedge we must take its future value at 7% p.a. The
interest rate is (7/100)  (180/360) = 0.035. Therefore the future value is
$996,998  1.035 = $1,031,892.93
The forward hedge provides slightly more dollar revenue.
d. Assume that the dollar interest rate and the exchange rates are correct. Determine
what sterling interest rate would make your firm indifferent between the two
alternative hedges.
Answer: We know that if interest rate parity is satisfied, the money market hedge and the
forward hedge will provide the same revenue. The pound interest rate that satisfies
interest rate parity is
1
1 + i(£)  = S($/£) × 1 + i($)  ×
F($/£)
The value of the right-hand side is $1.4945/£  1.035 / $1.4802/£ = 1.0450. Thus the
annualized pound interest rate that would make the firm indifferent between the forward
hedge and the money market hedge is 0.0450  100  (365/180) = 9.12%.
9. Suppose that there is a 0.5% probability that the government of Argentina will
nationalize its banking system and freeze all foreign deposits indefinitely during the
©2012 Pearson Education, Inc.
Chapter 6: Interest Rate Parity 11
next year. If the dollar deposit interest rate in the United States is 5%, what dollar
interest would Argentine banks have to offer in order to attract deposits from foreign
investors?
Answer: If the freezing of deposits is an idiosyncratic event, then the expected value of the
return should equal the risk free return of 5%. If investors effectively get a return of zero with
0.5% probability, they must get a return of (1 + X%) with 99.5% probability, such that
[(1 + X%)  0.995] + [0  0.005] = 1.05
When we solve this equation for X%, we find X% = 5.53%. Of course, the more that you
eventually recover in the event of a freeze of deposits, the smaller the interest rate can be.
10. Suppose the market price of a 20-year pure discount bond with a face value of $1,000 is
$214.55. What is the spot interest rate for the 20-year maturity expressed in percentage
per annum?
Answer: We know that the relationship between the price of a pure discount bond and the
spot interest rate at the 20 year maturity satisfies
$1,000
P(t) =
20
1 + i(t,20) 
Substituting the price of $214.55 and solving for i(t,20), we find
1/20
 $1,000 
i(t,20) = 
 $214.55 
- 1 = 0.08
Therefore, the spot interest rate for the 20-year maturity expressed in percentage per annum
is 8%.
11. Consider a 2-year euro-denominated bond that has a current market price of €970, a
face value of €1,000, and an annual coupon of 5%. Suppose the 1-year eurodenominated spot interest rate is 5.5%. What is the 2-year euro-denominated spot
interest rate?
Answer: The present value of a coupon paying bond is found by discounting each annual
coupon and the final principal payment at the appropriate spot interest rates for those
maturities. Thus, to find the 2-year euro-denominated spot interest rate we must solve for the
two-period spot interest rate in the following equation:
€50
€1050
€970 =
+
1.055 1+i(t,2) 2
The answer is i(t,2) = 6.68%.
©2012 Pearson Education, Inc.
12 Chapter 6: Interest Rate Parity
12. Consider some data drawn from Exhibit 6.5. The 1-year rates can be viewed as spot
interest rates, and the 2-year rates are yields to maturity in annualized percent. The
spot exchange rate is ¥132.192/£.
U.K.
Japan
1 year
1.105
0.370
2 year
1.770
0.430
What should be the 2-year forward rate to prevent arbitrage?
Answer: We know that if the coupon on a bond is equal to the yield to maturity on the bond, then
the bond is selling for face value. Therefore,without loss of generality, we assume that a twoyear coupon bond has a coupon of 1.77% in the U.K. and 0.43% in Japan. Thus, in the U.K. the
two-year spot interest rate satisfies
1
0.0177
1.0177

(1  0.01105) (1  i(2)) 2
Solving for i(2) gives 0.01776. Doing the same for the yen, we have
1
0.0043
1.0043

(1  0.0037) (1  i(2)) 2
Solving for i(2) gives 0.004301. Hence, the 2-year forward rate that prevents arbitrage would
satisfy
F (t , 2) 
¥132.192 1.0043012 ¥128.719


£
1.017762
£
13. Go to the website of the British Bankers’ Association (BBA). Find out which banks are
on the panel for the dollar, the euro, the yen and the Australian dollar.
Answer: The information can be found at http://www.bbalibor.com/panels/. The composition of
the panels on June 2, 2011 was the following:
US Dollar Panel
Please find a complete list below for all the 20 banks that currently contribute to the
fixing of US Dollar bbalibor. This panel was last reviewed in November 2010.


Bank of America
Bank of Nova Scotia
©2012 Pearson Education, Inc.
Chapter 6: Interest Rate Parity 13


















Bank of Tokyo-Mitsubishi UFJ Ltd
Barclays Bank plc
BNP Paribas
Citibank NA
Credit Agricole CIB
Credit Suisse
Deutsche Bank AG
HSBC
JP Morgan Chase
Lloyds Banking Group
Rabobank
Royal Bank of Canada
Société Générale
Sumitomo Mitsui Banking Corporation
The Norinchukin Bank
The Royal Bank of Scotland Group
UBS AG
West LB AG
Euro Panel
Please find a complete list below for all the 16 banks that currently contribute to the
fixing of Euro bbalibor. This panel was last reviewed in November 2010.
















Abbey National plc
Bank of Tokyo-Mitsubishi UFJ Ltd
Barclays Bank plc
Citibank NA
Credit Suisse
Deutsche Bank AG
HSBC
JP Morgan Chase
Lloyds Banking Group
Mizuho Corporate Bank
Rabobank
Royal Bank of Canada
Société Générale
The Royal Bank of Scotland Group
UBS AG
West LB AG
Japanese Yen Panel
Please find a complete list below for all the 16 banks that currently contribute to the
fixing of Japanese Yen bbalibor. This panel was last reviewed in November 2010.
©2012 Pearson Education, Inc.
14 Chapter 6: Interest Rate Parity
















Bank of Tokyo-Mitsubishi UFJ Ltd
Barclays Bank plc
Citibank NA
Credit Agricole CIB
Deutsche Bank AG
HSBC
JP Morgan Chase
Lloyds Banking Group
Mizuho Corporate Bank
Rabobank
Société Générale
Sumitomo Mitsui Banking Corporation
The Norinchukin Bank
The Royal Bank of Scotland Group
UBS AG
West LB AG
Australian Dollar Panel
Please find a complete list below for all the 8 banks that currently contribute to the fixing
of Australian Dollar bbalibor. This panel was last reviewed in November 2010.








Barclays Bank plc
Commonwealth Bank of Australia
Deutsche Bank AG
JP Morgan
Lloyds Banking Group
National Australia Bank Ltd
The Royal Bank of Scotland Group
UBS AG
Only Barclays Bank, Deutsche Bank AG, JP Morgan Chase, Lloyds Banking Group,
The Royal Bank of Scotland, and UBS AG are on all four panels.
©2012 Pearson Education, Inc.
Chapter
8
Purchasing Power Parity and Real
Exchange Rates
QUESTIONS
1. What does the purchasing power of a money mean? How can it be measured?
Answer: The purchasing power of a money is also known as its real value and indicates the
amount of goods and services that can be purchased with a given amount of the money. We
measure purchasing power by first calculating the price level, which is a weighted average of
the prices of the goods and services that people consume. The weights in the price level
reflect the shares of these goods and services in the consumption bundle of a typical
individual. The purchasing power of the money is then found by taking the reciprocal of the
price level. The units of the price level are an amount of money per consumption bundle, and
the units of purchasing power are consumption bundles per unit of money.
2. Suppose the government releases information that causes people to expect that the
purchasing power of a money in the future will be less than they previously had
expected. What will happen to the exchange rate today? Why?
Answer: Typically, when people think that the purchasing power of a money is going to
decline in the future, due to higher expected inflation, they try to sell that currency today to
get into a currency that will have more stable purchasing power. This reduced demand for the
currency causes that currency to weaken or depreciate immediately.
3. What is the difference between a price level and a price index?
Answer: The price level is a weighted average of the prices of the goods and services that
people consume. The price index is a ratio of a price level at one point in time to the price
level in some base year, with the ratio usually multiplied by 100. Thus, if the price level in a
given year is 30% higher than the price level in the base year, the price index would be 130.
Price levels give you information about the purchasing power of a currency. Price indexes
give you information about the rate of inflation between two points in time.
4. What do economists mean by the law of one price? Why might the law of one price be
violated?
©2012 Pearson Education, Inc.
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Chapter 8: Purchasing Power Parity and Real Exchange Rates
Answer: The law of one price says that the price of a good, when denominated in a particular
currency, is the same wherever in the world the good is being sold. The law of one price
relies on arbitrage in the goods market. If the good is being sold in one place at a low price
and is being sold in a different place at a high price, people have an incentive to arbitrage the
two markets. Therefore, anything that makes it difficult or costly to arbitrage in the goods
market can create a deviation from the law of one price. Clearly, transaction costs, such as
the costs of shipping, generate deviations from the law of one price that cannot be arbitraged.
Tariffs and quotas on imports and exports also create deviations. If markets are not
competitive and firms have some monopoly power, the corporation may decide to charge
different prices in different countries, but it must be able to segment the markets to prevent
arbitrage. If arbitrage cannot be done instantaneously, there will be a speculative element that
enters the calculations and the speculator may have to be compensated for the risk of loss
with an expected profit from buying in one market and selling in another market at a later
point in time. Finally, various goods markets are subject to a certain amount of price
stickiness because of the costs of changing prices. Because exchange rates are asset prices
and freely flexible, unanticipated changes in exchange rates will create deviations from the
law of one price if goods prices are sticky.
5. What is the value of the exchange rate that satisfies absolute PPP?
Answer: Absolute purchasing power parity requires that the internal purchasing power of a
currency equals its external purchasing power. The internal purchasing power is calculated
by taking the reciprocal of the price level, and the external purchasing power is calculated by
first exchanging the domestic money into the foreign money in the foreign exchange market
and then calculating the purchasing power of that amount of foreign currency in the foreign
country. Hence, the prediction of absolute PPP for the exchange rate of domestic currency
per unit of foreign currency is found by equating the internal purchasing power of the
domestic currency to the external purchasing power of the domestic currency:
1
1
1
= PPP ×
P  DC  S
P  FC 
where P(DC) is the domestic price level, P(FC) is the foreign price level, and S PPP signifies
the exchange rate of domestic currency per unit of foreign currency that satisfies the PPP
relation. By solving for SPPP, we find
P  DC 
SPPP =
P  FC 
6. If the actual exchange rate for the euro value of the British pound is less than the
exchange rate that would satisfy absolute PPP, which of the currencies is overvalued
and which is undervalued? Why?
Answer: The terminology of “overvalued” and “undervalued” refers to the relationship of the
exchange rate to the PPP theory. If the actual exchange rate of euros per pound is less than
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3
the PPP prediction, the euro is overvalued and the pound is undervalued. We know this is the
correct answer because if the actual exchange rate were to move to the PPP prediction, the
euro would have to weaken, and the pound would correspondingly have to strengthen, on the
foreign exchange market. The weakening of the euro would correct its overvaluation, and the
strengthening of the pound would correct its undervaluation.
7. What market forces prevent absolute purchasing power parity from holding in real
economies? Which of these represent unexploited profit opportunities?
Answer: Any of the forces that create a deviation from the law of one price can also cause a
deviation from PPP. See the answer to question 4. In addition, even if the law of one price
were satisfied for all goods, if the consumption bundles in the two countries put different
weights on the goods because of taste differences across countries, relative price changes
would be reflected in deviations from PPP. It is our opinion that deviations from PPP do not
represent unexploited profit opportunities.
8. Why is it better to use a PPP exchange rate to compare incomes across countries than
an actual exchange rate?
Answer: When comparing incomes across countries, one is interested in comparing the
quality of life that occurs from earning such incomes and consuming in those countries. One
way to do such a comparison is to examine the real values of the nominal incomes, that is, to
multiply each of the nominal incomes times the respective purchasing powers of the
currencies (which is equivalent to dividing the nominal income by the price level). The real
value of the income tells you the command over goods and services that the nominal income
provides when you consume in that country. If the real incomes in countries A and B were
the same, we would have
nominal income in country A nominal income in country B

price level in country A
price level in country B
If we multiply this expression by the price level in country A, we get
nominal income in country A 
price level in country A
 nominal income in country B
price level in country B
In the above expression, the ratio of the price level in country A to the price level in country
B is the purchasing power parity exchange rate. Hence, if we multiply the nominal income in
country B by the purchasing power parity exchange rate we get a nominal income that is in
the units of the currency of country A and that can be compared to the nominal income in
country A. If the nominal income in country A is higher than the purchasing power exchange
rate multiplied by nominal income in country B, people in country A are better off in terms
of their ability to consume than those in country B.
If you use the actual exchange rate rather than the PPP exchange rate to convert the nominal
income in country B into currency of country A, you are effectively saying you would like to
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Chapter 8: Purchasing Power Parity and Real Exchange Rates
earn the income in country B, but you want to consume it in country A. This can create
incorrect inferences about where is the best place to live. Suppose currency B is overvalued
relative to PPP. Then, the market exchange rate of currency A per unit of currency B,
denoted S, is greater than the PPP prediction,
SPPP =
price level in country A
price level in country B
That is S > SPPP. In such a situation, it can happen that
nominal income in country A > SPPP  nominal income in country B
in which case we know from the above discussion that we would prefer to earn income in
country A and consume there. Yet, when we compare incomes with the actual exchange rate,
we might find that the
nominal income in country A < S  nominal income in country B
The overvaluation of currency B causes us to think that the income in country B is preferred.
But, this is only correct if we earn the income in country B but consume in country A after
converting our income into the currency of country A.
9. What is relative PPP, and why does it represent a weaker relationship between
exchange rates and prices than absolute PPP?
Answer: The theory of relative PPP specifies that exchange rates adjust in response to
differences in inflation rates across countries to leave the deviation of the actual exchange
rate from absolute PPP unchanged. Intuitively, inflation is the rate of loss of the internal
purchasing power of a currency. Thus, if two currencies are losing internal purchasing power
at different rates because the rates of inflation in the two countries are not equal, the rate of
change of the exchange rate can offset the differential rates of inflation to leave the same
absolute relationship between the internal and external purchasing powers of the currencies.
The relative PPP theory is weaker than absolute PPP because relative PPP could be satisfied
even though there are deviations from absolute PPP. The requirement for relative PPP to hold
is that the deviations from absolute PPP do not change over time.
10. What is the real exchange rate, and how are fluctuations in the real exchange rate
related to deviations from absolute PPP?
Answer: The real exchange rate, say, of the dollar relative to the euro, is denoted RS(t,$/€). It
is defined to be the nominal exchange rate multiplied by the ratio of the price levels:
S(t,$/€)  P(t,€)
RS(t,$/€) =
P(t,$)
Notice that the real exchange rate would be 1 if absolute purchasing power parity held
because the nominal exchange rate, S(t,$/€), would equal the ratio of the two price levels,
P(t,$)/P(t,€). Similarly, if absolute PPP is violated, the real exchange rate is not equal to 1.
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Chapter 8: Purchasing Power Parity and Real Exchange Rates
5
Thus, fluctuations in the deviations from absolute PPP are fluctuations in the real exchange
rate.
11. If the nominal exchange rate between the Mexican peso and the U.S. dollar is fixed, and
there is higher inflation in Mexico than in the United States, which currency
experiences a real appreciation and which experiences a real depreciation? Why? What
is likely to happen to the balance of trade between the two countries?
Answer: If the peso is pegged to the dollar and the rate of inflation in Mexico is greater than
in the rate of inflation in the United States, the peso is appreciating in real terms and the
dollar is experiencing a real depreciation. The logic is that the rate of inflation in Mexico
measures the loss of internal purchasing power, while because the exchange rate is pegged,
the loss of the peso’s external purchasing power is measured by the U.S. rate of inflation. If a
currency’s loss of internal purchasing power is greater than its loss of external purchasing
power, that currency experiences a real appreciation.
The real appreciation of the peso tends to make Mexican residents think that U.S. goods are
relative bargains, while the real depreciation of the dollar relative to the peso, makes U.S.
residents think that Mexican goods are relatively expensive. Thus, the balance of trade
between Mexico and the United States on the Mexican balance of payments should
deteriorate with an increase in imports from the United States and a decrease in exports to the
United States.
PROBLEMS
1. If the consumer price index for the United States rises from 350 at the end of a year to
365 at the end of the next year, how much inflation was there in the United States
during that year?
Answer: Price indexes are ratios of the price level in a given year to the price level in a base
year. Because the base year is the same in the two price indexes under consideration, we can
take the ratio of the two price indexes and find the rate of inflation over that year. The ratio is
365/350 = 1.0429 or an inflation rate of 4.29%.
2. As a wheat futures trader, you observe the following futures prices for the purchase
and sale of wheat in 3 months: $3.00 per bushel in Chicago and ¥320 per bushel in
Tokyo. Delivery on the contracts is in Chicago and Tokyo, respectively. If the 3-month
forward exchange rate is ¥102/$, what is the magnitude of the transaction cost
necessary to make this situation not represent an unexploited profit opportunity?
Answer: The forward dollar price of wheat in Tokyo is the ratio of the futures price, ¥320 per
bushel, to the forward exchange rate, ¥102/$. This ratio is ¥320 per bushel / (¥102/$) = $3.14
per bushel. Since we can buy wheat for delivery in Chicago at $3 per bushel, if transaction
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Chapter 8: Purchasing Power Parity and Real Exchange Rates
costs of shipping wheat from Chicago to Tokyo are smaller than $0.14 per bushel, we could
make an arbitrage profit. Thus, the minimum magnitude of the transaction cost necessary to
make this situation not represent an unexploited profit opportunity is $0.14 per bushel.
3. Suppose that the price level in Canada is CAD16,600, the price level in France is
EUR11,750, and the spot exchange rate is CAD1.35/EUR.
a. What is the internal purchasing power of the Canadian dollar?
Answer: It is probably best to calculate the purchasing power of CAD10,000. If we divide
this amount by the price level in Canada of CAD16,600, we find
CAD10,000
=0.6024 consumption bundles
CAD16,600 / consumption bundle
b. What is the internal purchasing power of the euro in France?
Answer: Performing a similar calculation to the one in part a., we find
EUR10,000
= 0.8511 consumption bundles
EUR11,750 / consumption bundle
c. What is the implied exchange rate of CAD/EUR that satisfies absolute PPP?
Answer: The implied PPP exchange rate equates the internal purchasing power of the
CAD to its external purchasing power. This implies that the PPP exchange rate is the
ratio of the Canadian price level in Canadian dollars to the French price level in euros:
SPPP  CAD/EUR  =
CAD16,600 CAD1.4128
=
EUR11,750
EUR
d. Is the euro overvalued or undervalued relative to the Canadian dollar?
Answer: Because the actual exchange rate of CAD1.35/EUR is less than the PPP
exchange rate, the euro is undervalued on the foreign exchange market because it would
have to strengthen to move from CAD1.35/EUR to CAD1.4128/EUR.
e. What amount of appreciation or depreciation of the euro would be required to
return the actual exchange rate to its PPP value?
Answer: The exchange rate moves from the actual value of CAD1.35/EUR to the PPP
value of CAD1.4128/EUR for a percentage change of1.4128/1.35– 1 = 0.0466. This is a
4.66% appreciation of the euro versus the Canadian dollar.
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Chapter 8: Purchasing Power Parity and Real Exchange Rates
7
4. Suppose that the rate of inflation in Japan is 2% in 2011. If the rate of inflation in
Germany is 5% during 2011, by how much would the yen strengthen relative to the
euro if relative PPP is satisfied during 2011?
Answer: The approximately correct answer is that the yen should strengthen by the
differential in the rates of inflation or 5% - 2% = 3%. The exact answer is found from
equation (8.4) of the text, which incorporates a denominator correction, and we get
DC  π  t+1,DC  - π  t+1,FC 

s  t+1,
=
FC 
1 + π  t+1,FC 

Since we are concerned about the strengthening of the yen, let the yen be the foreign
currency (FC), and let the euro be the domestic currency (DC). Then, the relative PPP
formula states that the rate of appreciation of the yen is
0.05 - 0.02
 0.0294 or 2.94%
1 + 0.02
5. One of your colleagues at Deutsche Bank thinks that the dollar is severely undervalued
relative to the yen. He has calculated that the PPP exchange rate is ¥140/$, whereas the
current exchange rate is ¥105/$. Because interest rates are 3% p.a. lower in Japan than
in the United States, he thinks that this is a good time to speculate by borrowing yen
and lending dollars. What do you think?
Answer: Deviations from PPP are a weak reason to engage in speculation. While the data in
the problem indicate that the dollar is 33.33% undervalued, because that is the amount of
dollar appreciation that would be required to take the actual exchange rate from ¥105/$ to the
PPP prediction of ¥140/$, we know that the return to PPP will not be an overnight event.
The empirical analysis of the issue indicates that the half-life of PPP deviations is around 5
years. Thus, you might expect that the dollar will appreciate by 16.67% over the next 5 years.
But, uncovered interest rate parity actually suggests that the yen will appreciate in the short
run, because the yen interest rate is 3% less than the dollar interest rate. Notice, though, that
the correction back toward PPP can take place with differential rates of inflation in the two
countries. If Japanese rate of inflation falls below the U.S. rate of inflation, the PPP
prediction will begin falling toward the actual exchange rate. Finally, although the dollar is
33.33% undervalued, there is no guarantee that the undervaluation will begin to be corrected
now. It may, in fact, get worse. If the undervaluation of the dollar goes to 50% over the next
2 years, you would lose 16.67% in the foreign exchange market which would not be
compensated by the approximate 6% that you would earn by borrowing yen and lending
dollars. Finally, do not forget that your boss in proprietary trading at Deutsche Bank would
not be happy with such a situation.
6. Suppose that you are trying to decide between two job offers. One consulting firm
offers you $150,000 per year to work out of its New York office. A second consulting
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Chapter 8: Purchasing Power Parity and Real Exchange Rates
firm wants you to work out of its London office and offers you £100,000 per year. The
current exchange rate is $1.65/£. Which offer should you take, and why? Assume that
the PPP exchange rate is $1.40/£ and that you are indifferent between working in the
two cities if the purchasing power of your salary is the same.
Answer: We know from the extensive discussion in Question 8 that we should use the PPP
exchange rate to compare the pound salary to the dollar salary. If we do so, we find
$1.40/£  £100,000 = $140,000. This is less than the $150,000 that you are being offered in
New York. The fact that the dollar is undervalued on the foreign exchange markets makes the
perceived salary of $1.65/£  £100,000 = $165,000, calculated with the spot exchange rate,
seem more attractive. But, the key point is that to achieve $165,000 of spending in the United
States, you would have to work in London and consume in New York.
7. Suppose that in 2011, the Japanese rate of inflation is 2%, and the German rate of
inflation is 5%. If the euro weakens relative to the yen by 10% during 2011, what would
be the magnitude of the real depreciation of the euro relative to the yen?
Answer: The real exchange rate is
RS(t, ¥ / € ) =
S(t, ¥ / € )  P(t, € )
P(t, ¥)
We also know that a real depreciation of the euro means that this real exchange rate
decreases. The new real exchange rate will be the old real exchange rate with each term
multiplied by one plus the respective percentage rate of change. Thus, one plus the
percentage rate of change of the real exchange rate is
1 + s(t, ¥ / €)  1 +  (t, €)  1 - 0.10   1 + 0.05  0.9265
1 + rs(t, ¥ / € ) =
1 +  (t, ¥)
1 + 0.02
So, we conclude that the real depreciation of the euro is 7.35%.
8. Pick a particular brand of appliance, like a Bosch dishwasher with certain features, and
use the internet to compare its prices across countries. Be sure to have exactly the same
style of appliance in each country. How different are the prices when expressed in a
common currency?
We found the Bosch Ascenta series Model SHX6AP05UC on sale at Sears-Canada for
CAD1,149.99. The exact same model in the United States was available from Amazon
through AJ Madison for $728.10. The exchange rate on June 4, 2011 was CAD0.9772/USD.
Thus, a Canadian could purchase the U.S. dishwasher for CAD0.9772/USD x $728.10 =
CAD711.50. Buying the dishwasher from Sears-Canada would have cost 61.6% more.
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9. Go to the IMF’s web site at www.imf.org, find the Data and Statistics tab, locate World
Economic Outlook (WEO) data, and download the “Implied PPP conversion rate” for
the Indonesian rupiah and the Philippines peso versus the dollar. Calculate a rupiah per
peso PPP rate and compare it to the actual exchange rate. Which currency is
overvalued, and by how much?
Go to the IMF’s WEO site at
http://www.imf.org/external/pubs/ft/weo/2010/02/weodata/index.aspx
Request data for Indonesia and the Philippines on their Implied PPP rates versu the U.S.
dollar. The 2011 rates were 6,402.79 for Indonesia and 25.143 for the Philippines. The ratio
of these two gives the Implied PPP rate of IDR/PHP:
IDR6,402.79/USD
IDR254.65
=
PHP25.143/USD
PHP
The actual exchange rate was IDR197.153/PHP. Hence, the Philippines peso is undervalued
relative to the Indonesian rupiah because the peso would have to strengthen if the actual
exchange rate were to go to the Implied PPP rate. The peso would have to strengthen by
29.16%.
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Chapter
9
Measuring and Managing Real Exchange
Risk
QUESTIONS
1. As the vice president of finance for a U.S. firm, what do you say to your production
manager when he states, “We shouldn’t let foreign exchange risk interfere with our
profitability. Let’s simply invoice all our foreign customers in dollars and be done with
it.”
Answer: The production manager is poorly informed. Whenever goods are sold across
borders of countries that use different currencies, there will be foreign exchange risk that
must be born by someone. If your firm invoices only in dollars, you may lose export sales
that would go to importers that are not willing to bear the risk. Other competitors of yours
may be more flexible and willing to invoice in the local currency. The important point is that
the foreign exchange risk is present and must be managed by someone. Why not by you – the
trained international finance expert!
2. What do economists mean by pricing-to-market?
Answer: Pricing-to-market means that a producer charges different prices in different
markets for the same good. Clearly, this requires the markets to be segmented to prevent
arbitrage in the goods market, and the producer must have some degree of monopoly power
in the sense that the demand curve that it faces in each of the markets is not perfectly elastic.
3. Why does a monopolist not charge the same price for the same good in two different
countries?
Answer: The monopolist sets the prices in the two markets such that the marginal revenue in
each market equals the common marginal cost of producing the good. If the elasticities of
demand differ in the two markets, the producer optimally charges a higher price in the market
with the less elastic demand curve.
4. What determines how much a foreign producer allows the dollar price of a product sold
in the United States to be affected by a change in the real exchange rate?
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Chapter 9: Measuring and Managing Real Exchange Risk
Answer: Pricing-to-market interacts with changes in the real exchange rate to prevent the full
pass-through of the change in the exchange rate to the change in the price of the good. If the
real exchange rate moves in a favorable direction for the monopolist, the foreign price of the
good could be allowed to fall one-for-one with the appreciation of the foreign currency. But,
while the monopolist will allow the price to fall to allow the sale of more goods, the
monopolist will not let the price fall one-for-one with the exchange rate because the
monopolist has the opportunity to take enhanced profitability on all sales. Conversely, if the
real exchange rate moves in an unfavorable direction for the monopolist, the foreign price of
the good will be allowed to rise to decrease the amount sold, but the monopolist will also
accept some reduced profitability on all sales.
5. Why is the pass-through from changes in exchange rates to changes in the prices of
products not one-for-one?
Answer: Imperfect pass-through ultimately reflects imperfections in the competitiveness of
goods markets. If markets were perfectly competitive, pass-through would be full. For
additional discussion, see the answer to Question 5. These are really the same question.
6. Given that real exchange rates fluctuate, when would be the best time to enter the
market of a foreign country as an exporter to that market?
Answer: Firms often introduce new products in foreign markets when the foreign currencies
are strong in real terms. Doing so allows the new entrant to the market to set a comparatively
low foreign currency price for a product so that it can better compete and become an
established player in the market. This strategy allows the exporter to develop loyal customers
who will then potentially tolerate increases in the foreign currency price that the exporter
feels compelled to introduce when the foreign currency eventually depreciates relative to the
exporter’s currency.
7. You have been asked to evaluate possible sites for an Asian production facility that will
manufacture your firm’s products and sell them to the Asian market. What real
exchange rate considerations should you entertain in your evaluation?
Answer: You must be aware of the strength or weakness of the real exchange rates in the
various countries. Because your firm will be exporting from the country in which the plant is
located, your profits will be hurt by a future real appreciation of the currency of that country
relative to the currencies of countries to which you export. Your costs would rise with no
corresponding benefit in sales. Thus, if the potential production country currency is currently
severely undervalued on foreign exchange markets, this country may appear to be a low cost
production center, but it is likely that this cost advantage will be eroded by a real
appreciation in the future.
8.
Why is it important for an exporter to understand the distinction between a temporary
change in the exchange rate and a permanent change in determining whether to
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3
respond to a real depreciation of the home currency with increased production or sales
out of inventories?
Answer: Exporters benefit when their home currencies depreciate in real terms. If the
depreciation is temporary, drawing down inventory stocks without changing the production
process can meet the short-term increase in demand in the lowest cost way. The more
permanent is the perception of the real depreciation, the more likely it is that the firm’s
demand will be permanently higher, in which case it is more appropriate to increase
production as this is the lowest cost long-run response.
PROBLEMS
1. If there is 10% inflation in Brazil, 15% inflation in Argentina, and the Argentine peso
weakens by 21% relative to the Brazilian real, by how much has the peso strengthened
or weakened in real terms. What effect do you expect that this change in the real
exchange rate would have on trade between the two countries?
Answer: If s denotes the rate of change of the nominal exchange rate measured as Brazilian
real per Argentine peso, π(A) denotes the rate of Argentine inflation, and π(B) denotes the
rate of Brazilian inflation, the percentage change in the real exchange rate measured as
Brazilian real per Argentine peso is
rs 
1  s   1   ( A)   1  1  0.21  1  0.15  1  0.1741
1   ( B) 
1  0.10 
Thus, the Argentine peso has weakened by 17.41% in real terms. This is less than the 21%
by which it weakened in nominal terms because the Argentine rate of inflation was 5%
greater than the Brazilian rate of inflation.
2. Suppose that you have one domestic production facility that supplies both the domestic
and foreign markets. Assume that the demand for your product in the domestic market
is Q = 2,000 – 3P and in the foreign market, demand is given by Q* = 2,000 – 2P*.
Assume that your domestic marginal cost of production is 600. If the initial real
exchange rate is 1, what are your optimal prices and quantities sold in the two markets?
By how much will you change the relative prices of your product if the foreign currency
appreciates in real terms by 10%? What will you do to production?
Answer: From the domestic demand curve, we find that P = (2,000 – Q) / 3, and revenue
from domestic sales is
P × Q = [(2,000 × Q) – Q2] / 3
We know that when the monopolist sells output in the foreign market, the domestic real value
of revenue from foreign sales is the real exchange rate, RS, multiplied by the foreign relative
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Chapter 9: Measuring and Managing Real Exchange Risk
price, multiplied by foreign sales, or by substituting P* = (2,000 – Q*) / 2, we find that
domestic real revenue from foreign sales equals
RS × P* × Q* = [(RS × 2,000 × Q*) – RS × Q*2] / 2
The domestic marginal cost of production is constant at 600, and the total cost of production
is the per-unit cost multiplied by the total quantity produced for sale in each of the two
markets, or 600 × (Q + Q*).
A profit-maximizing monopolist produces an amount of the good such that the marginal
revenues earned from sales in each market are each equal to the common marginal cost. The
domestic marginal revenue is (2,000 – 2Q) / 3. Thus, the monopolist should sell a quantity in
the domestic market that satisfies
(2,000 – 2Q) / 3 = 600
or, by solving for Q, we find Q = 100. The monopolist charges P = 633.33 to achieve sales of
100.
The marginal revenue from the foreign market is
(RS × 2,000 – RS × 2Q*) / 2.
The optimal quantity in the foreign market satisfies
RS × 1,000 – RS × Q* = 600
or, once again solving for Q*, we find
Q* = [1,000 – (600 / RS)]
At the initial real exchange rate of 1, the monopolist should sell 400 in the foreign market by
charging the relative price of 800. The total real profit would be
(633.33 × 100) + (800 × 400) – [600 × (100 + 400)] = 83,333
Now, if there is a 10% real appreciation of the foreign currency, the new real exchange rate is
1.1. The real appreciation of the foreign currency benefits an exporting monopolist because
the domestic value of real revenue in the foreign country is now
1.1 × [(2,000 – Q*) × Q*] / 2
1.2
By equating the foreign marginal revenue to the unchanged domestic marginal cost of 600
and solving for Q*, we find
Q* = [1,000 – (600 / 1.1)] = 454.55
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Chapter 9: Measuring and Managing Real Exchange Risk
5
In order to sell the 454.55 units in the foreign market, the monopolist must lower the foreign
price per unit to
P* = (2,000 – 454.55) / 2 = 772.73
Because the marginal cost of production is constant, the domestic price per unit remains at
633.33, and the domestic sales remain at 100. Notice that although the foreign currency
appreciates by 10%, the monopolist only decreases the relative price in the foreign market by
3.4% because the ratio of the new foreign price to the old foreign price is
772.73 / 800 = 0.966
3. How would you respond in Problem 2 if the marginal cost of production were
increasing? Why?
Answer: If the marginal cost of production is increasing, it costs more to produce larger
quantities. After the real appreciation of the foreign currency, the monopolist would still
want to increase the quantity sold in the foreign market, but not by as much. Hence, the
foreign relative price would not fall as much. The monopolist would also increase the
domestic relative price to sell less in that market, and he would shift some sales from the
domestic market to the foreign market.
4. Suppose you are a monopolist who faces a domestic demand curve given by Q = 1,000 –
2P. Your domestic cost of production involves domestic costs per unit of 300 and a
foreign cost per unit produced of 150. If the real exchange rate is 1.1, what would be the
price you would charge and the quantity you would sell? How do these variables change
when the real exchange rate increases by 10%?
Answer: The monopolist will operate where marginal revenue equals marginal cost. Price is
(1,000 – Q) / 2, and total revenue is P × Q = (1,000 Q – Q2) / 2. Marginal revenue is therefore
(1,000 – 2Q) / 2 = 500 – Q.
Marginal cost has a domestic component of 300 and a foreign component of RS × 150. The
initial real exchange rate is 1.1. Therefore, marginal cost is 300 + 1.1 × 150 = 465. Equating
marginal revenue to marginal cost gives the optimal production:
500 – Q = 465
Q = 35.
In order to sell a quantity of 35, the monopolist must charge
P = (1,000 – 35) / 2 = 482.5.
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Chapter 9: Measuring and Managing Real Exchange Risk
If there is a 10% real appreciation of the foreign currency, the new real exchange rate is 1.1 ×
(1 + 10%) = 1.21. Marginal cost increases to 300 + 1.21 × 150 = 481.5, and the optimal
quantity falls to
500 – Q = 481.5
Q = 18.5.
The relative price in the domestic market increases to
P = (1,000 – 18.5) / 2 = 490.75.
The 10% increase in the real exchange rate causes marginal cost to increase by 3.55% from
465 to 481.5. The price of the product increases by a smaller percentage, 1.71%, from 482.5
to 490.75. Thus, pass-through from the change in the exchange rate to the product price is
less than one-for-one.
5. Use a program like Crystal Ball to generate Monte Carlo simulations of the profits of
Safe Air and Metallwerke under various contracting clauses.
These graphics indicate the profit margin with no inflation in either country and a standard
deviation of the dollar-euro exchange rate equal to 10%.
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Chapter 9: Measuring and Managing Real Exchange Risk
7
6. In 2008 Endo Pharmaceuticals, a U.S. firm, signed a five-year contracted with Novartis,
a Swiss firm, to obtain the exclusive U.S. marketing rights for Voltaren Gel, an antiinflammatory useful in treating osteoarthritis. Search the internet for information
about the contract. Who bore the real exchange risk?
©2012 Pearson Education, Inc.
8
Chapter 9: Measuring and Managing Real Exchange Risk
Searching for “Voltaren Gel aggreement” turned up this assessment from www.mmmonline.com:
Under the terms of the five-year agreement with Novartis, Endo will make an upfront cash
payment of $85 million. Novartis is also eligible to receive a one-time milestone payment of
$25 million if annual sales exceed $300 million. Under the deal, Novartis will receive
royalties on the net sales of Voltaren Gel in the US and will supply this product to Endo.
Thus, it appears that Novartis is bearing the real foreign exchange risk as Endo will receive
dollars from its customers and pay dollars to Novartis.
©2012 Pearson Education, Inc.
Chapter
10
Exchange Rate Determination and
Forecasting
QUESTIONS
1. What is the difference between the ex ante and the ex post real interest rate?
Answer: The ex post interest rate corrects the nominal interest rate with the realized or ex post rate of
inflation; whereas the ex-ante (or expected) real interest rate corrects the nominal interest rate for
expected inflation.
As a lender, you care about the real return on your investment, which is the return that measures
your increase in purchasing power between two periods of time. If you invest $1, you sacrifice
$1
1+i
real goods now, where P(t) is the price level. In 1 year, you get back
, where i is the
P(t)
P(t+1)
nominal rate of interest. We calculate the real return by dividing the real amount you get back by the
real amount that you invest. Thus, if rep is the ex post real rate of return and ex post real interest rate,
we have
⎛ 1+i ⎞
⎜ P(t+1) ⎟
⎠ = (1 + i )
= ⎝
⎛ 1 ⎞
⎛ P(t+1) ⎞
⎜ P(t) ⎟
⎜ P(t) ⎟
⎝
⎠
⎝
⎠
1 + r ep
Notice that the real rate of interest depends on the realization of the rate of inflation because
P(t + 1)/P(t) = 1 + π(t + 1), where π(t + 1) is the rate of inflation between time t and t + 1. For
simplicity, we drop the time notation and simply write
1 + r ep =
(1 + i)
(1 + π)
If we subtract 1 from each side, we have
r ep =
(1 + i) (1 + π)
i-π
=
(1 + π) (1 + π) (1 + π)
which is often approximated as
rep = i – π
The approximation involves ignoring the term (1 + π) in the denominator, which is close to 1 if
inflation is not too high. Thus, the ex post real interest rate equals the nominal interest rate minus the
actual rate of inflation.
Because the inflation rate is uncertain at the time an investment is made, the lender cannot
know with certainty the real rate of return on the loan. By taking the expected value of both sides of
the equation, conditional on the information set at the time of the loan, we derive the lender’s
expected real rate of return, which is also called the expected real interest rate, or the ex ante real
interest rate, which we denote re:
r e = E t [r ep ] = i(t) - E t [π(t+1)]
66
Chapter 10: Exchange Rate Determination and Forecasting 67
2. Suppose that the international parity conditions all hold and a country has a higher nominal
interest rate than the United States. Characterize the country’s inflation rate compared to the
United States, the country’s expected exchange rate change versus the dollar, the country’s
currency forward premium (or discount) versus the dollar, and the country’s real interest rate
compared to the U.S. real interest rate.
Answer: When all the parity conditions hold, real interest rates are equalized across countries, so the
country’s real interest rate should equal that of the United States. The country’s higher nominal
interest rate therefore must reflect a higher expected rate of inflation relative to the United States.
Since the parity conditions hold, a higher expected rate of inflation implies that country’s currency
should be expected to depreciate relative to the dollar, and the currency will trade at a forward
discount relative to the dollar.
3. How do fundamental analysis and technical analysis differ?
Answer: Fundamental analysis typically uses formal economic models of exchange rate determination
and macroeconomic fundamental data such as money supplies, inflation rates, productivity growth
rates, and the current account to predict exchange rates. Technical analysis uses only past exchange
rate data, and perhaps some other financial data, such as the volume of currency trade, to predict
future exchange rates.
4. Would technical analysis be useful if the international parity conditions held? Why or why not?
Answer: If the parity conditions held, technical analysis would not be useful in the sense of providing
profitable trading information or information about expected exchange rates that could not be
obtained elsewhere. If the parity conditions held, the best predictor of the future exchange rate would
be the forward rate, and exchange rate forecasts based on other indicators would not lead to
systematic profits on currency speculation.
5. Describe three statistics you should obtain from a currency-forecasting service in order to judge
the quality of its currency forecasts.
Answer: Three important statistics are the Root Mean Squared Error (RMSE) or Mean Absolute
Deviation of its forecasting record, which would provide information on accuracy; the percentage of
times they were on the correct side of the forward rate, which would provide useful information on
the profitability, and a risk–return statistic (such as the Sharpe ratio), which would provide a
characterization of the profitability of using their forecasts in a real time trading strategy.
6. Does a large increase in the domestic money supply always lead to a depreciation of the
currency?
Answer: Most theories of the determination of exchange rates would predict that a large increase in
the money supply would imply a depreciation of the currency, definitely in the long run, and
especially as economists say when “everything else is equal.” However, it is possible that the change
in the money supply is accompanied by an increase in real income that increases the demand for
money and thus offsets the money supply’s effect on the exchange rate.
68 Chapter 10: Exchange Rate Determination and Forecasting
7. Is a current account deficit always associated with a strong real exchange rate (that is, one that
is overvalued compared to the PPP prediction)?
Answer: Not necessarily. It is best to view the current account and the real exchange rate as being
determined in an equilibrium that depends on many forces, such as movements in net foreign assets,
government spending, productivity growth, and the expectations and risk tolerances of domestic and
foreign investors.
8. Describe how three macroeconomic fundamentals affect exchange rates.
Answer: According to the monetary exchange rate model, the domestic currency weakens
(strengthens) if the domestic (foreign) money supply increases today or if news arrives that leads
people to believe that the future domestic (foreign) money supply will increase. The domestic
currency also weakens if domestic real income falls, if foreign real income rises, or if news arrives
that causes people to expect lower domestic real growth or faster foreign real growth. Finally,
according to the equilibrium theory regarding the real exchange rate and the current account, an
increase in government spending or a decrease in taxes that causes a budget deficit should increase
the real exchange rate (and hence likely also the nominal exchange rate). This is because an increase
in government spending increases aggregate demand in the economy, which causes the real interest
rate to rise. The rise in the interest rate reduces investment and encourages private saving
9. Which simple statistical model yields some of the best exchange rate predictions available?
What does this imply for the value of models of exchange rate determination to multinational
businesses?
Answer: It is surprisingly difficult to beat the forecasts of the random walk model. This model uses
the current exchange rate as the predictor of the future exchange rate. If this model provided the best
forecast, the unbiasedness hypothesis (which says the forward rate is the best predictor) would be
violated. If there were a forward premium on the foreign currency, the forward rate would be above
the expected future spot rate, and you would want to sell the foreign currency in the forward market.
10. What is chartism?
Answer: Chartists graphically record the actual trading history of an exchange rate and then try to
infer possible future trends based on that information alone.
11. What is an x% filter rule?
Answer: An x% rule states that you should go long in the foreign currency (buy) after the foreign
currency has appreciated relative to the domestic currency by x% above its most recent trough (or
support level) and that you should go short in the foreign currency (sell) whenever the currency falls
x% below its most recent peak (or resistance level). Common x% filter rules are 1% or 2%.
Chapter 10: Exchange Rate Determination and Forecasting 69
12. What is a moving-average crossover rule?
Answer: Moving-average crossover rules use moving averages of the exchange rate to indicate trade
directions. An n-day moving average is just the sample average of the last n trading days, including
the current rate. A (y, z) moving-average crossover rule uses averages over a short period (y days)
and over a long period (z days). The strategy states that you should go long (short) in the foreign
currency when the short-term moving average crosses the long-term moving average from below
(above). Common rules use 1 and 5 days (1, 5), 1 and 20 days (1, 20), and 5 and 20 days (5, 20).
13. Have forecasting services been successful in forecasting exchange rates?
Answer: The direct evidence on the forecasting prowess of forecasting services is rather dated by now
(see, for example, a 1987 study by Robert Cumby and David Modest), but the results of these studies
suggested that most forecasting services were more often wrong than correct, but that most did make
profits. Academic studies have suggested that it has become more difficult to forecast currency
movements based on technical signals more recently relative to the 1980s; but it is possible that other
models may do better.
14. Are devaluations of pegged exchange rates totally unexpected?
Answer: While there is a debate about their predictability, some theories suggest that devaluations
may be partially predictable. These models argue that growing budget deficits, fast money growth,
and rising wages and prices usually precede devaluations. Increases in nominal interest rates typically
reflect a combination of the probability and magnitude of a possible devaluation.
15. Construct a list of a country’s economic statistics you would assemble to help determine the
probability of a devaluation of its currency within the coming year.
Answer: Based on theoretical and empirical work, the following economic variables should prove
useful predictors: PPP-based measures of currency overvaluation, current account balances and
monetary growth rates. In addition, if liquid financial markets exist, information about forward rates
or interest rates, currency option prices, and so on may prove useful in terms of forecasting
devaluations.
70 Chapter 10: Exchange Rate Determination and Forecasting
PROBLEMS
1. Suppose the 1-year nominal interest rate in Zooropa is 9%, and Zooropa’s expected inflation
rate is 4%. What is the real interest rate in Zooropa?
Answer: The expected real interest rate is approximately 9% - 4% = 5%. The correct computation is: (1 +
0.09) / (1 + 0.04) – 1 = 0.0481 or 4.81%.
2. You were recently hired by the Doolittle Corporation corporate treasury to help oversee its
expansion into Europe. Blake Francis, the CFO, wants to hire a foreign exchange forecasting
company. Blake has asked you to evaluate three different companies, and he has obtained
information on their past performances. Out of a total of 50 forecasts for the $/€ rate, the
companies reported the number of times they correctly forecast appreciations and
depreciations:
Morrissey Forex Advisors
Pixie Exchange Land
FOREX Cures
Correct Down Forecasts
20
20
12
Correct Up Forecasts
5
4
12
There are a total of 35 dollar appreciations (down periods) and 15 dollar depreciations (up
periods) in the sample. Blake wants to know two things:
a. Can anything be said about the companies’ forecasting ability with the available data?
Answer: Yes, one can compute the number of correct “directional” forecasts. Morrissey has the
highest correct proportion with 25 out of 50 correct, whereas the other firms have less than 50%
correct. However, note that the dollar over this period was relatively strong and appreciations (down
forecasts for the $/€ rate) dominate. Hence, forecasts in the down period may be more useful (see
footnote 3 in the chapter). If we look at correct conditional forecasts, we see that Morrissey is correct
20/35 or 57.14% of the time when the dollar appreciates, but only 5/15 or 33.33% of the time when
the dollar depreciates. According to the Henriksson–Merton test, the sum of these two proportions
should be over 1 for a firm to have market timing ability. However, the sum in this case is only
90.47%. While Morrissey obviously dominates Pixie Land Exchange, it is not clear that it is better
than FOREX Cures. The proportions of correct conditional forecasts of FOREX Cures are 12/35
(34.29%) and 12/15 (80%) for a sum of 114.29%. Consequently, only FOREX Cures shows
directional forecasting ability.
b. What additional information should Blake try to obtain in order to form a better
judgment?
Answer: Directional forecasting ability in the foreign exchange market is not particularly useful if the
forecasts are to be used in speculative strategies. To this end, it would have been more useful to know
whether the forecasting firms were on the correct side of the forward rate. Ideally, a full record of
forecasts would be obtained. Then, accuracy statistics (like the RMSE) and profitability statistics (like
the Sharpe ratio) could be computed.
Chapter 10: Exchange Rate Determination and Forecasting 71
3. Mini-Case: Currency Turmoil in Zooropa
Fad Gadget has never worked so hard in his entire life. It is near midnight, and he is
still poring over statistics and tables. Fad recently joined Smashing Pumpkins, a relatively
young but fast-growing British firm. Smashing Pumpkins produces and distributes an intricate
device that turns fresh pumpkins into pumpkin pie in about 30 minutes. Recently, the firm has
started exporting to Zooropa. Some of the largest and tastiest pumpkins are grown in Zooropa,
and Zooropa’s population boasts the highest per capita pumpkin consumption in the world. A
recent analysis of the pumpkin market in Zooropa has left the company’s senior managers very
impressed with the profit potential.
Although Zooropa consists of 10 politically independent countries, their currencies are
linked through a system called the Currency Rate Linkage System (CRLS) that works exactly
like the former Exchange Rate Mechanism (ERM) of the EMS worked before the currency
turmoil started in September 1992. The anchor currency is the banshee of Enigma, the leading
country in Zooropa.
Initial contacts with importers in Zooropean countries indicated that they typically
insist on payment in their own local currency. About a week ago, Cab Voltaire, the CEO of
Smashing Pumpkins, expressed concerns about this development and asked Fad to lead a
research team to further examine the present state of the currency system of Zooropa. Cab
viewed the outlook for the banshee relative to the pound quite favorably and did not predict
any substantial depreciation of the banshee against any other major currency. However, the
precarious economic situation of some of the countries in Zooropa and the growing importance
of speculative pressures in Zooropa’s currency markets last week suddenly made him
suspicious about the possibility of realignments within the system. He even doubted the longterm viability of the system. Cab instructed Fad to examine the following issues:
y Which currencies in the system exhibit the highest realignment risk?
y If a currency realigns and gets devalued, what are the effects on our sales and profit
margins in this particular country? Can we take the realignment possibility into
account in our pricing?
y Suppose a currency is forced to leave the CRLS. What are the effects on exchange
rates, interest rates, and the outlook for sales in that country? What is the likelihood
of this occurring for the different countries?
Fad Gadget felt nervous. A meeting was scheduled with Cab the day after tomorrow. He
wanted to write a thorough and insightful report. At the last management meeting, he had the
uneasy feeling that some senior managers doubted his abilities. Some managers were naturally
suspicious of a young Australian newcomer with his MBA. His earring and punk hairdo did not
exactly help either. His team of analysts had already assembled a table with relevant
macroeconomic and financial data (see Exhibit 10.11). “If only I could use this to rank the
different countries according to realignment risk,” he thought.
a) Realignment rankings
The data provided are a scrambled version of an Exhibit that appeared in the Economist of
September 19, 1992, when a currency crisis in Europe had just erupted. The Exhibit presented macroeconomic statistics for all the countries participating in the European system. To prevent students
guessing where the data are from, we scrambled the country names two ways. First, we gave each
European country another name that did provide a vague hint on the actual European country of origin.
However, we then randomly assigned the actual data to the fictitious countries. Here is the “key:”
72 Chapter 10: Exchange Rate Determination and Forecasting
Zooropa Country
Sinead
Carmen
Marquee
Fries
Ney
HelpIsink
Benfica
Che Ora
Vachement
Enigma
Reference to European Country
Ireland (Irish singer)
Carmen (Spanish opera)
UK (club in London)
Belgium (French fries are Belgian!)
Denmark (No in Danish)
the Netherlands (below sea level)
Portugal (soccer team)
Italy (only Italian Geert knows)
France (French stop word)
Germany (pop band)
Data from European country
Ireland
France
Spain
Portugal
Denmark
Belgium
the Netherlands
UK
Italy
Germany
We now reproduce the original Economist table from the article “A Ghastly Game of Dominoes.”
Who’s Next?
Legend for Chart:
A - Currency's ERM position Sept 15th (*)
B - Currency's over/under valuation, % (A)
C - Reserves, import cover (**)
D - Budget deficit as % of GDP, 1992 (B)
E - Inflation rate %, latest
F - GDP growth, %, 1992 (B)
G - Devaluation risk (AA)
Italy
Britain
Spail
Portugal
Denmark
Belgium
Holland
France
Ireland
Germany
A
27
-90
16
-3
-22
31
30
-36
-6
36
B
2
3
11
11
-2
-18
-16
-12
-10
--
C
0.5
2.6
8.2
11.7
2.5
1.3
1.5
3.1
2.9
1.7
D
-11.3
-4.6
-4.9
-5.4
-2.1
-5.5
-3.4
-2.3
-1.9
-3.4
E
5.2
3.6
5.7
9.5
2.2
2.1
3.5
2.7
3.6
3.5
F
1.3
-0.8
2.0
2.8
2.1
1.6
1.6
2.0
2.4
1.3
G
1
2
3
4
5=
5=
5=
8
9
--
Sources: OECD; IMF; government statistics; NatWest; The Economist poll of forecasters (*) % of
permitted divergence from central rate (A) Central rate against DM relative to PPP (**) Foreignexchange (mid September estimates), number of months' imports (B) Forecast (AA) 1=greatest risk,
9=least risk
Based on this article, we can actually use the data given to come up with a realignment ranking. For
example, the position in the CRLS system (the divergence indicator in the EMS, a summary measure of
the currency’s position in its bands relative to all other currencies), and the reserves import cover are
direct indicators of devaluation pressure. An overvalued currency, a large budget deficit, high inflation,
Chapter 10: Exchange Rate Determination and Forecasting 73
and low GDP growth are “bad” economic fundamentals that may contribute to speculative pressure on
the currency. The Economist did a very simple exercise. It ranked all the countries on these criteria from
“worst” (most speculative pressure) to “best” (least speculative pressure). It then added up the ranks and
came up with an overall devaluation risk ranking. Using the information provided on fundamentals leads
to a surprisingly accurate realignment risk ranking. These ranks are reproduced in the last column of the
Economist table. Italy and Britain were actually forced out of the EMS during the September currency
crisis. Spain was forced to devalue and Portugal later followed suit. The other countries with better
fundamentals duly survived.
Whether the currency crisis in 1992 was actually predictable is still a topic of academic debate. Some
important scholars in the area have argued that the crisis was almost completely unpredictable. Our case
seems to indicate otherwise, although more formal analysis is necessary (and is still being conducted by
many scholars). Finally, while some countries, such as France, still looked relatively “safe,” another
currency crisis erupted in July August 1993, which led to rather drastic changes in the operation of the
EMS, including a widening of the bands to 15%.
b) Effects of Realignments/Exits for the Firm
Since the British firm agrees to local currency pricing, the risk is that the Zooropa currencies get
devalued. Two cases must be considered:
(1) The price remains fixed. In this case, the revenue per unit sold in pounds decreases and the profit
margin is squeezed because the firm's costs are local (in pounds). Except for "dynamic effects"
(see below), there need not be any effect on the number of units sold. Sales may remain
unchanged in local currency, but sales go down in pounds.
(2) The firm tries to "pass through" the exchange rate change and raises the price of the pumpkin
device as in Chapter 9. The optimal response will be to raise the domestic price because the firm
does not want to sell as much quantity in that market. The amount of the price increase depends
on the elasticity of the demand curve. The price will rise less, the more elastic is the demand –
that is, the larger the percentage change in quantity with a given percentage change in price.
These are the immediate effects. The realignment restores the general competitiveness of the
Zooropean country. If the devaluation is successful, it accomplishes a decrease in real wages locally and
shifts resources to the export sector. It should also make potential local competitors to Smashing
Pumpkins more competitive. However, the case seems to indicate that these are non-existent. Initially,
this may lower the demand for all imports (the whole idea of the devaluation in the first place). If the
economy was not producing at full capacity, the increased competitiveness may spur considerable
additional economic growth. This, in fact, happened in Britain and Sweden after the 1992 devaluations.
Higher growth may then lead to higher imports and increase the demand for the pumpkin device. These
are potential dynamic effects. Eventually, this may cause inflationary pressures to creep back into the
economy. Unsuccessful devaluations will let higher import prices (if there is some pass through or most
import products are priced in foreign currency) affect wages and the general price level. In this case,
there may be only small effects for the British firm. Hence, the dynamic effects depend on the success of
the devaluation.
All of this analysis goes through for exits from the target zone. In fact, the effects for realignments
are probably considerably smaller, since an exit may lead to much lower exchange rates and in some
cases to lower interest rates, which further help the Zooropa economy become more competitive.
It has to be said that these are all "elaborate guesses," since in reality new shocks to the economy
may cause completely different outcomes.
74 Chapter 10: Exchange Rate Determination and Forecasting
c) Incorporating Realignment Risk into Pricing/Hedging
The market will anticipate the realignment. In fact, if UIRP holds, the interest differential with
Britain and the forward rate relative to the pound will reflect the expected currency depreciation (the
probability of a devaluation multiplied by the magnitude of the devaluation). Hence, hedging the risk will
automatically lead to lower pound revenue in the future. Ideally, one establishes a pricing scheme that
takes potential realignments into account, for example using forward rates. Your personal view on
realignment risk may differ from the forward rates though. Alternatively, a dynamic real exchange rate
risk sharing formula as in the SAFE AIR case could be proposed.
d) Effects of devaluation/exits on exchange and interest rates
Exchange rates fall, by definition. The effect on the interest rate however may be different in both
cases. With devaluation it is very likely that the interest rate will drop. That is because the interest rate was
most probably very high during the speculative attack preceding the realignment and it now drops back to
normal levels, which are still likely to be above the interest rate of the anchor currency. With an exit, the
pressure of a speculative attack gets relieved as well, and now the interest rate need not exceed the rate on the
anchor currency. However, the exiting currency loses its "inflation credibility mechanism" by leaving the
target zone, and hence, interest rates may go up reflecting higher expected inflation in the future. When
Britain exited the ERM, its interest rates dropped substantially at the short end, but they remained quite high
at the long end. In Mexico, after the December 1994 crisis, peso interest rates rose reflecting fears of future
depreciation and inflation. Both market responses seem justified both by the data at the time of the event and
the
subsequent
experiences
of
the
economies.
Chapter
11
International Debt Financing
QUESTIONS
1. What are the three main sources of financing for any firm?
Answer: Corporations rely on three primary types of financing for their capital expenditures:
internally generated funds, debt financing, and equity financing.
2. What is the difference between a centralized and decentralized debt denomination for
an MNC?
Answer: Under a decentralized debt-denomination model, MNCs issue debt in different
currencies to hedge the cash flows they earn in these currencies from their foreign
subsidiaries. Under a centralized model, debt is issued in the currency of the country in
which the MNC has its headquarters.
3. Will an MNC issuing debt in low–interest rate currencies necessarily lower its cost of
funds? Why?
Answer: No. The ultimate cost of the debt will also depend on currency movements. If
uncovered interest rate parity holds, the cost of the low interest rate debt, expressed in the
home currency, is expected to be identical to the cost of high interest rate debt. After the
fact, the debt will be either less expensive than corresponding debt denominated in the
domestic currency, if the foreign currency appreciates less than predicted by UIRP; or it will
be more expensive if the foreign currency appreciates more than predicted by UIRP.
4. Should an MNC borrow primarily short term when short-term interest rates are lower
than long-term interest rates? Or should it keep the maturity the same but use a
floating-rate loan rather than a fixed-rate loan? Explain.
Answer: First, if short-term interest rates are lower than long-term interest rates, this may be
an indication of impending increases in interest rates. In fact, if the expectations hypothesis
of the term structure of interest rates holds, the long rate is simply an appropriately weighted
average of short term rates. This implies that “timing” the loan by having a floating interest
rate that allows for low interest payments when short rates are low and high interest
payments when short rates are high does not add value. Second, the difference between
simply borrowing short-term and using a floating rate note is that the latter approach also
locks in the MNC’s credit spread. If the firm thinks its credit rating will improve over time, it
may not want to issue a floating rate note, preferring instead to borrow short-term and
borrow again at a better credit spread after the information is incorporated by the market.
66
Chapter 10: Exchange Rate Determination and Forecasting 67
5. What is financial disintermediation?
Answer: This concept refers to the phenomenon in which firms issue securities directly to
investors in the capital markets, rather than borrowing from financial institutions that in turn
raise funds from the capital markets.
6. What are the two main segments of the international bond market, and what types of
regulations apply to them?
Answer: One segment of the international bond market is the foreign bond market, where a
foreign issuer issues bonds in a particular domestic bond market, subject to local
regulations. The other segment is the Eurobond market, where bonds are issued
simultaneously in various markets, outside the specific jurisdiction of any country. Hence,
these bonds are not subject to the regulations of any particular country.
7. What is the difference between a foreign bond and a Eurobond?
Answer: See the answer to Question 6.
8. Why might U.S. investors continue to purchase Eurobonds, despite the fact that the
U.S. corporate bond market is well developed?
Answer: The Eurobond market gives them access to bonds of firms that are not available in
the US market thereby providing valuable diversification of default risk. Recall that the
Eurobond market is a highly liquid, unregulated, convenient market to issue bonds, which
has lead to a wide array of available bonds from which investors can choose. Also,
Eurobonds are not registered (ownership is anonymous), and it may therefore allow certain
tax avoidance benefits to non-scrupulous investors.
9. What is a global bond, and what role does the global bond market play in the blurring
of the distinctions in the international bond market?
Answer: Global bonds are issued simultaneously in a domestic market and in the Eurobond
market, and they therefore straddle the two segments of the international bond market,
making distinctions between them more difficult to draw.
10. What are the differences between a straight bond, a floating-rate note, and a
convertible bond?
Answer: A straight bond has no special features. It has a fixed coupon payment and a final
principal payment at maturity. A floating-rate note carries a floating interest rate that typically
varies with short-term LIBOR. Convertible bonds allow the holder to convert the bonds into a
certain amount of stock and therefore have an option feature.
11. What is a dual-currency bond?
68 Chapter 10: Exchange Rate Determination and Forecasting
Answer: Dual-currency bonds are issued in one currency and pay interest in that currency,
but the final principal payment is denominated in another currency.
12. What kind of activities do international banks engage in?
Answer: International banks typically develop a complete line of financial services to
facilitate the overseas trade of their customers. In addition to commercial credit, these
ancillary financial services include market making and trading in spot and forward
currencies, international trade financing, and risk management services. Unlike domestic
banks, international banks participate in the Eurocurrency market and are frequently
members of international loan syndicates, lending out large sums of money to MNCs or
governments. An international bank might also engage in the underwriting of Eurobonds and
foreign bonds, which are investment-banking activities.
13. Why is there a need for international banking regulation?
Answer: First, central banks are concerned that without an international regulatory
framework to ensure that an adequate level of capital is maintained in the international
banking system, bank failures could lead to a global financial crisis or at least domestic
crises could spill over into other countries.
Second, the variety of different national regulations potentially gives an unfair advantage
to banks from countries with laxer regulatory standards, and this could decrease the
soundness and safety of the international banking system overall. International regulations
can create a more level playing field that avoids potential under-regulation if individual
regulators compete to see who can be the least strict.
14. What are the differences between credit risk, market risk, and operational risk?
Answer: Credit risk is the risk that a company or government will default on its promised
payments on a loan or a bond. Market risk is the risk of losses in trading positions when
prices move adversely. Operational risk is the risk of direct or indirect loss resulting from
inadequate or failed internal processes, people, and systems or from external events, such
as computer failure, poor documentation, or fraud.
Chapter 10: Exchange Rate Determination and Forecasting 69
15. Which activity would require the largest capital charge under the 1988 Basel Accord:
a loan to another bank or a loan to a large MNC? Would this necessarily be true under
the Basel II?
Answer: Under Basel I, claims on other banks receive only a 20% weighting, meaning that
only 20% of the claim is counted against the 8% capital requirement. Some claims receive a
50% weighting, but virtually all claims on the non-bank private sector receive a 100% weight
and hence the full capital charge. Hence, the charge for the loan to the MNC would be
larger. Under Basel II, other risks are taken into account (market risk and operational risk),
and credit risk is measured differently, primarily to better reflect the true creditworthiness of
the borrower. Consequently, it is conceivable that the capital charge for the bank loan is
larger than for the MNC under Basel II.
16. What is VaR?
Answer: VaR stands for Value at Risk and measures the dollar loss that a given portfolio
position can experience with 5% probability over a given length of time.
17. What is the difference between a foreign branch and a subsidiary bank?
Answer: A foreign branch of a bank is legally a part of the parent bank, but it operates like a
local bank. Foreign branch banks are subject to both the banking regulations of their home
countries and the countries in which they operate. However, foreign branches of U.S. banks
are not subject to U.S. reserve requirements and are not required to have federal deposit
insurance. A subsidiary bank is also wholly or partly owned by a parent bank, but it is
incorporated in the foreign country in which it is located. Subsidiary banks are therefore
subject to the banking laws of the countries in which they are incorporated.
18. What is an offshore center?
Answer: Offshore banking centers conduct international banking activities in a “lightly”
regulated setting. Most of the transactions involve nonresidents as counterparties; the
transactions are typically initiated outside the financial center, and the majority of the
financial institutions involved are controlled by nonresidents who do business primarily with
nonresidents. Offshore banking centers can be found in places such as Aruba, the Cayman
Islands, and parts of the West Indies.
70 Chapter 10: Exchange Rate Determination and Forecasting
19. What is the difference between an Edge Act bank and an international banking
facility?
Answer: Edge Act banks are federally chartered subsidiaries of U.S. banks that are physically
located in the United States but are allowed to engage in a full range of international banking
activities. Such activities include accepting deposits from foreign customers, trade financing,
and transferring international funds. Edge Act banks are not prohibited from owning equity in
U.S. corporations, as are domestic commercial banks. Consequently, U.S. parent banks own
foreign subsidiaries and affiliate banks through an Edge Act setup. An international banking
facility (IBF) is a separate set of asset and liability accounts that is segregated on the parent
bank’s books, so it is not a unique physical or legal entity. Any U.S.-chartered depositary
institution (including a U.S. branch, a subsidiary of a foreign bank, or a U.S. office of an Edge
Act bank) can operate an IBF. An IBF operates as a foreign bank in the United States and is
consequently not subject to domestic reserve requirements or FDIC insurance regulation.
However, IBFs may only accept deposits from non-U.S. citizens and make loans to foreigners.
The bulk of an IBF’s activities relate to interbank business.
20. What is the difference between a Eurocredit, a Euronote, and a Euro-medium-term
note?
Answer: Eurocredits are typically very large international loans extended by a consortium or
syndicate of banks that share the risk of the loan. Eurocredits are typically issued at floating
interest rates. Euronotes are short-term, negotiable promissory notes, established by a
Euronote facility. Typically, in such a facility, a syndicate of banks commits to distribute for a
specified period, typically 5 to 7 years, the borrower’s notes (the “Euronotes”), with
maturities ranging between 1 month, 3 months, 6 months, and 12 months. In case the notes
cannot be placed in the market, the syndicate banks in many Euronote facilities stand ready
to buy them at previously guaranteed rates.
Euro-Medium-Term Notes (Euro-MTN) are securities issued directly to the market and
bridge the maturity gap between Euronotes and the longer-term international bond, with
maturities as short as 9 months to as long as 10 years. Like Euronotes, the Euro-MTN is a
facility with notes offered continuously or periodically rather than all at once, like a bond
issue. Unlike conventional underwritten debt securities, medium-term notes can be issued in
relatively small denominations and issuing costs are low, but they are not underwritten.
21. Why are Eurocredits not extended by one bank but by a large syndicate of banks?
Answer: Eurocredits are typically very large so that banks appreciate the opportunity to
share the risk of default on the loan with other banks.
22. What is the all-in cost of a 5-year loan? What are its main components?
Answer: The all-in cost (AIC) has three components: The “default free” interest rate, the
credit spread, and transaction costs. The default free interest rate is the rate available on
risk-free government securities of the same maturity. The credit spread is the difference
between the borrowing cost of the company and the borrowing cost of the government and
reflects the market’s assessment of the ability of the company to repay its debt. Finally,
Chapter 10: Exchange Rate Determination and Forecasting 71
transaction costs reflect the fees that a company pays to arrange the bond, which also
effectively raise the interest rate payable on the loan.
23. What is a credit rating? What is a credit spread?
Answer: For credit spread, see the answer to Question 23. The credit spread a company
faces in the market place is typically closely related to its credit rating. Companies that
supply credit ratings, such as Moody’s Investors Service and Standard & Poor’s (S&P),
provide information on the credit worthiness of companies across the world by producing a
“rating” for the securities they issue. They classify bond issues into categories based on the
creditworthiness of the borrower. The ratings are based on an analysis of current
information regarding the likelihood of default and the specifics of the debt obligation. The
ability of a firm to service its debt depends on the firm’s financial structure, its profitability,
the stability of its cash flows, and its long-term growth prospects.
24. Should corporations issue bonds in countries where they face the lowest credit
spreads? Be very specific about the concept of credit spread you use.
Answer: The answer here is potentially yes. When expressed in a multiplicative sense (by
dividing one plus the interest rate the company faces by one plus the rate on a comparable
government bond), lower credit spreads do indeed translate into lower borrowing costs,
provided the company can cheaply hedge the cash flows involved into its desired borrowing
currency .
72 Chapter 10: Exchange Rate Determination and Forecasting
PROBLEMS
1. In 1985, R.J. Reynolds (RJR for short) acquired Nabisco Brands and financed the deal
with a variety of financial instruments, including three dual-currency Eurobonds. The
first dual-currency bond, lead-managed by Nikko, raised JPY25 billion (which was
equivalent to USD105.5 million at the time of issue). Coupons were paid in yen, but
the required final principal payment was not JPY25 billion but USD115.956 million.
The coupon was 7.75%, even though a comparable fixed-rate Euroyen bond at that
time carried only a 6.375% coupon. The actual 5-year forward rate at the time was
around JPY200/USD.
a. Given the “fat” coupon, is this bond necessarily a great deal for the investors?
Answer: No, it isn’t a particularly great deal for the investor because the payment at the end
is worth substantially less than the face amount of the bond. To see this, note that the yen
value of final payment can be found by multiplying the USD115.956 million by the forward
rate:
USD115.956 million × JPY200/USD = JPY23.191 billion
which is less than JPY25 billion, the original principal.
Of course, the coupon is higher than the coupon on a straight Euroyen bond, so we
shouldn’t expect the final principal payment to be JPY25 billion otherwise the rate of return
on the bond would be 7.75%. If we hedge the dual currency bond and find the internal rate
of return on the yen cash flows, we find the value, y, which sets the discounted yen payoffs
equal to the cost of the bonds:
¥25 billion =
5
0.0775 × ¥25billion
i=1
(1 + y )
∑
+
i
(¥200/$) × $0.115956 billion
(1 + y )
5
Using Excel’s IRR command, we find that the internal rate of return on the bond is 6.48%,
which is greater than the rate of return offered by the straight Euroyen bond. Thus, the bond
is a good deal for investors if they can hedge at the forward rate of ¥200/$.
b. At maturity, in August 1990, the exchange rate was actually JPY144/USD. Was the
bond a good deal for investors?
Answer: We need to calculate the return to investors if the investors were unhedged.
Investors received
USD115.956 million × JPY144/USD = JPY16.698 billion
which is almost ¥7 billion less than if they had sold the face amount forward at the forward
rate prevailing in August 1985. This loss happened because the yen appreciated by much
more than was predicted by the forward rate. It is therefore also unlikely that the “fat
coupon” would have made up for this huge capital loss. In fact, it is straightforward to
compute the actual internal rate of return investors made on an unhedged investment in this
bond. It is the rate that solves:
¥25 billion =
5
0.0775 × ¥25billion
i=1
(1 + y )
∑
i
+
¥16.698 billion
(1 + y )
5
We find y = 1.28%. This is a much lower return than the yield offered in 1985 by a regular
Euroyen bond! This is not so hard to understand considering that the payment at the end
represents a capital loss of approximately 30%!
Chapter 10: Exchange Rate Determination and Forecasting 73
2. GBA Company wishes to raise $5,000,000 with debt financing. The funds will be
repaid with interest in 1 year. The treasurer of GBA Company is considering three
sources:
i. Borrow USD from Citibank at 1.50%
ii. Borrow EUR from Deutsche Bank at 3.00%
iii. Borrow GBP from Barclays at 4.00%
If the company borrows in euros or British pounds, it will not cover the foreign
exchange risk; that is, it will change foreign currency for dollars at today’s spot rate
and buy foreign currency back 1 year later at the spot rate prevailing then. The GBA
Company has no operations in Europe.
A representative of GBA contacts a local academic to provide projections of the
spot rates 1 year in the future. The academic comes up with the following table:
Projected Rate 1 Year in the
Currency
Spot Rate
Future
USD/GBP
1.5
1.55
USD/EUR
0.95
0.85
a. What is the expected interest rate cost for the loans in EUR and GBP?
Answer: For the EUR, the expected cost is
(1 + .03) × (0.85/0.95) - 1 = -0.0784 or -7.84%
For the GBP, the expected cost is
(1 + 0.04) x (1.55/1.50) - 1 = 0.0747 or 7.47%
These costs reflect both the interest costs and the expected capital gains or losses on
the currency positions. If the academic’s projections prove accurate, the interest cost in
GBP is higher than the GBP interest because the pound is expected to appreciate
relative to the dollar, and GBA will need more than $5,000,000 to repay the pound loan.
In contrast, the EUR is expected to decrease in value by more than 10% relative to the
dollar, providing a large capital gain to GBA, which borrows in a depreciating currency
and hence must use much less than the initial $5,000,000 to repay the euro loan.
b. What are the projected USD/GBP rate and USD/EUR rate for which the expected
interest costs would be the same for the three loans?
Answer: These are the exchange rates that satisfy Uncovered Interest Rate Parity,
E t [S(t+1,$/FC) ] = S(t,$/FC) ×
(1 + i($) )
(1 + i(FC) )
where FC indicates either the EUR or the GBP. For the euro we find
E t [S(t+1,$/FC) ] =
$0.95 1.015 $0.9362
×
=
€
1.03
€
Hence, the euro must depreciate only a little bit for the euro loan to be as cheap as the
USD loan. For the pound, we obtain
E t [S(t+1,$/FC) ] =
$1.50 1.015 $1.4639
×
=
£
1.04
£
74 Chapter 10: Exchange Rate Determination and Forecasting
c. Should the company borrow in the currency with the lowest interest rate cost?
Why or why not? Would your answer change if GBA did generate cash flows in
the UK and continental Europe?
Answer: When using the forecasts of the academic, the lowest interest cost occurs in
EUR. However, the academic’s forecast is quite far away from the “break-even” rates
computed in part b., which may be closely related to the market determined forward
rates. Moreover, currency forecasters do not have the best of records (see Chapter 10).
Consequently, it is not at all clear that the “expected” low interest cost will actually be
realized. If anything, the empirical evidence suggests that borrowing in low interest
countries (in this case the US) may eventually save money (see Chapter 7 on the
deviations from Unbiasedness). What a company can do is to investigate in what country
its (multiplicative) credit spread is minimized, borrow in that country and hedge back to
dollars when there is no reason, as in this case, to hold foreign exchange risk. If GBA
generates cash flows in Europe, borrowing in currencies there may provide a natural
hedge.
3. FE Company wishes to raise $1,000,000 with debt financing. The treasurer of FE
Company considers two possible instruments:
i. A 2-year floating-rate note at 1% above 1-year dollar LIBOR on which interest is
paid once a year
ii. A 2-year bond with an interest rate of 5%
Currently, the dollar LIBOR is 1.50%.
a. Is it obvious which security the Treasurer should pick?
Answer: It is not at all obvious which debt to pick. While the two-year floating rate starts
out at a lower rate (2.50% versus 5%), it is not clear at all what the eventual cost of the
note will be to the company. The cost will also depend on the reset of the interest rate in
the second year. If that interest is high enough, the 2-year bond may ex-post prove to be
the cheapest financing vehicle. Typically, an upward sloping yield curve suggests the
market does indeed expect that short-term interest rates will rise in the future.
b. Suppose the Treasurer believes that 1-year LIBOR, 1 year from now, will rise to
4.50%. Which security has the lowest expected AIC if borrowing fees are similar
for the two instruments?
Answer: The AIC for the two-year bond is simply 5%. For the two-year floating rate note,
we must compute the y that satisfies:
1,000,000 =
25,000
55,000
1,000,000
+
+
2
2
(1 + y ) (1 + y )
(1 + y )
where we computed the coupon payments as 2.5% for year 1 and 5.5% (4.5% +1%) for
year 2 on the $1,000,000 principal. The solution for y is 3.97%. Hence, at this forecast,
the floating rate note is cheaper than the bond.
Chapter 10: Exchange Rate Determination and Forecasting 75
4. K3 Company wants to borrow $100 million for 5 years. Investment bankers propose to
either do a syndicated Eurocredit or issue a Eurobond. The Eurocredit would be
denominated in dollars, but the Eurobond would be denominated in different
currencies for different markets (these issues are called tranches):
Terms:
Syndicated Eurocredit
Amount:
USD100 million
Upfront fees: USD1.25%
Interest rate: Interest payable every 6 months; LIBOR plus 1.00%
Terms:
Eurobond
Tranche 1: USD 50 million, Interest rate: 3.50%
Tranche 2: ¥ 5,952 million (equivalent of USD50 million), Interest rate 1.5%
a. What are the net proceeds in USD for K3 for the Eurocredit loan?
Answer: The net proceeds for the Euro credit are (1 - 0.0125) × $100 million = $98.75
million (the fees amount to $1.25 million).
b. Assuming that the 6-month LIBOR in USD is currently at 2.00%, what is the
effective annual interest cost for K3 for the first 6 months of the loan?
Answer: The LIBOR convention is simple interest, so the 6-month interest rate is [2% +
1%] / 2 = 1.5%. To obtain the effective annual interest rate, we must annualize using
compounding, (1 + 0.015)2 - 1 = 0.0302 or 3.02%
c. Compute an effective annualized interest rate cost (all-in cost) for the USD tranche
of the Eurobond.
Answer: The interest rate is 3.5% and is likely payable just once a year. Hence, this
would also be the AIC for the loan. Of course, the question omits mentioning the costs of
issuing the bond, and these costs should be taken into account in a proper AIC
computation.
d. What information would you need to obtain the dollar all-in cost of the yen
tranche?
Answer: In addition to the transaction costs associated with the loan, we must know the
terms for converting yen payments into dollar payments. For example, we could use the
swap market (see Chapter 21), and we would need the terms for that, or we could use
forward contracts, and we would need to know the available forward rates to convert
dollars into yen for 1, 2, 3, 4, and 5 years into the future.
76 Chapter 10: Exchange Rate Determination and Forecasting
e. What elements would you take into account to choose between the two
possibilities?
Answer: With all the information given above (interest rate costs, loan issuance costs,
and information on yen conversion rates), we can compute the AIC on the two tranches
of the Eurobond issue. K3 can then compare its fixed borrowing costs with the Eurobond
relative to the variable costs involved in the Eurocredit. While it appears that the floating
rate Eurocredit will have interest expenses that are less than the Eurobond’s in the first
year or so, this by no means guarantees that it will ex-post have the lowest costs. K3
should think of why it is optimal for the firm to incur interest rate risk. Perhaps its cash
flows are cyclical and increase when short term interest rates increase, mitigating the
interest rate risk embedded in the floating rate loan.
5. Suppose Intel wishes to raise USD1 billion and is deciding between a domestic dollar
bond issue and a Eurobond issue. The U.S. bond can be issued at a 5-year maturity
with a coupon of 4.50%, paid semiannually. The underwriting, registration, and other
fees total 1.00% of the issue size. The Eurobond carries a lower annual coupon of
4.25%, but the total costs of issuing the bond runs to 1.25% of the issue size. Which
loan has the lowest all-in cost?
Answer: To keep things simple, we express the cash flows on bonds with a face value of
100, instead of $1 billion. We use a cash flow diagram similar to the one used in the PointCounterpoint.
The U.S. bond is special as it features semi-annual coupon payments (of 4.5%/2 =
2.25%). It is best to simply compute the AIC using 10 half-years. This AIC is then a semiannual rate which must be annualized to be comparable to the annual AIC of the Eurobond.
Because there are so many periods, we only show the first few and the last few. Negative
numbers are in parentheses.
1. US Bond
Half-Year
Dollar Cash Flows
0
100 – 1.00 = 99.00
1
-2.25
2
-2.25
….
….
9
-2.25
To annualize this AIC, we compute (1 + 0.0236)2 – 1 = 0.0478 or 4.78%.
For the Eurobond, the computations are more standard:
2. Eurobond
Year
Euro Cash Flows
0
100 – 1.25 = 98.75
1
-4.25
2
-4.25
3
-4.25
4
-4.25
Chapter 10: Exchange Rate Determination and Forecasting 77
Hence, we see that, on an annualized basis, the Eurobond is substantially cheaper (by 24
basis points) than the U.S. bond.
Chapter
12
International Equity Financing
QUESTIONS
1. What are the differences between public, private, and banker’s bourses?
Answer: In public bourses the government appoints brokers, typically ensuring them a
monopoly over all stock market transactions. With the deregulation wave in the 1980s and
1990s, most stock markets are now private. A private bourse is owned and operated by a
corporation founded for the purpose of trading securities. Sometimes these corporations are
publicly traded, or they may be owned by a set of financial institutions, in which case they are
known as banker’s bourses.
2. What is the difference between a price-driven trading system and an order-driven
trading system? Which system lends itself most easily to automation?
Answer: In a price-driven system, dealers who act as market markers for certain stocks
stand ready to buy at a bid price and sell at an ask price. In an order-driven system, share
prices are determined in an auction that brings together the supply and demand of shares.
The order-driven system can be most easily automated, as it is easy to let a computer store
demand and supply schedules, and determine the equilibrium price.
3. Do we have a global stock market, as we have a global foreign exchange market?
Answer: In the global foreign exchange markets, it is possible to trade any currency almost
anywhere in the world at any time in the day. This is not true in the stock market, even
though globalization has had profound effects on stock market trading. First, there has been
increased cross listing of firms on exchanges throughout the world, with London and the US
as important listing markets. Second, exchanges have extending their trading hours to
make their markets more accessible to foreign traders located in other time zones. In
addition, some exchanges have merged or created alliances with foreign exchanges to
automatically cross-list their stocks. For example, Euronext in Europe combines the stock
exchanges of Amsterdam, Brussels, Paris, Lisbon and LIFFE, the London derivatives
market. Very recently (in 2007), the NYSE and Euronext merged to form a new company
called NYSE Euronext, Inc., getting ever closer to a truly global stock market.
4. What is turnover?
Answer: Turnover is the total volume traded on an exchange during a year (or some other
period) divided by the exchange’s market capitalization. It is often viewed as a liquidity
indicator.
86
Chapter 12: International Financing 67
5. What are the three primary components of transaction costs in trading stocks?
Answer: Trading costs consist of direct costs such as brokerage commissions, the bid–ask
spread, and market impact (the fact that the price may move against you when you trade a
large order).
6. Does high turnover always signal lower transaction costs?
Answer: No, the tables in the Chapter indicate a clear negative relation between the two,
but it is not perfect. There are a number of high turnover emerging markets (such as
Taiwan) that may have higher transaction costs than some lower turnover developed
markets. The Illustration Box on the Casablanca exchange provides another example of an
imperfect relation between turnover and trading costs.
7. What is the difference between an ADR and a GDR?
Answer: An American depositary receipt (ADR) is used to list shares in the American
market. It represents a certain number of original shares issued in the home stock market,
and held in custody by a depositary bank. Global depositary receipts (GDRs) are similar to
ADRs, but can be traded on many exchanges in addition to U.S. exchanges.
8. What motivates companies to cross-list their shares?
Answer: Cross-listing a stock can lower a company’s cost of capital through several
channels, including improved liquidity and better corporate governance. It can heighten the
awareness of the firm’s brands, provide direct access to foreign capital, and make future
capital access easier.
9. Has cross listing been beneficial for most listed companies? If yes, why doesn’t every
company cross-list?
Answer: It appears that indeed cross-listing has mostly brought benefits for the firms that
cross-list. However, firms for which cross listing is not beneficial should, of course, not do
so. The costs associated with cross-listing have to do with the direct costs of registration,
the potentially higher costs of more demanding accounting and reporting requirements, and
the increased scrutiny and corporate governance that may erode the private benefits of
controlling managers. Clearly, not every firm will have an incentive to cross-list.
68 Chapter 12: International Equity Financing
10. What is the difference between a GDR and a GRS?
Answer: A GDR, like an ADR, represents negotiable claims on home-market ordinary shares
(in bearer or registered form) and is issued by a depositary bank. Settlement of cross-border
trades takes place daily through ADR issuances or cancellations (“conversions”) conducted
by the depositary bank, and there are fees for such transactions. Finally, the depositary
bank maintains ownership records and processes corporate actions. Global registered
shares (GRSs) trade simultaneously in different markets around the world, in different
currencies, with the shares being completely fungible across markets. They do not require
the intervention of a depositary bank, but of course, shares can then also not be bundled or
unbundled to facilitate trading in different markets. Finally, share ownership is more direct
with a GRS than with a GDR. Holding a GRS gives investors the same voting privileges,
rights to receive dividends, and so forth, as a regular shareholder has, whereas the
depositary intermediary may impose certain restrictions.
11. What is a strategic alliance?
Answer: A strategic alliance is an agreement between legally distinct companies to share
the costs and benefits of a particular investment.
12. What is a joint venture?
Answer: A joint venture is a type of strategic alliance where two or more independent firms
form and jointly control a different entity, which is created to pursue a specific objective. The
new entity tries to combine the strengths of each partner.
Chapter 12: International Financing 69
PROBLEMS
1. The following table shows how average share prices jump (in percentage) after the
announcement that the stocks will be cross-listed (see Miller, 2000). The price
response should be interpreted as corrected for risk and market movements that
happened on the same day:
3. All ADR
4. Capital
5. Non-Capital
Issues
Raising
Raising
2.
6. Emerging markets
7. 1.5
8. 0.9
9. 2.8
10. Developed markets
11. 0.9
12. 0.7
13. 0.9
14. Total
15. 1.2
16. 0.8
17. 1.4
Although these numbers appear small, it is important to realize that announcements
of equity issues, which are by definition capital raising, in a domestic context lead to
an average negative return response of 2% to 3% (see, for instance, Masulis and
Korwar, 1986). The main reason is that capital-raising equity issues are viewed as a
signal of the managers that the firm may be overvalued in the stock market.
Given what you learned in chapter, answer the following:
a. Why is there a positive price response when a company’s shares are cross-listed?
Answer: The positive response likely reflects the reduction of the cost of capital (which
increases the valuation of the firm) associated with cross listing. As indicated in Question
7, there are a variety of channels that may lead to a lower cost of capital, such as
improved liquidity, a wider shareholder base, improved corporate governance, and
effective integration within global capital markets.
b. Why might the response for emerging-market firms be larger than for developedmarket firms?
Answer: Because their own stock markets have poorer liquidity and corporate
governance, the benefits may be relatively larger for emerging market firms. In
particular, while most firms from developed markets are subject to “global pricing,” most
emerging markets are still “segmented” from global capital markets, and listing in a
developed market effectively integrates the firm into global capital markets. The move
from segmented to global pricing tends to increase valuations because global discount
rates tend to be lower than discount rates in segmented emerging markets.
c. Without knowing that equity issues in a domestic context are associated with
negative price responses, is the difference between capital-raising and noncapital-raising ADRs a surprise? Why or why not?
Answer: Ignoring the negative signal of raising capital through the equity market, it is
surprising that capital-raising ADRs would lead to a smaller price response than noncapital raising ADRs. That is because the fact that companies raise capital through the
international capital market would suggest they have substantial growth opportunities
that should raise the value of the firm.
2. Suppose you are a U.S.-based investor, and you would like to diversify your stock
portfolio internationally. What advantages do ADRs offer you? Would it be wise to
restrict your international portfolio to only ADRs?
70 Chapter 12: International Equity Financing
Answer: As we will discuss in Chapter 13, diversifying your portfolio internationally will offer
significant benefits. However, since not all international firms have ADRs, the set of firms to
invest in may not be large enough to exhaust the benefits of international diversification. In
particular, it would tend to be the larger, more internationally oriented firms that will first
cross-list, and these firms may be exactly the ones that are more heavily correlated with
domestic firms (see Chapter 13 for more discussion on correlation and diversification
benefits).
Chapter
13
International Capital Market
Equilibrium
QUESTIONS
1. Is the volatility of the dollar return to an investment in the Japanese equity market the
sum of the volatility of the Japanese equity market return in yen plus the volatility of
yen/dollar exchange rate changes? Why or why not?
Answer: It is not. Even though the dollar return on investing in Japanese equity is
approximately the yen return on the Japanese equity market plus the rate of change in the
dollar/yen exchange rate, the volatility of this sum is not the sum of the volatilities. Intuitively,
because the equity risk and currency risk are not highly correlated, part of the volatility of the
individual components is diversified away. Technically, the variance of the dollar returns can
be written as follows:
Var[r(t + 1,¥) + s(t + 1)] = Var[r(t + 1,¥)] + Var[s(t + 1)] +2ρVol[r(t + 1, ¥)]Vol[ s(t + 1)]
where r(t + 1,¥) is the yen-denominated equity return, s(t+1) is the rate of change in the
dollar/yen exchange rate, and ρ is the correlation between the yen equity return and
dollar/yen exchange rate changes. Because volatility, Vol, is the square root of the variance,
we know that the volatility of the dollar return on a Japanese equity investment is
Vol[r(t + 1,¥) + s(t + 1)] = {Vol[r(t + 1,¥)]2 + Vol[s(t + 1)] 2 +
2ρVol[r(t + 1, ¥)]Vol[ s(t + 1)]}0.5
Clearly, only when the correlation is exactly 1 will the right-hand side have the form
(A2 + 2AB + B2)0.5 = [(A + B)2]0.5 = (A + B)
and hence, only then will the volatility of the sum be the sum of the volatilities. Because of
the perfect correlation, there is no natural diversification advantage to having exposure to
two sources of risk. However, as long as ρ < 1, the total dollar volatility will be less than the
sum of the two volatilities.
2. Why is the variance of a portfolio of internationally diversified stocks likely to be
lower than the variance of a portfolio of U.S. stocks?
Answer: With international stocks, the investor can diversify away U.S.-specific sources of
volatility (e.g. U.S.–specific business cycle movements, changes in U.S. monetary policy,
changes in U.S. interest rates, etc.). Technically, the variance of an equally weighted
portfolio converges to the average covariance between these stocks when the number of
stocks gets very large. The average covariance among U.S. stocks is higher than the
average covariance among a set of U.S. and international stocks.
91
Chapter 13: International Capital Market Equilibrium 67
3. How can you increase the Sharpe ratio of a portfolio? What type of stocks would you
have to add to it in order to do so?
Answer: To increase the Sharpe ratio on your portfolio, you must add stocks that increase
the expected return on your portfolio and/or reduce the volatility of the portfolio (for instance,
because the stocks exhibit low correlation with the portfolio you already have). One way to
think of the problem is to compute the following hurdle rate,
Hurdle rate = rf + ρ ×
E[r]
× Vol [r* ]
Vol[r]
In this equation rf is the risk free rate, ρ is the correlation between the portfolio you have and
the stock you want to add to the portfolio, E[r] and Vol[r] are the expected return and
volatility of the portfolio you are holding, and Vol[r*] is the volatility of the stock you want to
add. The hurdle rate is higher when the existing portfolio has a high Sharpe ratio, the stock
you are adding is more volatile, or there is high correlation between the return on the
portfolio and the return on the stock you are adding to the portfolio.
4. Why is the hurdle rate in Section 13.2 lower for Japan than for Canada? Should U.S.
investors still invest in Canada?
Answer: From the formula in the answer to Question 3, we see that the two main drivers of
the hurdle rates are the correlations between Canadian and U.S. returns and between
Japanese and U.S. returns (reported in Exhibit 13.6), and the volatilities of Canadian and
Japanese returns (reported in Exhibit 13.1). The most important number is the correlation.
Of the G7 countries, the Canadian market returns have the highest correlation with U.S.
returns, whereas the Japanese returns have the lowest correlation. It is this difference that
makes Japan have the lowest hurdle rate and Canada the highest. Whether U.S. investors
should still invest in Canada depends on their opportunity set. The hurdle rate for Canada,
reported in Exhibit 13.7, suggests that even if the expected return on Canadian stock is a bit
lower than that of the U.S., it is still a valuable investment that increases the Sharpe ratio.
However, if the U.S. investor can invest in Japanese securities first, it is quite likely that the
Canadian hurdle rate will exceed the expected return of the U.S.-Japan diversified portfolio.
In that case, it may not be optimal to go long Canadian securities. Note that this answer
depends on the historical numbers reported in the Exhibits. Some theories of portfolio
choice (such as the CAPM) postulate that investors should hold portfolios that are well
diversified and include all securities in line with their market capitalizations.
5. What is the mean standard deviation frontier, and what is the mean-variance-efficient
(MVE) portfolio?
Answer: The mean standard deviation frontier is the locus of the portfolios in expected
return–standard deviation space that have the minimum variance for each expected return.
It is therefore also often referred to as the minimum-variance frontier. The MVE is the
portfolio on that frontier that maximizes the Sharpe ratio. It can be found by drawing a line
emanating from the risk free rate that is just tangent to the mean standard deviation frontier.
The tangency point represents the MVE’s expected return and standard deviation. The MVE
is therefore also referred to as the tangency portfolio.
68 Chapter 13: International Capital Market Equilibrium
6. What is the prediction of the CAPM with respect to optimal portfolio choice?
Answer: All investors should hold the same portfolio for risky assets, the market portfolio.
The market portfolio contains all securities, and the proportion of each security is its market
value as a percentage of total market value.
7. What is it prediction of the CAPM with respect to the expected return on any security?
Answer: The CAPM implies that the expected return of any security equals the risk-free rate
plus the beta of the security multiplied by the market risk premium. The beta of the security
is the covariance of its return with the return on the market portfolio divided by the variance
of the market portfolio return. Hence, the risk premium on an individual security is a function
of its covariance with the market portfolio.
8. What is the beta of a security?
Answer: As indicated in Question 7, the beta of the security is the covariance of its return
with the return on the market portfolio divided by the variance of the market portfolio return.
This beta can be estimated from a regression of excess returns on the security in question
onto excess returns on the market portfolio (proxied by the world market portfolio return, for
example). Sometimes, industry portfolios are used to reduce the sampling error in estimating
the betas.
9. Why might it be useful to estimate the beta for a stock from returns on stocks within
its industry rather than from the stock itself?
Answer:Estimating a beta using a regression is often imprecise because a firm’s returns
exhibit considerable idiosyncratic volatility. That is, much of the variation in a firm’s return is
driven by firm-specific events. This idiosyncratic volatility reduces the fit of the regression
and increases the standard errors of the estimates. If firms in the same industry have about
the same systematic risk, which is a reasonable assumption, their betas will be about the
same as well. A portfolio of firms diversifies away a lot of idiosyncratic risk and is
consequently much less variable than an individual firm’s stock returns. Therefore, beta
estimates from industry portfolios are more precise, and provide reasonable estimates for a
firm’s beta.
10. What does it mean for an equity market to be integrated or segmented from the world
capital market?
Answer: Markets are integrated when assets of identical risk command the same expected
return, irrespective of their domicile. Hence, in an integrated equity market, stocks are priced
using global discount rates. In a segmented market, discount rates are country–specific.
Segmentation usually arises through governmental interference with free capital markets.
For example, if foreign investors are taxed or otherwise prohibited from holding the equities
of a country, then that country’s assets are not part of the world market portfolio, and that
country is said to be segmented from international capital markets. It is also conceivable that
Chapter 13: International Capital Market Equilibrium 69
other factors (such as poor corporate governance or liquidity) keep foreigners from investing
in an equity market, causing it to be effectively segmented.
11. What would you expect to happen to the risk-free rate and equity returns when a
segmented country opens its capital markets to foreign investment?
Answer: When a country unexpectedly opens its capital markets to foreign investors, we
expect the real interest rate to decrease, and the stock market to rise in value. The real
interest rate in the country should fall because the country’s residents are now free to
borrow and lend internationally (which may reduce domestic demand for local funds), and
there is additional foreign supply of capital. It is conceivable that before the liberalization, the
government may have kept interest rates artificially low—for instance, through interest rate
ceilings—in which case the interest rate may rise upon liberalization.
The equities of the country will now be priced globally, rather than locally. Using the
intuition from the CAPM, equity discount rates will now be based on their covariances with
the return on the world market portfolio and no longer on their covariances with the local
market. The latter covariances are likely to be much larger than the covariances with the
world market; hence the liberalization should lead to a lower risk premium for domestic
stocks. Together with the lower risk free rate, the discount rates for local stocks should
decrease, and, consequently, their valuations should increase. Simply put, foreign investors
will bid up the prices of local stocks in an effort to diversify their portfolios, while all investors
will shun inefficient sectors. Thus, equity prices should rise (as expected returns decrease)
when a market moves from a segmented to an integrated state.
12. What accounts for the home bias phenomenon?
Answer: Home bias refers to the phenomenon that investors, even in the developed world,
have not fully internationally diversified their portfolios which are consequently heavily
invested in their own stock markets. No well-accepted explanation for why investors forego
the benefits of international diversification exists.
Home bias is definitely declining over time, which suggests that the direct barriers to
international investment did play a role in the past. For most countries, these barriers have
been dismantled and can no longer explain why investors do not invest abroad.
Arguments such as the idea that currency risk increases the riskiness of foreign
investments or that foreign investments are costlier than domestic ones are unlikely to be
valid explanations. Because currency changes show little correlation with local equity
markets, they add little to the volatility that U.S. investors face when investing in foreign
equity markets. Moreover, currency volatility can be hedged. Transaction costs may play a
role, but in order to generate the observed portfolio proportions of U.S. investors, U.S.
investors would have to think that the average returns on foreign stocks were 2% to 4% per
annum less than the realized average returns on foreign assets. It may be that these figures
represent U.S. investors’ perceived transaction costs of foreign investing, but it is unlikely.
Moreover, the huge volume of international capital flows is also inconsistent with the
transaction costs story, as is the fact that foreign countries are home biased.
Perhaps the most popular explanation of home bias is that international investors
have an informational disadvantage relative to local investors, which cause international
investors to invest less abroad, or to not invest at all in unknown foreign markets. For public
investments, this story also is not entirely appealing. It is easy enough to obtain information
on foreign companies or to set up or use local investment managers. However, it may be
that the quality of the information and a poor regulatory framework in terms of investor
protection and corporate governance keep out U.S. institutional investors. This may explain
70 Chapter 13: International Capital Market Equilibrium
why foreign companies like to list ADRs, which can thus be more easily included in
institutional investors’ portfolios. Again, such an explanation would not explain why even
investors in countries with poor corporate governance are still home biased. Ultimately, it
appears that the main variable most negatively and robustly correlated with the degree of
home bias is “distance,” suggesting that people invest more in countries with which they are
more familiar.
13. Explain the basic principle of the APT.
Answer: The arbitrage pricing theory (APT) recognizes that the return on the market portfolio
may not be the only potential source of systematic risks that affect the returns on equities.
The APT postulates that other economy-wide factors can systematically affect the returns on
a large number of securities. These factors might include news about inflation, interest rates,
gross domestic product (GDP), or the unemployment rate. Changes in these factors will
affect the future profitability of corporations, and they may affect how investors view the
riskiness of future cash flows. This, in turn, will affect how investors discount future uncertain
cash flows. When there are economy-wide factors that affect the returns on a large number
of firms, the influences of these factors on the return to a well-diversified portfolio are still
present. The influences of these factors cannot be diversified away. Consequently, the risk
premiums on particular securities are determined by the sensitivities of their returns to the
economy-wide factors and by the compensations that investors require because of the
presence of each of these different risks.
14. Suppose AZT is a small value stock and that you use both the CAPM and the FamaFrench model to compute its cost of capital. Under which model is the cost of capital
for AZT likely to be higher?
Answer: It is likely to be higher under the Fama-French model. The reason is that the FamaFrench model has two additional factors in addition to the return on the value-weighted
market portfolio in excess of the risk-free return, as in the CAPM. These factors are the
difference in the return on a portfolio of small firms and the return on a portfolio of big firms
(small minus big [SMB]) and the difference between the return on a portfolio of firms with
high values of book equity to market equity (BE/ME) and the return on a portfolio of firms
with low values of BE/ME (high minus low [HML]). These two factors carry positive risk
premiums. As a small value stock, AZT stock will have positive exposures to these two
factors and therefore likely have a higher cost of capital, than if only the CAPM were used.
Chapter 13: International Capital Market Equilibrium 71
PROBLEMS
1. The EAFE is the international index comprising markets in Europe, Australia, and the
Far East. Consider the following annualized stock return data:
Average U.S. index return:
14%
Average EAFE index return:
13%
Volatility of the U.S. return:
15.5%
Volatility of the EAFE return:
16.5%
Correlation of U.S return and EAFE return:
0.45
a. What would be the return and risk of a portfolio invested half in the EAFE (Europe,
Australia and Far East index) and half in the U.S. market?
Answer: Using standard formulas for the expected return and volatility of a portfolio of
two assets, we find:
E[r P ] = (0.5)×14% + (0.5)×13% = 13.5%
P
2
2
2
2
2
VOL[r ] = [(0.5) (15.5%) + (0.5) (16.5%) + 2(0.5) 0.45(15.5%)(16.5%)]
= 0.5[(15.5%) + (16.5%) + 2 × 0.45 × 15.5% ×16.5%]
2
2
1
2
1
2
= 13.63%
Note that this is lower than the volatility of either of the two indexes.
b. Market watchers have noticed slowly increasing correlations between the United
States and the EAFE index, which some ascribe to the increasing integration of
markets. Given that the volatilities remain unchanged, is it possible that the
volatility of a portfolio that is equally weighted between the two indexes has
higher volatility than the U.S. market?
Answer: Yes. For example, when ρ = 1.00, the variability of the equally weighted
portfolio would just be the average volatility. There would be no risk reduction through
diversification.
2. Let the expected pound return on a UK equity be 15%, and let its volatility be 20%.
The volatility of the dollar/pound exchange rate is 10%.
a. Graph the (approximate) volatility of the dollar return on the UK equity as a
function of the correlation between the UK equity’s return in pounds and changes
in the dollar–pound exchange rate.
Answer: The formula to use is:
Vol[r($)] = [{Vol[r(£)]}2 + {Vol[s]}2 + 2 ρ Vol[r(£)] Vol[s]]1/2
where ρ is the correlation. It is easy to see that the dollar volatility will be an increasing
function of ρ. In particular:
Vol[r($), ρ = -1] = 10%
Vol[r($), ρ = 0] = 22.36%
Vol[r($), ρ = 1] = 30%
This formula assumes away the “cross-term.”
72 Chapter 13: International Capital Market Equilibrium
b. Suppose the correlation between the UK equity return in pounds and the
exchange rate change is 0. What expected exchange rate change would you
expect if the UK equity investment is to have a Sharpe ratio of 1.00? (Assume that
the risk-free rate is 0 for a U.S. investor.) Does this seem like a reasonable
expectation?
Answer: The Sharpe ratio =
E[r($)]
, and Vol(r($)) = 22.36%, see Question a.
Vol[r($)]
We also have: E[r($)] ≈ E[r(£)] + E[s] = 15% + E[s], as the expected pound return was
given, but the expected exchange return must be computed to make the Sharpe ratio
equal to one. That is, we must have
15% + E[s]
= 1 , or E[s] = 7.36%.
22.36%
It seems rather unreasonable for the expected exchange rate change to be 7.36%
unless there is a large interest differential between the two currencies (with the U.K.
interest rate substantially lower than the U.S. interest rate).
3. Suppose General Motors managers would like to invest in a new production line and
must determine a cost of capital for the investment. The beta for GM is 1.185, the beta
for the automobile industry is 0.97, the equity premium on the world market is assumed
to be 6%, and the risk-free rate is 3%. Propose a range of cost-of-capital estimates to
consider in the analysis.
Answer: The formula to use is the following:
Cost of GM equity capital = risk free rate + beta times market risk premium.
We compute two estimates, using the two available beta estimates, one for GM and one for the
automobile industry, which may be more precise (assuming GM’s financial leverage is not too
different from that of the industry as a whole). Using GM’s beta, we obtain 3% + 1.185 x 6% =
10.11%. Using the industry beta, we obtain 3% + 0.97 x 6% =8.82%. So, considering a range
between 8.80% and 10.20% is a reasonable range of cost-of-capital estimates to consider. In
fact, there is also considerable uncertainty about the size of the equity premium on the world
market, which may call for an ever-wider range of cost of capital estimates.
Chapter 13: International Capital Market Equilibrium 73
4. Thom Yorke is a typical mean-variance investor. He likes high-expected returns and
hates high variability in his portfolio returns. He is currently invested 100% in a
diversified U.S. equity portfolio. The expected return on the portfolio is 12.46%, and the
portfolio’s volatility (standard deviation) is 15.76%. Thom is considering adding some
alternative investments to his portfolio. One investment he is considering is the STCMM
fund, which invests in U.S. small-capitalization, high technology firms. Yorke has
determined that the expected return on the fund is 14.69%, that its volatility is 32.5%,
and that its correlation with his current portfolio is 0.7274. He is also intrigued by the
LYMF fund, which invests in several emerging markets. The expected return on the fund
is only 12%; it has 35% volatility and a correlation of 0.2 with his portfolio. The
correlation of the LYMF fund with the STCMM fund is 0.15. Assume that the risk-free rate
is 5%.
a. If Yorke is interested in improving the Sharpe ratio of his portfolio, will he invest a
positive amount in one of the funds? Which one? Carefully explain your
reasoning.
Answer: We established that you will add an asset to your portfolio if
E[r*] - rf
E[r] - rf
> corr[r, r*]×
Vol[r*]
Vol[r]
with * indicating the new funds.
Plugging in the numbers, we obtain:
Sharpe Ratios
Investment
Threshold
(Hurdle Rate)
U.S. portfolio
0.4734
STCMM fund
0.2982
0.3444
LYMF
0.2
0.0947
For example, 0.2982 = [14.69% - 5%]/0.325 and 0.3444 = 0.4734 x 0.7274.
Although the LYMF (“Lose Your Money Fast”) fund has a much lower Sharpe ratio than
the STCMM (“Short-Term Money Mis-Management”) fund, it will get added to the
portfolio, because of its low correlation with Thom's portfolio. The STCMM fund pretty
much looks like a levered version of the portfolio Thom already has and seems not to
eliminate much systematic risk.
b. Suppose Yorke is moderately risk averse (meaning he hates variability quite a bit),
but his friend, Nick Cave, is really quite risk tolerant and focuses primarily on
expected returns. Both cannot short-sell securities, and both are thinking of splitting
their entire portfolio between the U.S. portfolio that Yorke is currently holding, the
STCMM fund, and the LYMF fund. They also do not invest in the risk-free asset and
do not consider levering up risky portfolios. Compare the two investors’ optimal
holdings. Who will invest more in the LYMF fund, and who will invest more in the
STCMM fund? Why?
Answer: While it is impossible to answer this question precisely without more information
about how the two funds correlate, some outcomes are very likely. Maybe somewhat
surprisingly the "risky" emerging markets fund will be held by the least risk-tolerant
investors. Although very risky by itself, when added in small proportions to the portfolio
Thom already has, the emerging market fund is a wonderful diversifier. He will surely hold
74 Chapter 13: International Capital Market Equilibrium
the fund, since he can lower his risk without lowering expected returns much. Nick Cave on
the other hand may actually invest a bit in the STCMM fund. If his preferences are such that
he requires more than 12.46% return, he must hold some of the fund, since he cannot
reach a better return with the two other investments. Needless to say, he will move along
the mean-standard deviation frontier in riskier territory.
5. International economists continue to be puzzled by the phenomenon that investors
worldwide seem to be plagued by the home asset bias. Economists have pointed out
that investors with mean-variance preferences (that is, they like higher expected returns
and dislike higher volatility) ought to allocate much more of their wealth to foreign
equities and bonds. Three explanations for the phenomenon are given below, all of them
based on empirical facts. For each one of them, discuss whether the statements are true
or false and in what sense they help rationalize or fail to rationalize the home bias
puzzle. In answering the questions, assume that investors indeed have mean-variance
preferences.
a. Investors should not hold foreign equities because they are more volatile and have
been yielding lower returns than U.S. stocks in recent years.
Answer: This explanation is totally false. We established that you should add foreign
securities to your portfolio as soon as the foreign Sharpe ratio exceeds the American
Sharpe ratio times the correlation between the U.S. portfolio return and the foreign security
return. Since these correlations are quite low, foreign securities definitely belong in your
portfolio (at even rather low expected returns). The dimension totally forgotten in the
statement here is correlation! Moreover, the statement seems to suggest that returns from
the recent past will extrapolate into the future, whereas what drives optimal asset
allocations is the expected return.
b. Home bias arises because investors face an additional risk when investing
internationally—namely, currency risk. Because currency risk makes returns more
volatile but does not lead to a higher expected return, investing more in domestic
assets is rational.
Answer: This is a much more subtle and rather sensible statement at first. Currency
volatility drives up the volatility of foreign investment returns, although not by as much as
one would think because the correlations between currency returns and equity returns are
small. The problem is worse for bond returns though. Is the additional risk rewarded? Well,
if the unbiasedness hypothesis holds, the foreign expected return on a hedged and
unhedged investment is the same, so it is not rewarded. Moreover, most of the currency
risk can be hedged away using forward contracts. This latter point makes this statement an
unlikely explanation for the home bias phenomenon under UIRP, because one can
eliminate the unrewarded risk using a rather "cheap" hedge. If UIRP does not hold,
investors in some countries will earn risk premiums by investing internationally, which
should make international investing attractive for at least a number of investors.
c. Home bias arises because investors have a non-traded domestic asset that they
care about as well—namely human capital. The returns to this asset can be thought
of as labor income. It has been empirically determined that labor income correlates
quite highly with U.S. stock returns.
Chapter 13: International Capital Market Equilibrium 75
Answer: If the empirical statement about the correlation is true, human capital makes the
home asset bias worse! This was the conclusion of an article by Marianne Baxter and
Urban Jermann, published in the American Economic Review. To improve your portfolio's
risk profile, you want to add assets, which have low correlations with your domestic assets.
If investors turn out to have another domestic asset that correlates high with U.S. stocks
(and which they really cannot get rid of!), they will be looking even harder for assets with
low correlation with these domestic assets, which are to be found in the international
securities markets.
76 Chapter 13: International Capital Market Equilibrium
6. Consider Softmike, a software company. Softmike’s world market beta is 1.75. When a
regression is run of Softmike’s return on the world market return and the global HML
factor, the betas are 1.50 and –1.2, respectively. Assume that the world equity premium
is 6%, the HML premium is 3%, and the risk-free rate is 5%. Compute the cost of equity
capital using both the CAPM and the Fama-French model. Is Softmike a value company
or a growth company?
Answer: According to the CAPM, Softmike’s cost of equity capital is:
5% + 1.75 x 6% = 15.50%.
According to the two-factor international Fama-French model, the cost of capital is:
5% + 1.50 x 6% -1.2 x 3% = 10.40%.
The Fama-French model yields a much smaller cost of capital because Softmike is a growth
company and loads negatively on the value factor, which in the Fama-French model is
assumed to carry a positive premium.
Chapter
14
Political and Country Risk
QUESTIONS
1. Describe the differences between country risk and political risk. What is sovereign
risk?
Answer: Political risk is the risk that a government action will negatively affect a company’s
cash flows. In the most extreme form of political risk, governments seize property without
compensating the owners in a total expropriation (or nationalization).
Country risk is a broader concept that encompasses both the potentially adverse effects of a
country’s political environment and its economic and financial environment. For example, a
recession in a country that lowers its aggregate demand and reduces the revenues of
exporters to that nation is a realization of country risk. Labor strikes by a country’s
dockworkers, truckers, and transit workers that disrupt production and distribution of
products, thus lowering profits, also qualify as country risks. Clashes between rival ethnic or
religious groups that prevent people in a country from shopping can also be considered
country risks. In international bond markets, country risk refers to any factor related to a
country that can cause a borrower to default on a loan. When country risk is taken in a
narrow sense to be the risk associated with a government defaulting on its bond payments,
it is called sovereign risk.
2. What economic variables would give some indication of the country risk present in a
particular country?
Answer: To help investors discriminate between financially and economically sound and
financially and economically troubled countries, a number of economic variables are used,
including the following:
y The ratio of a country’s external debt to its GDP
y The ratio of a country’s debt service payments to its exports
y The ratio of a country’s imports to its official international reserves
y A country’s terms of trade (the ratio of its export to import prices)
y A country’s current account deficit
These variables are directly related to the ability of the country to generate inflows of
foreign exchange. Factors such as inflation and real economic growth are useful as well.
101
Chapter 14: Political and Country Risk 67
3. Suppose an MNC is considering investing in Bolivia. Will an overall assessment of
Bolivia’s country risk suffice to understand the political risk present in the
investment?
Answer: First, an analysis of country risk may definitely be informative about political risk in
a narrow sense. The better a country’s economic situation, the less likely it is to face political
and social turmoil that will inevitably harm foreign and domestic companies. However, as the
answer to question 1 notes, country risk is broader than political risk. Consequently, the
MNC should try to find measures and analyses that focus more narrowly on political risk in
Bolivia (such as the political risk ratings from the PRS group).
Second, the industry in which a multinational corporation operates can affect its
exposure to political risk. Calculating a company’s industry-specific risk is not as
straightforward as calculating more general political risks. The MNC should consider issues
such as whether it has primarily local competitors (more subject to political risk) rather than
primarily foreign competitors (less subject to political risk). Analogously, if the MNC is the
source of considerable foreign exchange earnings for the host country or is the vehicle for
important technology transfer, it might be less subject to government interference than one
without such advantages. The MNC must also ask whether the region in which it operates
has more or less political risk than Bolivia as a whole. This raises questions such as: How
much power do the country’s regional governments have versus the national government?
What is the attitude of local communities to the MNC’s proposed projects? Are there any
armed opposition groups in the area, and how do they view the presence of a foreign
company?
4. What are three political risk factors?
Answer: Political risk factors include the risk of expropriation (see Question 1), contract
repudiation (when government revoke contracts without compensating companies for their
existing investments in projects or services), currency controls that prevent the conversion of
local currencies to foreign currencies, and laws that prevent MNCs from transferring their
earnings out of the host country. Corruption, civil strife, and war are also factors.
5. When, where, and why did the Debt Crisis start?
Answer: The Debt Crisis started in Mexico on August 12, 1982 when Mexico announced that
it could no longer make the scheduled payments on its foreign debt. Mexico requested loans
from foreign governments and the IMF, and it started negotiating with its commercial bank
creditors. This constituted the start of the Debt Crisis. By the end of the year, 24 other
countries had requested restructuring on their commercial bank debts.
The Debt Crisis indirectly resulted from the large oil price increases that occurred in
the 1970s. The OPEC countries saved their windfall income in the form of Eurocurrency
deposits at international banks (usually denominated in dollars) at floating interest rates. The
banks in turn loaned these “petrodollars,” as they were called at the time, to developing
countries, typically in the form of Eurocredits that were quoted at a spread above the floating
interest rate they paid to the OPEC countries.
Banks viewed the lending as profitable and relatively riskless for three reasons. First,
the loans were made at a spread over the banks’ borrowing costs. Thus, the banks were not
exposed to changes in interest rates, as they would have been if they had borrowed short
term and loaned at long-term fixed rates. Second, the banks eliminated exchange rate
68 Chapter 14: Political and Country Risk
exposure as the debts were denominated in dollars, which was the currency the OPEC
countries had deposited. Third, the banks syndicated the loans, taking diversified exposures
to a number of countries to avoid too much exposure to a single country. As a result, during
the 1970s, the debt of non-OPEC developing countries owed to banks in industrialized
countries, especially banks in the United States, increased significantly.
A mix of external shocks affecting industrialized countries and developing countries in
the 1980s and macroeconomic mismanagement in developing countries triggered the actual
Debt Crisis. The steep increase in the oil price in the late 1970s was met with a staunchly
anti-inflationary monetary policy in a number of countries, particularly in the United States
under Federal Reserve Bank Governor Paul Volcker. The macroeconomic situation in the
developed world was now totally different than it had been in the early 1970s: Real interest
rates were high, the global economy was in recession, and the dollar was strong. This
situation contributed to low prices of commodities on the world markets and low demand for
the exports of developing countries.
With the huge dollar appreciation and high dollar interest rates, the developing countries
faced steep interest payments in dollars at the same time as their export revenues were
falling. Suddenly, the default risk of the loan portfolios of international banks had greatly
increased. The situation was exacerbated by the fact that developing countries often had not
used the money they borrowed very productively and had run what were ultimately seen to
be unsustainable economic policies.
6. What is debt overhang?
Answer: Debt overhang is the notion that a country saddled with a huge debt burden has
little incentive to implement economic reforms or stimulate investment because the resulting
increase in income will simply be appropriated by the country’s creditors to pay an
outstanding large debt. From this perspective, it may be better in certain situations for
countries to stop or severely restrict repaying their debts.
7. What is a debt buyback? Why was a program of debt buybacks not sufficient to
resolve the Debt Crisis?
Answer: A debt buyback is one example of the policies that many countries attempted to
employ in an effort to reduce their debt burden. In a debt buyback, the country repays a loan
at a discount. Such efforts did not suffice to resolve the Crisis for various reasons. First,
programs such as debt buybacks require monetary resources, which were in limited supply.
Second, such programs may not be very effective in reducing the outstanding debt. Several
economists argue that when a country uses its own resources to buy back its troubled debt
at a discount, the country’s creditors are the only ones that benefit. Essentially, the debt
buyback program drives up the secondary market price of the debt, reducing its
effectiveness. For example, in the famous case of the 1988 Bolivia debt buyback, Bolivia
used $34 million in donations to reduce the market value of its debt by only $8.8 million. It is
ultimately more effective to deal with a solvency problem by taking a comprehensive
approach that involves debt relief. That is essentially what the Brady plan set out to do.
Chapter 14: Political and Country Risk 69
8. What were the main characteristics of the Brady Plan?
Answer: The 1989 Brady Plan, developed by then U.S. Treasury Secretary Nicholas
Brady, had the following important characteristics: 1) It put pressure on banks to offer
some form of debt relief to developing countries. 2) It called for an expansion in secondary
market transactions aimed at debt reduction. 3) The IMF and the World Bank were urged
to provide funding for these “debt or debt service reduction purposes.” 4) It offered banks a
menu of different debt-reduction methods, including providing new loans. Each bank could
choose the restructuring option that it found most suitable from a menu of possibilities
established in a debt-reduction agreement between the debtor-country government and its
creditor banks. In order to mitigate free-rider problems, no bank could opt out. Among the
options available to the banks were the following:
y Buybacks: The debtor country was allowed to repurchase part of its debt at an agreed
discount (a debt-reduction option).
y Discount bond exchange: The loans could be exchanged for bonds at an agreed
discount, with the bonds yielding a market rate of interest.
y Par bond exchange: The loans could be exchanged at their face value for bonds
yielding a lower interest rate than that one on the original loans.
y Conversion bonds combined with new money: Loans could be exchanged for
bonds at par that yielded a market rate of return, but banks had to provide new money
in a fixed proportion of the amount converted (an option for banks unable or unwilling
to participate in debt reduction or debt service reduction).
Because the bond options were particularly popular choices, the Brady Plan ended
up securitizing the debt into easily tradable bonds, called Brady Bonds. Quite a few Brady
bonds have “official enhancements” attached to them, such as collateral provisions funded
by international organizations and certain governments.
9. Why should the discount rate not be adjusted for political risk?
Answer: Consider a multinational corporation with a shareholder base that is globally
diversified. In this case, the discount rate should reflect only international, systematic risks.
Chapter 13 showed that systematic risks are typically related to how an MNC’s return in a
particular country covaries with the world market return. If the risk of loss from political risk
does not covary with the world market return, no adjustment to the discount rate is
necessary. Positive covariation between the cash flows from the project and the world
market return increases the required global discount rate. Consequently, unless political
risk, which adversely affects the MNC’s investment returns, is systematically high when the
world market return is low, political risk should not enter the calculation of the discount rate.
Instead, the company’s cash flows should be adjusted for the presence of political risk.
To fully understand this argument, suppose a company takes out an insurance policy
against political risk and that the policy covers all contingencies and has no deductible. In
this case, a company would simply compute its expected cash flows as if there were no
political risk and then subtract the insurance premium it must pay each year from the cash
flows of the project. The cash flows would then be discounted at the usual discount rate.
While it is possible to purchase political risk insurance, it is seldom the case that an
investment can be fully insured. If a company chooses not to purchase political risk
insurance, it must incorporate into its forecasts of future cash flows how they might be
affected by various political risks, such as expropriation, unexpected taxation, and so forth.
70 Chapter 14: Political and Country Risk
10. What are some examples of organizations that provide country risk ratings?
Answer: Organizations such as Euromoney, Institutional Investor, the Economist Intelligence
Unit, and Political Risk Services Group produce country risk ratings for most countries in the
world. Both quantitative information from countries and qualitative information obtained from
experts are used to evaluate country and political risks.
11. How can we use current quantitative information to predict future political events,
such as expropriation?
Answer: Most risk-rating services look for measurable attributes and indicators that, in the
past, have been correlated with future risk events. For example, left-wing governments may
be associated with actions that harm foreign investors, such as stricter labor regulations or
outright nationalization. Countries with unstable governments and frequent, forced elections
have a higher probability of electing left-wing officials within a particular period than
countries with stable governments. This is true even if a right-wing government may be in
power currently. Consequently, the frequency of government changes is used as a risk
attribute. Generally, political risk services examine indicators of political risk, such as the
following:
y Political stability (for example, the number of different governments in power over time)
y Ethnic and religious unrest; the strength and organization of radical groups
y The level of violence and armed insurrections; the number of demonstrations
y Property rights enforcement
y The extent of xenophobia (fear of foreigners); the presence of extreme nationalism
The different political variables are then weighted and added to provide one country
score. Such overall scores may be the best indicators of an extreme political risk event, such
as expropriation. Some services, such as the PRS Group, do provide subcomponents that
may be more correlated with the specific political risk event, such as “democratic
accountability” and “government stability.” In particular, one subcomponent, Investment
Profile, specifically considers risk factors that directly affect the risk of expropriation.
12. Suppose a multinational corporation is particularly worried about ethnic warfare in a
few countries in which it is considering investing. Do country risk ratings have
information on this particular risk?
Answer: Yes, some rating services, such as the PRS Group’s ICRG (International Country
Risk Guide) system have subcomponents within their overall political risk rating. It so
happens that “ethnic tensions” is one such subcomponent, providing assessment of
disagreements and tensions between various ethnic groups that may lead to political unrest
or civil war. Other subcomponents that may also be worthwhile investigating are “internal
conflicts” (an assessment of internal political violence in the country) and “religious tensions”
(an assessment of the activities of religious groups and their potential to evoke civil dissent
or war).
Chapter 14: Political and Country Risk 71
13. Can Brazil issue a bond denominated in dollars at the same terms (that is, at the same
yield) as the U.S. government? Why or why not?
Answer: When a sovereign borrower issues bonds in its own currency, there is technically
no default risk because the government can typically simply print money to pay back the
debt holders. When a sovereign borrower issues bonds in a different currency, though, a
default is possible because the government must earn foreign exchange to pay off the
bondholders. This possibility of default will be priced into the yield on the bond. Hence,
Brazil will face a higher yield on its dollar borrowings than the U.S. government does. The
difference between the two yields is called the country credit spread. For example, if the
yield on a 5-year U.S. Treasury bond is 5%, and the yield on a 5-year dollar bond issued by
the Brazilian government is 10%, the Brazilian country credit spread is 5%. These spreads,
which vary over time as the bonds trade in secondary markets, are, of course, an indication
of country risk.
14. What stops governments from defaulting on loans or bonds held by foreigners?
Answer: Sovereign defaults are different from a company going bankrupt because it is very
difficult to take a country to court, and there are no formal bankruptcy proceedings in place
for sovereigns. Nonetheless, sovereigns still must worry about the consequences of
defaulting because of the following issues:
y The assets of the country located in the jurisdiction of a creditor may be seized.
y The country will not be able to borrow as readily in the future, which can have grave
economic consequences.
y The country could find its ability to engage in international trade severely curtailed.
These costs of defaulting must be weighed against the benefit that the debt must no
longer be serviced. Governments have defaulted on bonds periodically throughout history, a
recent example being Argentina in 2001.
15. What is a Brady bond?
Answer: Brady bonds were created as a consequence of the Brady plan which aimed at
resolving the Debt Crisis for many countries. In February 1990, Mexico became the first
country to issue Brady bonds, and Brady deals were subsequently done by Argentina,
Brazil, Bulgaria, Costa Rica, the Dominican Republic, Jordan, Nigeria, Philippines, Poland,
Uruguay, and Venezuela.
The vast majority of outstanding Brady bonds are U.S. dollar denominated, and they
tend to have very long maturities (20 to 30 years). The bonds are evenly divided between
fixed and floating-rate instruments.
Brady bonds have a number of special features:
y Principal collateral: All par and discount bonds are collateralized by U.S. Treasury
zero-coupon securities having similar maturities.
y Interest collateral: For some bonds, the government issuing the Brady bonds deposits
money with the New York Federal Reserve Bank in amounts covering 12 to 18 months’
of interest payments on a “rolling” basis.
y Sovereign portion: The remaining cash flows are subject to sovereign risk.
Bonds sometimes also include detachable warrants or recovery rights predicated on
a country’s economic performance. Mexico’s Value Recovery Rights (VRRs), for example,
72 Chapter 14: Political and Country Risk
were based on numerous variables, including oil prices, GDP, and oil production levels. In
June 2003, Mexico retired the last of $35 billion in Brady bonds.
16. Should the “stripped” yield on a Brady bond typically be higher or lower than the
regular yield? Explain.
Answer: It should be higher as the stripped yield removes the effect of the collateral
enhancements. It is the yield-to-maturity of the unenhanced interest stream after removing
the present value of the U.S. Treasury zero-coupon bond that collateralizes the principal and
the present value of the guaranteed interest stream. This stripped yield is truly based on the
credit quality, or sovereign risk, of the issuing nation. The collateral enhancements imply
that the difference between the yield-to-maturity on the Brady bond and a U.S. Treasury
bond of comparable maturity (sometimes called the “blended” yield) cannot really be viewed
as a country spread.
17. How is a political risk probability related to a country spread?
Answer: First, recall that the country spread is an indication of the default risk of a bond.
However, although a government might default on its bonds as a result of a political event,
this does not necessarily mean that it will also expropriate the assets of the MNCs that lie
within its borders. Hence, the correlation between political risk and sovereign default risk is
far from perfect.
Second, even when we assume that the political risk probability is perfectly
correlated with the probability of default, the probability of default is not easily recovered
from the yield spread. In fact, the information needed is not the spread itself but the bond’s
price, coupon rate, U.S. interest rates (assuming the bond is dollar denominated) and
potentially information on collateral enhancements. We can then estimate this probability by
making some additional assumptions:
y the political risk probability is constant over time.
y the recovery value in the case of default is zero (although computations could be made
assuming a particular recovery value).
y default is an idiosyncratic risk.
The computations should also take into account any collateral enhancements.
As a simple example, assume a bond with price equal to $92 (per $100 par value).
Assume that the coupon rate is 7%, that the bond has only 2 years to go, and that the oneyear and two-year U.S. dollar interest rates are 5%. We denote the probability of default by
p. The first year, the probability that $7 is paid to the bondholders is 1 – p. The second year,
there is a probability of (1 – p)2 that the bond will not be in default, and there is a probability
of (1 – p) p that there will be a default. It therefore must be the case that
<DM> 92 = (1 - p)
7
107
+ (1 - p)2
1.05
1.052
Here, we equate the value investors assign to the bond with the present value of the
expected cash flows, discounted at U.S. risk-free rates. We can do this because the
possibility of default is taken into account in the probabilities, and we assume that default is
an idiosyncratic risk. This equation can be solved for p, the probability of default. We find p =
6.01%. If we believe sovereign risk as reflected in this default probability is perfectly
correlated with the political risk embedded in a cash flow analysis for capital budgeting, this
is the probability we should use.
Chapter 14: Political and Country Risk 73
18. What are Cetes? What are Tesobonos?
Answer: Cetes are treasury bills issued by the Mexican government, denominated in
Mexican peso. Tesobonos are also treasury bills issued by the Mexican government, but
they are effectively U.S. dollar denominated. That is, while both the purchase amount and
the principal payment are denominated and made in pesos, the principal payment is fully
indexed to the change in the exchange rate between the dollar and the peso.
Let’s consider an example using a 3-month Tesobonos. Suppose the yield on the
Tesobonos is 5%. If the Mexican peso exchange rate didn’t change in value, the investor
would receive
<DM> 1 +
0.05
= MXN1.0125
4
after 3 months. Suppose though that the Mexican peso devalues by 5% over the 3-month
period. Then, the amount paid to the investor will be
⎛
⎝
<DM> ⎜1 +
0.05 ⎞
⎟1.05 = MXN1.063125.
4 ⎠
Note that this represents a 25.25% (6.3125% × 4) return on an annualized basis. Hence,
Tesobonos provided investors with protection against peso devaluation.
19. What are the three main types of political risk covered by political risk insurance?
Answer: Insurance is typically available for currency inconvertibility (when a company is
unable to convert its foreign earnings to its home currency or otherwise transfer the earnings
out of the host country), expropriation (protects MNCs and lenders against confiscation,
expropriation, nationalization, and other acts by the host government that adversely affect
the MNC’s cash flows, including “creeping expropriation” – a series of acts that cumulatively
result in some expropriation of value – discriminatory legislation, the deprivation of assets or
collateral, the repudiation of a concession, and the failure of a sovereign entity to honor an
arbitration award issued against it), and war and political violence (compensates a company
when war or civil disturbances cause damage to the MNC’s assets or cash flows).
20. What are some organizations or firms that provide political risk insurance?
Answer: There are three potential sources of political risk insurance: international
organizations aimed at promoting foreign direct investment (FDI) in developing countries,
government agencies, and the private market. Among international organizations providing
insurance, the World Bank’s Multilateral Investment Guarantee Agency (MIGA), the InterAmerican Development Bank (IDB), and the Asian Development Bank (ADB) are the best
known. Most OECD countries have national agencies that provide domestic companies with
political risk insurance. Examples include the Overseas Private Investment Corporation
(OPIC; United States), Nippon Export and Investment Insurance (formerly EID/MITI; Japan),
the Export Development Corporation (EDC; Canada), the Export Credits Guarantee
Program (ECGD; United Kingdom), and the Export Finance and Insurance Corporation
(EFIC; Australia). The private market has grown significantly and now includes firms such as
Lloyd’s, American International Group (AIG), Sovereign Risk Insurance Ltd., and Zurich
Emerging Markets Solutions.
74 Chapter 14: Political and Country Risk
21. How is it possible to embed political risk insurance in a capital budgeting analysis?
Answer: Assuming that political risk insurance would be complete and perfect, it is
straightforward to embed political risk insurance in capital budgeting analysis because such
insurance simply generates an annual cost. The cost of the premium must be deducted from
the cash flows, and the discount rate should only reflect systematic, not political risk. Of
course, political risk insurance is typically somewhat incomplete, so it may be necessary to
consider cash flow scenarios in which political risk events still lead to loss of cash flows in
computing the expected cash flows from a project.
22. What is project finance?
Answer: Project financing is a method of financing that is specific to a particular project,
typically industrial in the nature, in which the providers of the funds are repaid primarily from
the cash flows generated by the project.
PROBLEMS
1. In February 1994, Argentina’s currency board was in place, and 1 peso was
exchangeable into 1 dollar. The following interest rates were available:
U.S. LIBOR 90 days:
3.25%
Peso 90-day deposits:
8.99%
Dollar interest rate in Argentina, 90-day deposits: 7.10%
The latter two rates were offered by Argentine banks. What risk does the
difference between the 7.10% dollar interest and 3.25% LIBOR reflect? What risk does
the difference between the rate on 90-day pesos and 90-day dollar deposits by
Argentine banks reflect?
Answer: The difference between the 7.10% dollar interest rate and the 3.25% LIBOR rate
reflects country risk, the chance that the Argentine banks will not repay the loan. Both
deposits are in dollars so the interest rate difference does not reflect currency risk. The
difference between the rate on 90-day pesos and 90-day dollar deposits by Argentine banks
reflects currency risk. The deposits are offered by Argentine banks (so the credit risk is the
same), but if the currency board is abandoned, the peso may no longer be worth 1 dollar.
2. Consider the numbers in the previous question. Assume that if the peso were to
depreciate, investors figure it will depreciate by 25%. Also, assume that if the
Argentine bank were to default on its dollar obligations, it would pay nothing to
investors. Compute the probability that the peso will devalue and the probability that
there will be a default.
Answer: We can follow the analysis done on the Tesobonos case in Chapter 14 to compute
the default probability. We equate the return of the LIBOR rate [iLIBOR] with the return for
dollar deposits in Argentina [iARG], taking into account a default probability of p.
1+i
Consequently:
LIBOR
= (1 + i )(1 - p) + 0×p
ARG
Chapter 14: Political and Country Risk 75
0.0325
4
p=1= 0.95% , or almost 1%.
0.0710
1+
4
1+
The devaluation probability computation was first illustrated in chapter 7. Under Uncovered
Interest Rate Parity, the expected return on the peso and dollar deposits at Argentine banks
should offer the same expected return. Consequently, we should have
E[S(t+1)] ⎡
0.0899 ⎤
0.0710
1+
=1+
⎢
⎥
S(t) ⎣
4 ⎦
4
(*)
where S(t+1) is the spot exchange rate at time t+1 in dollars per peso. Hence, E[S(t+1)] is
the expected exchange rate. Let q be the probability of devaluation. We have
E[S(t+1)] = (1 - q) S(t) + q S(t) (1 - 0.25) = S(t)[1 - 0.25×q]
where S(t)=1. Substituting in Equation (*), we obtain
0.0710 ⎤
⎡
1+
⎢
1
4 ⎥ = 1.85%
q=
× ⎢1 ⎥
0.25 ⎢ 1 + 0.0899 ⎥
⎣
4 ⎦
The probability of a 25% devaluation is 1.85%.
However, these computations implicitly assume that the devaluation and default
events are independent. In this case, they very likely are not. As long as the currency board
is in place, Argentine banks are much less likely to default on the dollar deposits. Let’s see
what happens under the following assumptions. There are three possible states:
1. No default occurs, and the currency board remains in place.
2. The peso depreciates, but the Argentine banks do not default.
3. Both the currency board collapses and the banks default on all their deposits and pay
depositors nothing.
We know the probability of scenario 3 occurring, as it is simply the probability of
default, p = 0.95%. Given the correlation between default and depreciation, what is the
probability of the second scenario? Let’s call it q*. The total probability of the peso
depreciating is consequently q*+p. However, when scenario 3 materializes, holders of peso
deposits receive nothing. So the expected gross dollar return on peso deposits is:
(1 - p - q*)(1 +
0.0899
0.0899
) + q*(1 +
)0.75 + p×0
4
4
where we used the fact that if the currency devalues it devalues to $0.75 / peso.
This return must equal the return on dollar deposits in the U.S. Therefore, we obtain:
0.0899 ⎤
0.0325 ⎤
⎡
⎡
(1 - p) - ⎢1 +
⎢⎣1 +
⎥
4 ⎦
4 ⎥⎦
⎣
q* =
0.0899 ⎤
⎡
0.25 ⎢1 +
4 ⎥⎦
⎣
Using p = 0.95%, we find:
q* = 1.81%.
Consequently, the total chance of some bad event happening (scenarios 2 or 3) is slightly
reduced under this assumption.
76 Chapter 14: Political and Country Risk
3. Consider a 10-year Brady bond issued by Brazil. The coupon payment is 6.50%, and
the par value has been collateralized by a U.S. Treasury bond. The current price of the
bond is $98 (per $100 in par value). Compute the (blended) yield-to-maturity for the
bond. What is the stripped yield? Assume that the spot rates on the dollar are the
ones reported in Exhibit 14.8.
Answer: We list the cash flows as in Exhibit 14.8:
Year
1
2
3
4
5
6
7
8
9
10
Dollar Cash Flows
6.5
6.5
6.5
6.5
6.5
6.5
6.5
6.5
6.5
106.5
Dollar Spot Rates
3.50
4.10
4.65
5.05
5.55
5.85
6.05
6.25
6.35
6.50
The (blended) yield to maturity for the bond is the solution to the following equation:
98 =
6.5
6.5
106.5
+
+ ... +
2
1+y
(1 + y)
(1 + y)10
Using Excel, we find:
y = 6.78%
The stripped yield takes into account that part of the bond value is collateralized by U.S.
Treasuries, in this case the par value of the bond. The current value of $100 worth of par
value is:
Collateral value =
$100
= $53.27.
(1 + 0.065)10
This means that the “stripped” price equals $98.00 - $53.27 = $44.73.
The stripped yield, y , then follows from re-doing the computation above, adjusting the
price and stripping out the par value repayment:
44.73 =
6.5
6.5
6.5
+
+
...
+
1+y
(1 + y)2
(1 + y)10
It follows that y = 7.45%. The stripped yield is substantially higher than the blended yield.
Chapter 14: Political and Country Risk 77
4. Right at the height of the Mexican peso crisis in January 1995, the default
probabilities on U.S. dollar-denominated emerging-market bonds were quite high. A
British investment bank, assuming that these bonds would pay 15 cents on the dollar
upon default, calculated a 61% chance of default on Venezuelan bonds. Consider a
bond with 5 years left to maturity, paying a coupon of 12%. The par value is 80%
collateralized by American Treasury bonds. Assume that the U.S. interest rate is 5%
for all maturities. What is the price of a bond with $100 par?
Answer: The first step in the computation is to compute the value of the collateral,
Value collateral =
80$
= $62.68.
(1.05)5
To figure out the value of the remaining cash flows, we list the cash flows and probabilities
in an exhibit:
Year
1
2
3
4
5
Discount
Factor
0.9524
0.9070
0.8638
0.8227
0.7835
No Default Case
Cash
Probability
Flow
12
0.39
12
(0.39)2
12
(0.39)3
12
(0.39)4
32
(0.39)5
Default Case
Cash
Probability
Flow
15
0.61
15
0.61(0.39)
15
0.61(0.39)2
15
0.61(0.39)3
15
0.61(0.39)4
The cash flow in year 5 reflects the coupon of 12 and the non-collateralized part of the par
value (20). Note that the probability of retrieving this $32 in full in year 5 is (0.39)5 = 0.009 <
1%. The current value of these cash flows is now simply the probability-weighted sum of the
cash flows, discounted using U.S. discount rates (see the formula in Equation (14.4)). The
n
⎛ 1 ⎞
discount factor in the 2 column reflects these interest rates and is given as ⎜
⎟ for the
⎝ 1.05 ⎠
nd
n-th year in the future. The present value of the “no default” cash flow is $7.18. The value of
the “default” cash flows is $13.77. Hence, the total value of the bond is:
$62.68 + $7.18 + $13.77 = $83.63.
The collateral represents the most important part of the value.
78 Chapter 14: Political and Country Risk
5. Badwella United Company (BUC) is worried that its banana plantation in El Salvador
will be expropriated during the next 2 years. However, BUC, through an agreement
with El Salvador’s central bank, knows that compensation of $100 million will be paid
if the plantation is expropriated. If the expropriation does not occur, the plantation
will be worth $400 million 2 years from now. A wealthy El Salvadoran has just offered
$160 million for the plantation. BUC would have used a discount rate of 23% to
discount the cash flows from its Honduran operations if the threat of expropriation
were not present. Evaluate whether BUC should sell the plantation now for $160
million. (Hint: Set up a cash flow diagram.)
Answer: Let’s first make the simplifying assumption that the probability of expropriation is
constant and let’s denote it by p. There are three possible scenarios as indicated in the
following diagram:
Scenario
Probability
Value
Discount
Factor
2
No expropriation
(1 – p)
400
1
Expropriation in year
1
p
100
Expropriation in year
2
(1 - p) p
100
= 0.6610
1.232
1
= 0.8130
1.23
1
= 0.6610
1.232
We assume that the 23% discount rate applies to the expected cash flows of the project,
and we account for the possibility of expropriation in computing expected cash flows. Hence,
we have:
400 × (1 − p) 100 × p 100 × p(1 − p)
Value project =
+
+
2
2
1.23
(1.23)
(1.23)
2
Because the problem does not mention the probability of expropriation, we cannot come up
with a final answer. BUC should evaluate the probability of expropriation in El Salvador and
check whether the value of the project is more or less than 160 million. A useful computation
is to find that value of p for which the value of the project is exactly 160 million. Using trial
and error, we find that p = 33.05%. This looks like a rather high probability of expropriation,
implying that there is only a (1 – p)2 = 44.82% chance that the full value of the project will be
realized two years from now.
Chapter 14: Political and Country Risk 79
6. You are the chief financial officer of Clad Metal, a U.S. multinational with operations
throughout the world. Your capital budgeting department has presented a proposal to
you for a 5-year ore-extraction project in Mexico. The expected year-end net dollar
cash flows are as follows:
Year
Net Cash Flow
1
$100,000
2
200,000
3
250,000
4
250,000
5
250,000
The initial required investment in plant and equipment is $500,000, and the cost of
capital is 16%.
a. What is the present value of the project? Should the project be undertaken?
Answer: We can construct the following cash flow diagram:
Year
Dollar Cash
Flows
Discount
Factors
Present Value
of the Cash
Flows
1
2
3
4
5
100,000
200,000
250,000
250,000
250,000
0.8621
0.7432
0.6407
0.5523
0.4761
86,207
148,633
160,073
138,073
119,028
Consequently, the present value of the project is 652,105 and the NPV 152,105. The project
should be undertaken.
b. You notice that the proposal does not include any analysis of political risk, but
you are concerned about potential expropriation of the investment. You therefore
decide to call a meeting to discuss political risk. Who would you invite to this
meeting? What information or data would you need? How would you arrive at a
political risk probability estimate?
Answer: You could invite people familiar with the local political and economic situation or, if
you do not have the in-house expertise, consult political ratings and the accompanying
information from any one of the political ratings services discussed in this chapter. If
available, you may also consult price information on Mexican bonds (preferably issued in
dollars) and information on premiums for political risk insurance for projects in Mexico. As
discussed at length in this chapter, it is not straightforward to convert information on country
spreads into expropriation probabilities but under certain assumptions, it can be done (see
Question 17 for an example). Political insurance premiums directly give an idea of how
much should be subtracted each year from expected cash flows to account for political risk.
80 Chapter 14: Political and Country Risk
c. Assume that, at the end of the meeting, you decide that the probability of
expropriation is between 5% and 7%. Also assume that there is no compensation
in the case of expropriation. Would you approve the project?
Answer: Let p be the probability of expropriation. We recompute the present value of the
cash flows, taking the probability of expropriation into account. This implies multiplying the
cash flow in year t by (1 – p)t. Doing this reduces the present value to 557,921 in the case of
p = 5% and 532,822 in the case of p = 7%. In both cases, you should continue to approve
the project!
d. Given the possibility of expropriation, might you want to reconsider converting
Mexican peso expected cash flows at forward rates?
Answer: It depends how these forward rates were derived. If the forward exchange rates
come from the Chicago Mercantile Exchange, they only reflect currency risk (as the CME is
an AAA organization). If the cash flow computations take into account expropriation risk,
these are the appropriate forward rates to use. If, however, the forward exchange rates were
derived using local interest rates, they will also partially reflect country and political risk.
Taking into account expropriation risk in the cash flow computations would therefore
account for the political risk twice.
Chapter
15
International Capital Budgeting
QUESTIONS
1. Can an investment project of a foreign subsidiary that has a positive net present value when
evaluated as a stand-alone firm ever be rejected by the parent corporation? Assume that the
parent accepts all projects with positive adjusted net present values.
Answer: Yes, we know that countries impose withholding taxes on the dividends that are repatriated
from subsidiaries to parent corporations. These taxes lower the value of the project to the parent. The
parent must also be aware of the possibility of future problems accessing the foreign exchange market
from the subsidiary’s country. In general, political risk could be different for a subsidiary of a
multinational corporation versus a local stand-alone firm.
2. How do licensing agreements, royalties, and overhead allocation fees affect the value of a
foreign project?
Answer: Licensing agreements, royalties, and overhead allocation fees are true costs to the subsidiary
or to the stand-alone firm that would be operating in the foreign country producing and selling the
products of the multinational corporation. Thus, licensing agreements, royalties, and overhead
allocation fees reduce the income in the foreign country. Nevertheless, these cash flows provide profit
to the parent corporation. Licensing agreements and royalties provide pure profit to the parent as no
costs are incurred, and overhead fees provide net profit as they cover costs incurred by the parent.
Thus, these cash flows are quite valuable to the parent.
3. Why does an adjusted net present value analysis treat the present value of financial side effects
as a separate item? Isn’t interest expense a legitimate cost of doing business?
Answer: The adjusted net present value approach to capital budgeting starts by valuing the free cash
flows to the all-equity cash firm. It then adds other sources of value associated with how the firm is
financed. Compared to the weighted average cost of capital approach, the numerator cash flows are
the same – the free cash flow to the all equity firm. In contrast to WACC analysis which discounts
these cash flows with a discount rate that is a weighted average of the after-tax required return on the
debt and the rate of return on the levered equity, the ANPV analysis uses the rate of return on the
unlevered assets to get the all-equity value. Students sometimes think that the deductibility of interest
as a business expense is therefore missing, and they want to reduce the all-equity free cash flows by
the after-tax interest payments. This misses the fact that the value of the interest tax shields is being
added as a separate source of value in ANPV, whereas it is included in WACC. Also, it misses the
fact that when the equity holders lever the firm, they get the principal on the debt up front and don’t
have to put as much equity into the firm for its investments. The present value of the future cash
outflows for interest payments and repayment of principal equal the initial value of the principal, in
which case it is only the tax shield that needs to be valued. ANPV does this separately.
66
Chapter 15: International Capital Budgeting 67
4. What is meant by the net present value of the financial side effects of a project?
Answer: Generally, these effects arise from the costs of issuing securities, the taxes or tax deductions
associated with the type of financing instrument used (including the tax deductibility of the interest
paid on the debt), the costs of financial distress, and the availability of subsidized financing from
governments.
5. Why is it costly to issue securities?
Answer: The investment bankers who handle the issuing of securities either to the public or to private
investors are financial intermediaries, and they must be compensated for the use of their scarce
resources. This compensation includes a monetary fee, but it also often includes an underwriting
discount, or spread. The underwriting discount between what the corporation receives from issuing
the securities and what the public pays for the securities is often a large part of the compensation of
the investment bank that underwrites the issue.
6. What is an interest tax shield? How do you calculate its value?
Answer: The interest tax shield on a debt is the deduction for interest expense. Therefore, it is equal to
the corporate tax rate times the amount of interest, τ rD D . This tax deduction is discounted at the
stated debt rate, which is the market debt rate associated with that debt. Thus, the discounted present
value of a perpetual interest tax shield is
τ rD D
(1 + rD )
+
τ rD D
(1 + rD )
2
+
τ rD D
(1 + rD )
3
+ ... = τ D
7. What is an interest subsidy? How do you calculate its value?
Answer: Interest subsidies arise when governments are willing to lend to corporations at below
market interest rates. Such subsidies add value to a project. The appropriate discount rate for an
interest subsidy is the market’s required rate of return on the debt of the corporation because the
corporation is just as likely to default on a subsidized loan from the government as it is on a normal
loan at market interest rates. Suppose that the government lets a corporation borrow a principal of D
for one period at a subsidized interest rate of rS < rD, which is the market’s required rate of return on
the corporation’s debt. The corporation borrows D in the first period, and it repays (1 + rS)D in the
second period. Because the actual interest payment is deductible, the corporation also gets a tax
deduction of τ rS D in the second period. The present value of the cash flows of the subsidized debt
discounted at the market’s required rate of return on the corporation’s debt is therefore
D-
(1 + rS ) D
(1 + rD )
+
( r - r ) D + τ rS D
τ rS D
= D S
(1 + rD ) (1 + rD ) (1 + rD )
The value of a loan at a subsidized, below-market, interest rate has two components: the present value
of the interest subsidy, which is the difference between the interest paid on a market loan and the
interest on the subsidized loan, plus the present value of the actual interest tax shield. In both cases,
the present value is taken at the market’s required rate of return on the debt.
68 Chapter 15: International Capital Budgeting
8. What are growth options? Provide an example of one in an international context.
Answer: A growth option arises when a firm undertakes a project and obtains an option to do another
project in the future. The option to do the second project adds value to the first project. A growth
option might include a firm’s ability to sell a new product that is successful in the domestic market in
the international marketplace. Growth options are specific examples of real options that also include
the ability of a firm to shut down a plant or a mine until operating conditions improve or to delay an
important operating decision until more information can be gathered. Real options are valuable.
9. What is the difference between EBIT and NOPLAT?
Answer: The acronym EBIT is earnings before interest and taxes. It represents the before-tax
operating profit of the firm. The acronym NOPLAT is net operating profit less adjusted taxes. It is
found by taking the taxes out of EBIT that would be paid by the all-equity firm. It is therefore the
after-tax operating profit of the all-equity firm.
10. Why is it important to understand and manage net working capital?
Answer: The stock of net working capital is the amount of inventory, cash, and accounts receivable
minus accounts payable that the firm must have on hand to run its business. If the business can be run
with a lower net working capital, this amount of assets could be given to investors. Conversely,
increases in net working capital use after-tax profits that the firm could otherwise use to finance
capital expenditures or pay to investors. As such, changes in net working capital are investments that
the firm makes in its future profitability.
11. What does CAPX mean, and why is it a firm’s engine of growth?
Answer: CAPX is an acronym that is short for capital expenditures. These are investments that the
firm is making in physical plant and equipment that will produce output in the future. Consequently,
if the firm wants to grow, it will have to do CAPX, and in this sense, CAPX is the firm’s engine of
growth.
12. Why is it sometimes assumed that CAPX equals depreciation in the later stages of a project?
Answer: As a project matures, there are no more planned investments in which case the scale of the
project is fixed. But, the physical plant and equipment have an economic lifetime and must be
replaced. If accounting depreciation matches economic depreciation, setting CAPX equal to
depreciation is appropriate. You should be aware that accounting depreciation often fails to match
economic depreciation because of inflation. The higher the rate of inflation, the more severe this
problem is unless the accounting depreciation is indexed to inflation in some way. Because CAPX
will be spent on real plant and equipment, the nominal amount of expenditures may be somewhat
greater than the amount the accounts are allowed to deduct for the book value of depreciation.
Chapter 15: International Capital Budgeting 69
13. What is the terminal value of a project? How is it calculated?
Answer: The terminal value of a project is the present discounted value of all future free cash flows in
the years beyond an explicit forecasting horizon. If we generate explicit forecasts of free cash flows
for the next 10 years, the terminal value is the present discounted value of free cash flows in years 11
to infinity. One typically assumes that future free cash flows will grow at the rate g, and the discount
rate for these perpetual cash flows is r. The starting value in year 11 is (1+ g) higher than the expected
free cash flows in year 10. From the perpetuity formula for a growing cash flow, we know that
Terminal value in year 10 =
E t [FCF(t+10)] (1 + g )
(r - g)
After calculating the terminal value in year 10, that quantity must then be discounted to year
0 by multiplying by the appropriate discount factor, which is 1 / (1 + r)10:
Terminal value in year 0 =
Terminal value in year 10
(1 + r )
10
The growth rate g should reflect the expected rate of inflation in the currency of the forecasts
because the project’s real capacity from its CAPX assumptions will be fully utilized, and new real
investments would have to be made for there to be additional real growth. These real investments are
typically not in the forecasts, so the only source of growth in nominal terms is expected inflation.
14. What is meant by the cannibalization of an export market?
Answer: When you choose to change how you service a market to which you are exporting, either
because you are building a new plant in the foreign country or you are expanding production in an
existing plant, you would like to know the incremental profitability of this new project.
Cannibalization of exports refers to the lost exports in this market that you are now serving differently
if no market can be found for the goods that were formerly being exported to that country. These lost
exports could be from the parent or from another one of its foreign subsidiaries in a different country.
The lost profits on these exports must be considered to be a cost of accepting the new project. If the
exports that were formerly being sent to the country can be sold elsewhere in the world, there is no
cannibalization.
15. What are the primary sources of value to IWPI-U.S. in establishing a Spanish subsidiary?
Answer: The primary sources of value for IWPI-U.S. are the dividends that will be received by the
parent that represent the after-tax free cash flows of the subsidiary, the profits from royalties and
licensing fees, and the profits on intermediate parts that are sold to the Spanish subsidiary.
16. Why are the profits on exports of intermediate goods by IWPI-U.S. to IWPI-Spain included as
part of the value of the project?
Answer: Even though the intermediate goods are sold by IWPI-U.S. to IWPI-Spain at an internally
determined transfer price, this price should incorporate profit to the parent. We explicitly discuss
transfer pricing issues in Chapter 19 where we argue that the government authorities require that
transfer prices be done at market prices that would be observed between third parties. If IWPI-U.S.
sells replacement parts for its hinges and handles, it will have a retail price for these intermediate
parts, and those prices will determine the transfer prices.
70 Chapter 15: International Capital Budgeting
17. What risks are present in the IWPI-Spain project? How do they affect the value of the project?
Answer: The primary source of risk is the business risk of selling wooden furniture in Europe. The
expected free cash flows of the project are taken from a probability distribution that represents the
possible ups and downs of the business due to cyclical fluctuations in Europe as well as idiosyncratic
events particular to IWPI. The systematic business risk of the project is reflected in the fact that the
beta of the project is 1.1. The beta is the perceived covariance of the return on the project with the
return on the world market portfolio divided by the variance of the return on the world market
portfolio. Thus, assuming an equity risk premium of 8.5%, the expected free cash flows are
discounted by an all-equity required rate of return that is 9.35 percentage points above the risk free
interest rate.
PROBLEMS
1. What percentage of the adjusted net present value of the IWPI-Spain project arises from cash
flows that will occur more than 10 years in the future?
Answer: The present value of the cash flows from years 11 to infinity is €32.06 million. The total
ANPV of the project is €84.64 million. Thus, the terminal value of the project contributes 37.9% of
the ANPV of the project.
2. How sensitive is the value of IWPI-Spain to the assumed discount rate of 20%? What happens
to the value of the project if the rate is 22% instead?
Answer: When the project was discounted with 20%, upon adding together all the costs and benefits
of the project, we found
ANPV of IWPI-Spain = – €78.40 million in initial costs
+ €70.66 million from dividends
+ €62.64 million from royalties and fees
+ €27.60 million from exports
+ €0.38 million from the interest tax shield
+ €1.76 million from the interest subsidy
= €84.64 million
When the project is discounted at 22%, the values change to
ANPV of IWPI-Spain = – €78.40 million in initial costs
+ €59.31 million from dividends
+ €53.43 million from royalties and fees
+ €23.60 million from exports
+ €0.38 million from the interest tax shield
+ €1.76 million from the interest subsidy
= €60.08 million
A 10% increase in the discount rate from 20% to 22% causes the value of the project to fall by 29%.
Furthermore, if there is cannibalization of exports, the value of the project becomes negative because
the present value of lost exports is €64.05 million.
Chapter 15: International Capital Budgeting 71
3. What would be the terminal values of the profits from IWPI-Spain if they were expected to
grow in real terms at 1% rather than 0%?
Answer: We know that the ability of the project to grow in real terms requires additional real
investments, that is, additional capital expenditures. If these capital expenditures are zero NPV
projects, the terminal value will increase by the amount of the investment.
4. How much does the value of IWPI-Spain, viewed as a stand-alone firm, change if the royalty fee
is increased by 1% and the overhead allocation fee is reduced by 1%? What is the change in
value to IWPI-U.S.? What is the source of this change in value?
Answer: We know that because the royalty and the overhead fee are costs to the stand-alone firm and
are calculated as a percentage of revenue, the profitability of the stand-alone firm is not affected by
lowering the fee from 2% to 1% and raising the royalty rate from 5% to 6%. The present value of the
after-tax royalties and fees also doesn’t change because the firm gets a tax credit for the withholding
tax paid, and it can fully utilize the tax credit. Therefore, the after-tax value of the royalties and fees
remains €62.64 million even though the royalty is taxed at a lower rate.
5. Valuing Metallwerke’s Contract with Safe Air, Inc.
Consider the discounted expected value of the 10-year contract that Metallwerke may sign with
Safe Air in Chapter 9. In the initial year of the deal, Metallwerke sells an air tank to Safe Air
for $400. It costs €696 to produce an air tank. The current exchange rate is €2/$. Assume that
15,000 air tanks will be sold the first year. Make the following other assumptions in your
valuation:
a. The demand for air tanks is expected to grow at 5% for the second year, 4% for the third
and fourth years, and 3% for the remaining life of the contract.
b. Euro-denominated costs are expected to increase at the euro rate of inflation of 2%.
c. The base dollar price of the air tank will be increased at the U.S. rate of inflation plus onehalf of any real depreciation of the dollar relative to the euro, but the base dollar price will
be reduced by one-half of any appreciation of the dollar relative to the euro. The U.S. rate
of inflation is expected to be 4%.
d. The dollar is currently not expected to strengthen or weaken in real terms relative to the
euro.
e. The German corporate income tax rate is 50%.
f. The appropriate euro discount rate for the project is 17%.
g. Metallwerke typically establishes an account receivable for its customers. At any given time,
the stock of the account receivable is expected to equal 10% of a given year’s revenue.
h. Accepting the Safe Air project will not require any major capital expenditures by
Metallwerke.
Can you determine the value of the contract to Metallwerke?
Answer: The value of the project can be determined by discounting the expected incremental free
cash flows from the project. The following spreadsheet demonstrates how to do this.
0
US Inflation
Euro Inflation
Euros per dollar
Retail Price per tank (dollars)
Cost per tank (euros)
Growth in demand
tanks sold
All cash flows below are in euros
Revenue
Cost of goods sold
EBIT
NOPLAT @ 50% tax
Working Capital
Change in Working Capital
Free Cash Flow
Discount factors @ 17%
Present value of FCF
Value of Project
72
2.0000
Valuing Metallwerke's 10-year Contract with Safe Air
Year
1
2
3
4
5
6
7
8
9
10
4%
2%
1.9615
4%
2%
1.9238
4%
2%
1.8868
4%
2%
1.8505
4%
2%
1.8149
4%
2%
1.7800
4%
2%
1.7458
4%
2%
1.7122
4%
2%
1.6793
4%
2%
1.6470
400
696
416
710
433
724
450
739
468
753
487
768
506
784
526
799
547
815
569
832
15,000
5%
15,750
4%
16,380
4%
17,035
3%
17,546
3%
18,073
3%
18,615
3%
19,173
3%
19,748
3%
20,341
11,769,231 12,604,846 13,371,221 14,184,191 14,901,911 15,655,948 16,448,139 17,280,415 18,154,804 19,073,437
10,440,000 11,181,240 11,861,059 12,582,212 13,218,872 13,887,747 14,590,467 15,328,744 16,104,379 16,919,260
1,329,231 1,423,606 1,510,161 1,601,979 1,683,039 1,768,201 1,857,672 1,951,670 2,050,425 2,154,176
664,615 711,803 755,081 800,990 841,520 884,101 928,836 975,835 1,025,212 1,077,088
1,176,923 1,260,485 1,337,122 1,418,419 1,490,191 1,565,595 1,644,814 1,728,041 1,815,480 1,907,344
1,176,923
83,562
76,637
81,297
71,772
75,404
79,219
83,228
87,439
91,863
-512,308
628,242
678,443
719,693
769,748
808,697
849,617
892,608
937,774
985,225
0.8547
0.7305
0.6244
0.5337
0.4561
0.3898
0.3332
0.2848
0.2434
0.2080
-437,870
458,939
423,600
384,064
351,091
315,261
283,088
254,199
228,258
204,964
2,465,593
The first lines establish the background data. U.S. inflation is forecast to be 4% and German
inflation is forecast to be 2%. The real exchange rate is forecast to be constant, so the nominal
euro/dollar exchange rate is forecast to satisfy relative PPP. The first year nominal exchange rate
is therefore
€2 1.02
€1.9615
×
=
$ 1.04
$
The first year retail price is set at $400, and it is assumed to grow at the U.S. rate of inflation
because there are no forecasts of real appreciation or real depreciation of the dollar. The first year
unit cost of production is €696, and it is expected to grow at the German rate of inflation.
Demand in the first year is 15,000 tanks, and demand is expected to grow at 5% in year 2, 4% in
years 3 and 4, and 3% in all remaining years. Revenue is the €/$ exchange rate times the dollar
retail price times the number of units sold. Cost of goods sold is the euro cost per unit times the
number of units. EBIT (Earnings before interest and taxes) is revenue minus costs of goods sold.
NOPLAT (Net operating profit less adjusted taxes) subtracts the 50% tax rate times EBIT from
EBIT. The only investment that the project requires is an increase in the firm’s working capital.
The stock of working capital is forecast to be 10% of revenue, and the change in working capital
in the first year is therefore €1,176,923. Subtracting the change in net working capital from
NOPLAT gives expected free cash flow because there is no incremental depreciation and no
capital expenditures. This expected free cash flow is discounted at 17%, a rate that reflects the
riskiness of the project. The value of the 10-year project is therefore €2,465,593. This valuation
assumes that Metallwerke has the spare capacity to produce the extra tanks, and that it does not
incur any additional capital expenditures because of the increased use of its capital. It also
assumes that Metallwerke does not issue any debt to finance the project.
6. Deli-Delights Inc.
Deli-Delights Inc. is a U.S. company that is considering expanding its operations into Japan.
The company supplies processed foods to storefront delicatessens in large cities. This requires
Deli-Delights to have a centralized production and warehousing facility in each of these cities.
Deli-Delights has located a possible site for a Japanese subsidiary in Tokyo. The cost to
purchase and equip the facility is ¥765,000,000. Perform an ANPV analysis to determine
whether this is a good investment, under the following assumptions:
a. The average per-unit sales price will initially be ¥400.
b. First-year sales will be 15 million units, and physical sales will then grow at 10% per annum
for the next 3 years, 5% per annum for the 3 years after that, and then stabilize at 3% per
annum for the indefinite future.
c. First-year variable costs of production will be ¥225 per unit of labor and $1.75 per unit of
imported semi-finished goods. Administrative costs will be ¥300 million.
d. Depreciation will be taken on a straight-line basis over 20 years.
e. Retail prices, labor costs, and administrative expenses are expected to rise at the Japanese
yen rate of inflation, which is forecast to be 1%. Dollar prices of semi-finished goods are
expected to rise at the U.S. dollar rate of inflation, which is expected to be 4%.
f. The yen/dollar exchange rate is currently ¥85/$, and the yen is expected to appreciate at a
rate justified by the expected inflation differential between the yen and dollar rates of
inflation.
g. There will be a 4% royalty paid by the Japanese subsidiary to its U.S. parent.
h. The Japanese corporate income tax rate is 37.5%, and there is a 10% withholding tax on
dividends and royalty payments.
i. The yen-denominated equity discount rate for the project is 13%.
73
74 Chapter 15: International Capital Budgeting
j.
k.
l.
m.
n.
Net working capital will average 6% of total sales revenue.
Capital expenditures will offset depreciation.
All of the Japanese subsidiary’s free cash flow will be paid to the parent as dividends.
The corporate income tax rate for the United States is 34%.
Deli-Delights Inc. has sufficient other foreign income that will allow it to fully utilize any
excess foreign tax credits generated by its Japanese subsidiary.
o. Deli-Delights Inc. does not plan to issue any debt associated with this project.
Answer: The solution is presented in the following spread sheet pages. The first lays out the facts.
Inflation is expected to be 4% in the United States and 1% in Japan. The current exchange rate is
¥85/$ and is expected to satisfy relative purchasing power parity in which case the yen is expected to
appreciate. Deli-Delights expects to sell 15 million units at ¥400 per unit, and its retail price is
expected to grow at the Japanese rate of inflation. Expected growth in volume is given as 10% for
three years, then 5% for three years after that, and then 3%. The imported part initially costs $1.75 per
part, and that price is expected to grow at the U.S. rate of inflation.
The next Exhibit builds the value of the subsidiary as a stand-alone firm. Revenue is retail
price time quantity. Costs of goods sold is total labor and material costs. The royalty payment is a
cost to the stand-alone firm of 4% of revenue. Depreciation is 5% of the initial investment of ¥765
million. Administrative costs are ¥300 million and growing at 1%. Revenue minus costs is EBIT.
Notice that the project is unprofitable for the first 6 years, in which case the stand-alone firm will not
owe any tax, and it will be able to avoid future taxes by taking advantage of tax loss carry forwards.
Thus, NOPLAT equals EBIT. Working capital is 6% of revenue, and we get the subsidiary’s free cash
flow by subtracting the change in net working capital from NOPLAT under the assumption that
expected future capital expenditures equal depreciation. With the low Japanese rate of inflation, this
is not a terrible assumption. Notice that free cash flows are forecast to be negative until year 10.
The discount rate is 13%, and the terminal value is calculated as a perpetuity beginning in
year 11, growing at 1%, and discounted at 13%. Thus, the terminal value is
¥10 million × 1.01
( 0.13 - 0.01) × (1.13)
10
= ¥24 million
While we are told that the demand will be growing in real terms, we have chosen the conservative
assumption that growth is equal to inflation because we have not included any additional capital
expenditures that would be necessary to finance the additional real growth.
The initial investment is ¥765 million, in which case we find that the value of the stand-alone
firm is negative ¥1,492 million. Thus, no one would want to license the Deli-Delights name and pay a
royalty to the U.S. corporate headquarters to operate in Japan.
The third exhibit takes the Deli-Delights parent perspective. The first thing to determine is the
present value of any dividends that will be received from the subsidiary. The dividends are the
positive free cash flow from the subsidiary. These only arrive in year 10. The firm must pay a 10%
withholding tax on the dividend, and it will receive that amount as a tax credit to offset U.S. taxes.
The grossed-up dividend is just the gross dividend because there is no credit given for Japanese
income taxes paid, because the Japanese subsidiary is not sufficiently profitable to have to pay tax.
Thus, the U.S. parent owes 34% of the gross value of the dividend, but it only has to pay that amount
minus the tax credit that it receives for the withholding tax.
The real value to the parent from the subsidiary comes in the form of royalty payments. These are
also subject to a Japanese withholding tax of 10%, and it will receive that amount as a tax credit to
offset U.S. taxes. The grossed-up royalty is just the gross royalty. Thus, the U.S. parent owes 34% of
the gross value of the royalty, but it only has to pay that amount minus the tax credit that it receives
for the withholding tax. The after-tax value of the royalty starts at ¥158 million in year 1 and grows to
¥292 million in year 10. The terminal value of future royalty payments, discounted to the present is
¥723 million.
Chapter 15: International Capital Budgeting 75
The net present value of the project adds the present value of the after-tax dividends and the present
value of the after-tax royalties, and subtracts the initial investment and the present value of the
negative free cash flows in years 1-9 that the parent will have to send to the subsidiary as additional
investments. The net present value of the project is ¥565 million or $7 million at the current exchange
rate.
This analysis understates the value of the project if there is profit on the intermediate parts. Since
no information was given on the profit to the parent from these parts, we assumed that this source of
value was zero.
Valuing Deli-Delights Japanese Subsidiary as a Stand-alone Firm: Basic Data
Year
1
2
3
4
5
6
7
0
USD Inflation
JPY Inflation
Yen per dollar
Retail Price (yen)
Growth in Unit Sales
Unit Sales (in millions)
Labor Cost per unit (yen)
Total Labor Cost (millions of yen)
Imported Part Cost (dollars)
Imported Part Cost (yen)
Total Part Cost (millions of yen)
76
85.00
4%
1%
82.55
4%
1%
80.17
4%
1%
77.85
4%
1%
75.61
400
404
10%
16.50
227
3,750
1.82
145.90
2,407
408
10%
18.15
230
4,166
1.89
147.36
2,675
412
10%
19.97
232
4,628
1.97
148.84
2,972
15.00
225
3,375
1.75
144.46
2,167
4%
4%
1%
1%
73.43 71.31
4%
1%
69.25
416 420
425
5%
5%
5%
20.96 22.01 23.11
234 236
239
4,908 5,205 5,520
2.05 2.13
2.21
150.32 151.83 153.35
3,151 3,342 3,544
8
9
10
4%
1%
67.25
4%
4%
1%
1%
65.31 63.43
429
433 437
3%
3%
3%
23.81 24.52 25.26
241
244 246
5,743 5,974 6,215
2.30
2.39 2.49
154.88 156.43 157.99
3,687 3,836 3,990
Chapter 15: International Capital Budgeting 77
Valuing Deli-Delights Japanese Subsidiary as a Stand-alone Firm: The Cash Flows
All cash flows below are in millions of yen
Revenue
Cost of goods sold
Royalty
Depreciation
Administrative Costs
EBIT
Potential Tax @ 37.5%
Actual Tax
NOPLAT
6,000
5,542
240
38
300
-120
-45
0
-120
6,666
6,157
267
38
303
-99
-37
0
-99
7,406
6,840
296
38
306
-75
-28
0
-75
8,228
7,600
329
38
309
-48
-18
0
-48
8,726
8,060
349
38
312
-33
-12
0
-33
9,254
8,547
370
38
315
-17
-6
0
-17
9,814
9,064
393
38
318
0
0
0
0
10,209
9,430
408
38
322
11
4
0
11
10,620
9,810
425
38
325
23
9
0
23
11,048
10,205
442
38
328
35
13
0
35
Working Capital
Change in Working Capital
CAPX = Depreciation
Free Cash Flow
360
360
400
40
444
44
494
49
524
30
555
32
589
34
613
24
637
25
663
26
-480
-139
-119
-98
-63
-49
-34
-12
-2
10
Discount factors @ 13%
0.88
0.78
0.69
0.61
0.54
0.48
0.43
0.38
0.33
0.29
Present value of FCF years 1-10
Terminal Value
Initial Investment
-425
-109
-83
-60
-34
-23
-14
-5
-1
3
24
765
NPV of Stand-alone Subsidiary
NPV of Stand-alone Sub (in $s)
-1,492
-18
78 Chapter 15: International Capital Budgeting
All cash flows below are in millions of yen
Dividends Declared
Withholding Tax @ 10%
Net of Tax Dividends Received
Foreign Tax Credit
Grossed Up Dividend
Potential U.S. Tax @ 34%
Actual U.S. Tax
After-Tax Dividends
Discount factors @ 13%
PV of Dividends yrs 1-10
Terminal Value
Royalty Cash Flows
Withholding Tax @ 10%
Net of Tax Royalty Received
Foreign Tax Credit
Grossed Up Royalty
Potential U.S. Tax @ 34%
Actual U.S. Tax
After Tax Royalty
Discount factors @ 13%
PV of Royalty yrs 1-10
Terminal Value
Initial Investment
Aditional investments
PV of additional investments
NPV to Parent
NPV of Stand-alone Sub (in $s)
Valuing Deli-Delights Japanese Subsidiary - The Parent Perspective
Year
1
2
3
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.88
0.78
0.69
0.61
0.54
0
0
0
0
0
18
6
7
8
9
10
0
0
0
0
0
0
0
0
0.48
0
0
0
0
0
0
0
0
0
0.43
0
0
0
0
0
0
0
0
0
0.38
0
0
0
0
0
0
0
0
0
0.33
0
10
1
9
1
10
3
2
7
0.29
2
442
44
398
44
442
150
106
292
0.29
86
240
24
216
24
240
82
58
158
0.88
140
267
27
240
27
267
91
64
176
0.78
138
296
30
267
30
296
101
71
196
0.69
136
329
33
296
33
329
112
79
217
0.61
133
349
35
314
35
349
119
84
230
0.54
125
370
37
333
37
370
126
89
244
0.48
117
393
39
353
39
393
133
94
259
0.43
110
408
41
368
41
408
139
98
270
0.38
101
425
42
382
42
425
144
102
280
0.33
93
425
376
109
85
83
57
60
37
34
19
23
11
14
6
5
2
1
0
723
765
563
7
Chapter
17
Risk Management and the Foreign
Currency Hedging Decision
QUESTIONS
1. Why would an entrepreneur find it desirable to hedge his or her foreign exchange risk?
Answer: An entrepreneur would find it desirable to hedge foreign exchange risk because the
profits from the entrepreneurial venture are a significant part of the entrepreneur’s wealth. Unlike
regular investors, entrepreneurs are unable to diversify away such risks through transactions in
their own portfolios. Hence, if forward rates are unbiased predictors of future spot rates, riskaverse entrepreneurs will choose to hedge their future foreign currency cash flows because doing
so will reduce the variance of the flows without changing their expected values in the domestic
currency. Therefore, reducing the variance of future profits would increase the entrepreneur’s
expected utility.
2. Explain Modigliani and Miller’s argument that hedging is irrelevant. What are the most
likely violations of Modigliani and Miller’s assumptions in actual markets?
Answer: Modigliani and Miller argued that a corporation’s financial policies, such as issuing debt,
hedging foreign exchange risk, and other purely financial risk management activities, do not
change the value of the firm’s assets unless these financial transactions lower the firm’s taxes,
affect its investment decisions, or can be done more cheaply than individual investors’
transactions can be done.
The reason that reducing the uncertainty of future cash flows, per se, does not lead to a
rationale for hedging is that it may not change investors’ perceptions of the firm’s systematic risk.
We know from modern portfolio theory that the required rate of return on the equity cash flows of a
corporation does not depend on the standard deviation of the firm’s cash flows but only on the
systematic risk associated with those cash flows. The fact that a firm’s cash flows are uncertain is
a necessary but not a sufficient condition for discounting the cash flows at a discount rate higher
than the risk-free interest rate. Hence, unlike in the case of an entrepreneurial firm, if hedging
merely reduces the unsystematic risk of the corporation’s cash flows while leaving unchanged
both the systematic risk and the expected value of the cash flows, hedging will not have any effect
on the firm’s value. Investors will still discount the same expected cash flows at the same required
rate of return that is appropriate for the firm’s systematic risk.
The assumptions of Modigliani and Miller are strong. The investment policy of the firm is
probably not invariant to the hedging decisions of the firm because of the asymmetric information
environment in which the firm operates. A primary argument for hedging is to assure the
management of a sufficiently large internally generated cash flow so that the investment decisions
of the firm are not affected by adverse fluctuations in exchange rates. Hedging also probably can
reduce the taxes that a firm pays by shifting income from good states of the world in which the firm
is profitable to bad states of the world in which the firm would otherwise be unprofitable.
137
80 Chapter 17: Risk Management and the Foreign Currency Hedging Decision
3. Suppose that after joining the treasury department of a large corporation, you find out that
it avoids hedging because the cost of hedging comes out of the treasury department’s
budget. What argument could you make to the CFO to get the firm interested in letting you
be the firm’s hedging guru?
Answer: There is something wrong with the firm if losses on hedges are booked to treasury
whereas the gains on the underlying assets that are being hedged are booked somewhere else.
You should explain to the CFO that hedging is about avoiding losses that would adversely affect
the performance of the firm. Hedging involves investing in derivative securities whose values go
down when the underlying assets of the firm go up in value, while the values of the derivative
securities rise when the underlying assets of the firm fall in value.
It is appropriate for the costs of hedging to be borne by the treasury department, but these
costs should be the personnel costs for those who are involved in the process.
4. Your CFO thinks that the value of your firm fluctuates enormously with the yen–dollar
exchange rate, but he does not want to hedge because he thinks it is an impossible risk to
hedge. Can you convince him otherwise?
Answer: If the value of the firm fluctuates with the yen-dollar exchange rate, the firm must first
determine the sign of the covariance. Suppose that the value of the firm goes up when the yen
strengthens relative to the dollar and the value of the firm is low when the yen is weak versus the
dollar. Then, the firm effectively has yen assets whose dollar value increases when the yen
appreciates. An appropriate hedge would be to denominate some of the firm’s debt in yen, thereby
getting yen liabilities which increase in value when the yen strengthens. The firm could also sell
yen forward. The profits or losses on these contracts would be
⎡ 1
⎤
1
⎢ F(t,¥/$) - S(t+k,¥/$) ⎥ × yen sold forward
⎣
⎦
There would be profit when the future exchange rate of yen per dollar rose unexpectedly, that is,
when the yen weakened and the value of the firm was low. Finally, the firm could buy yen puts,
which would give the firm the right but not the obligation to sell yen at a fixed strike price of dollars
per yen. These contracts would also provide profits when the dollar strengthened relative to the
yen.
5. What does it mean for a tax code to be convex? If a country’s corporate tax rate is flat,
does it make sense for a firm to hedge?
Answer: A convex tax code imposes a larger tax rate on higher incomes and a smaller tax rate on
lower incomes. If a country’s tax rate is flat, a key question is how losses are treated. If losses are
subsidized immediately at the same rate that gains are taxed, there is no tax advantage to
hedging. But, losses are usually not subsidized, as losses are typically only allowed to be
deducted against future income. These tax-loss carry-forwards usually do not grow with the time
value of money; nor are they indexed to inflation. Thus, the subsidy associated with a loss is less
than the tax associated with a profit, and the tax code is effectively convex. There are also other
legitimate reasons to hedge that are not tax related.
Chapter 17: Risk Management and the Foreign Currency Hedging Decision 81
6. If the tax code is convex and the forward rate equals the expected future spot rate, why
would a firm prefer to pay taxes on the hedged value of a foreign currency cash flow rather
than wait to pay the taxes on the realized foreign currency cash flow?
Answer: In the presence of a convex tax code and if the forward rate equals the expected future
spot rate, a firm would prefer to pay tax on its expected income with certainty rather than paying
its expected tax by taking the probability weighted average of the taxes on possible incomes in the
uncertain future states of the world. This is because hedging allows the firm to shift income across
different states of the world. Increasing income in states with losses avoids the low subsidy rates
and thus hedging reduces expected taxes. This increases the firm’s value.
7. Why is the gain in a firm’s value greater when more of its future foreign currency income is
in the low tax region of the tax code?
Answer: This question is somewhat poorly phrased. If all of the firm’s foreign currency income
accrued in the low tax region of the tax code, there would be no gain to hedging. The gain in a
firm’s value (from hedging) arises from the ability to shift income from states in which it is subject
to high taxes to states in which it is subject to low taxes.
8. Why would the managers of a firm take a foreign project with a lower domestic currency
NPV and a higher return variance rather than a foreign project with a higher domestic
currency NPV but a lower return variance?
Answer: This is an example of the asset substitution issue that we covered in Chapter 16.
Because shareholders only gain in good states of the world, they like the variance of the firm to be
high. When the variance of the firm is higher, the shareholders gain more in the good states of the
world. The bondholders get paid their full amount in good states of the world, and they get the
value of the firm in the bad states of the world. By accepting a high variance project, managers
may be able to shift some value from bondholders to shareholders in an asset substitution.
9. Why would a firm ever forgo a positive NPV project? How can hedging help prevent this
situation from arising?
Answer: If the firm has debt in its capital structure, we know that the managers may forego a
positive NPV investment that must be financed by shareholders because too much of the increase
in firm value accrues to bondholders. A hedging policy can help to avoid such as situation by
avoiding the losses that may plunge the firm into financial distress and make the debt risky in the
first place. By reducing the variance of income, the hedging policy makes the debt less risky in
which case it sells for a price closer to face value.
82 Chapter 17: Risk Management and the Foreign Currency Hedging Decision
10. Suppose the cash flows from financial hedging are pooled with the cash flows from a firm’s
operations and that the shareholders cannot ascertain the ultimate sources of profits and
losses. Would the managers of the firm want to hedge or to speculate in the forward
foreign exchange market?
Answer: The Peter DeMarzo and Darrell Duffie (1995) argument is the following. Shareholders
must gauge the quality of the firm’s managers based on their observations of the firm’s profitability
and its earnings, as disclosed in its accounting data. From this perspective, hedging makes good
sense at first glance. Hedging reduces the amount of “noise” in earnings data that is not due to
actions of the managers. That is, hedging increases the informational content about a manager’s
ability that is conveyed by the firm’s reported profits. DeMarzo and Duffie demonstrate that in this
situation, the accounting treatment of hedging and the optimal hedging policy are intimately linked.
Because managers are better able to gauge the different financial risks the company faces, they
have an incentive to hedge these risks to reduce the variability of the firm’s earnings and, with
that, the variability of their own income stream, which will be linked to the firm’s earnings. A
manager does not want to face an unexpected currency depreciation that adversely affects the
firm’s profits.
The disclosure of information, though, interacts with the ability of shareholders to gauge
the true ability of a manager. With additional precision, shareholders can make the managers’
compensation more sensitive to the firm’s performance. To avoid this additional variability in their
income, managers may chose not to hedge. If the additional informational content of hedged
earnings is sufficiently high, the shareholders may optimally decide not to disclose the firm’s
hedging activities, to give managers an incentive to hedge.
11. Why is an internally generated cash flow of such importance to Merck? Can’t Merck use the
financial markets as a source of funds?
Answer: Merck realized that it was operating in an environment of asymmetric information. They
needed to be assured of generating sufficiently large internal cash flows such that they could
finance their research and development projects over the course of many years. An alternative
would be to potentially suffer losses in foreign exchange markets and try to fund its investment
projects in the external capital markets. They key question to address is the following: Can the firm
successfully raise the funds that it needs at reasonable required rates of return in those states of
the world? The answer appears to be no, because the firm will be going to the financial markets
when it is unprofitable. As a result, participants in the financial markets must assess why the firm
is unprofitable. They will attribute some of the losses to adverse fluctuations in exchange rates,
but they might also assign some of the blame to poor managerial decisions. In such a case, the
firm’s managers will find it difficult to pursue the projects they believe will keep the firm
competitive. Hedging would prevent this from happening.
Chapter 17: Risk Management and the Foreign Currency Hedging Decision 83
12. True or false: The cost or benefit of hedging foreign exchange risk when a firm is selling
the foreign currency forward is accurately measured by the forward discount or premium
on the foreign currency.
Answer: We know that if the firm sells the foreign currency in the forward market when the foreign
currency is at a discount, it will generate less domestic currency revenue than if the foreign
currency had been sold at the spot rate. But, the important point is that the cash flows are in the
future. They cannot be valued directly with the spot rate because the spot rate is for current cash
flows or the present values of foreign currency amounts. When the foreign currency is at a
discount, we know that the foreign currency interest rate is higher than the domestic currency
interest rate. Thus, we must use this high foreign currency interest rate to get a present value if we
are going to use the spot rate to value the cash flow. Alternatively, we can convert the foreign
currency into domestic currency in the forward market and then discount it to the present with the
domestic interest rate. In either case, we end up with the same amount of domestic currency if
covered interest rate parity is satisfied. Thus, a forward discount does not represent a true cost of
hedging, and, by analogy, a forward premium does not supply a benefit to hedging.
PROBLEMS
1. Chapeau Rouge has a Swiss project that will return either CHF300 million or CHF250
million per year of free cash flow indefinitely. Each of the possible CHF cash flows is
equally likely. Chapeau Rouge’s CHF discount rate for these cash flows is 13% per annum,
the cost of the project is €1,100 million, and the current exchange rate is CHF1.67/EUR.
Should Chapeau Rouge accept the project? Suppose that Chapeau Rouge has a €400
million line of credit with its bank. Will Chapeau Rouge have trouble hedging the CHF cash
flows?
Answer: We need to take the present value of the project in Swiss francs and then convert to
euros at the current spot rate. Since the project’s cash flow is a perpetuity with an expected value
of CHF275 million per year, we know that the present value, when discounted at 13%, is
Present value in Swiss francs =
CHF275 million
= CHF2,115 million
0.13
Converting this present value into euros at the current spot exchange rate of CHF1.67/EUR gives
CHF2,115 million / (CHF1.67/EUR) = €1,266.70 million. Since this exceeds the cost of the
investment of €1,100 million, Chapeau Rouge should accept the project.
If Chapeau wanted to hedge the cash flows, they would want to sell CHF275 million for euros
in each year out into the indefinite future. Their credit line of €400 million would not be adequate to
allow such a substantial exchange-rate exposure. Moreover, we know that the transactions costs
of entering into longer term forward contracts increase substantially, which would significantly
increase the cost of hedging if they contract to sell more than a few years forward. Consequently,
Chapeau Rouge would continue to have a large exposure of the value of the project to a
depreciation of the Swiss franc relative to the euro.
2. Fleur de France has a project that will provide £20 million in revenue in 1 year. The project
has a euro cost of €30 million that will be paid in 1 year. The cost of the project is certain,
but the future spot exchange rate is not. Assume that there are only two possible future
spot exchange rates. Either the spot rate in 1 year will be €1.54/£ with 55% probability, or it
will be €1.48/£ with 45% probability. Assume that the French tax rate on positive income is
45%, that a firm’s losses are immediately refunded at a rate of 35%, and that the forward
84 Chapter 17: Risk Management and the Foreign Currency Hedging Decision
rate of euros per pound equals the expected future spot rate.
a. If Fleur de France chooses not to hedge its foreign exchange risk, what is the expected
value of its after-tax income on the unhedged project?
Answer: If Fleur de France is unhedged, it will either experience a positive after-tax income of
€0.44 million that will be taxed at 45% with 55% probability because
{[(€1.54/£) × £20 million] – €30 million} × (1 – 0.45) = €0.44 million
or Fleur de France will experience an after-tax loss, which is subsidized at 35%, of €0.26
million with 45% probability because
{[(€1.48/£) × £20 million] – €30 million} × (1 – 0.35) = - €0.26 million
The expected euro value of Fleur de France’s after-tax income on the unhedged project is
therefore the probability weighted average of the two possibilities:
[0.55 × €0.44 million] + [0.45 × (- €0.26 million)] = €0.125 million
b. If Fleur de France chooses to hedge its foreign exchange risk, what is the expected
value of its after-tax income on the hedged project?
Answer: The expected future spot rate is the probability weighted average of the two possible
realizations:
(0.55 × €1.54/£) + (0.45 × €1.48/£) = €1.513/£
If the forward rate equals the expected future spot rate, Fleur de France will sell the £20 million
forward and will have a sure income. Its after-tax income on the hedged project is
{[(€1.513/£) × £20 million] – €30 million} × (1 – 0.45) = €0.143 million
c. How much does Fleur de France gain by hedging?
Answer: By hedging, Fleur de France shifts income from the good state of the world with
pound appreciation to the bad state of the world with pound depreciation. It also avoids the
loss that is only subsidized at the 35% rate. Its after-tax income in the good state falls from
€0.44 million to €0.143 million, while its after-tax income in the bad state rises from a loss of
€0.26 million to €0.143 million. If Fleur de France hedges, its gain is the difference between its
after-tax income and its expected after-tax income, which is
€0.143 million - €0.125 million = €0.018 million
The gain is due to the convexity of the tax schedule. It can be demonstrated that the gain is
the probability of the bad state, multiplied by the income in the bad state, multiplied by the
difference in the tax rates or
(0.45) × {[(€1.48/£) × £20 million] – €30 million} × (0.35 – 0.45) = €0.018 million
Chapter 17: Risk Management and the Foreign Currency Hedging Decision 85
3. How would your answer to problem 2 change if instead of allowing refunds at 35%, the
refund rate were only 25%?
Answer: We know that the larger the difference between the tax rates, the larger the gain to
hedging. If the subsidy rate is only 25%, Fleur de France will experience an after-tax loss if it does
not hedge of €0.30 million with 45% probability because
{[(€1.48/£) × £20 million] – €30 million} × (1 – 0.25) = - €0.30 million
The expected euro value of Fleur de France’s after-tax income on the unhedged project is
therefore the probability weighted average of the two possibilities:
[0.55 × €0.44 million] + [0.45 × (- €0.30 million)] = €0.107 million
If Fleur de France hedges, its gain is the difference between its after-tax income and its expected
after-tax income, which is
€0.143 million - €0.107 million = €0.036 million
Notice that this is double the gain in Problem 2 because the gain is the probability of the bad state,
multiplied by the income in the bad state, multiplied by the difference in the tax rates or
(0.45) × {[(€1.48/£) × £20 million] – €30 million} × (0.25 – 0.45) = €0.036 million
4. How would your answer to problem 2 change if the possible exchange rates in the future
were €1.56/£ and €1.46/£?
We know that with a larger variance of the possible future exchange rates, the gain to
hedging is increased. Here are the numbers:
a. If Fleur de France chooses not to hedge its foreign exchange risk, what is the expected
value of its after-tax income on the unhedged project?
Answer: If Fleur de France is unhedged, it will experience a positive after-tax income of €0.66
million that will be taxed at 45% with 55% probability because
{[(€1.56/£) × £20 million] – €30 million} × (1 – 0.45) = €0.66 million
or Fleur de France will experience an after-tax loss, which is subsidized at 35%, of €0.52
million with 45% probability because
{[(€1.46/£) × £20 million] – €30 million} × (1 – 0.35) = - €0.52 million
The expected euro value of Fleur de France’s after-tax income on the unhedged project is
therefore the probability weighted average of the two possibilities:
[0.55 × €0.66 million] + [0.45 × (- €0.52 million)] = €0.129 million
b. If Fleur de France chooses to hedge its foreign exchange risk, what is the expected
value of its after-tax income on the hedged project?
Answer: The expected future spot rate is the probability weighted average of the two possible
realizations:
(0.55 × €1.56/£) + (0.45 × €1.46/£) = €1.515/£
If the forward rate equals the expected future spot rate, Fleur de France will sell the £20 million
forward and have a sure income. Its after-tax income on the hedged project is
{[(€1.515/£) × £20 million] – €30 million} × (1 – 0.45) = €0.165 million
c. How much does Fleur de France gain by hedging?
Answer: If Fleur de France hedges, its gain is the difference between its after-tax income and
its expected after-tax income, which is
€0.165 million - €0.129 million = €0.036 million
86 Chapter 17: Risk Management and the Foreign Currency Hedging Decision
5. Assume that U.S. Machine Tool has $50 million of debt outstanding that will mature next
year. It currently has cash flows that fluctuate with the dollar–pound exchange rate. Over
the next year, the possible exchange rates are $1.50/£ and $1.90/£, and each exchange rate
is equally likely. The company thinks that it will generate $30 million of cash flow from its
U.S. operations, and its expected pound cash flow is £12 million.
a. If U.S. Machine Tool does not hedge its foreign exchange risk, what will be the current
market value of its debt and equity, assuming, for simplicity, that the appropriate
discount rates are 0?
Answer: If U.S. Machine Tool does not hedge, the dollar value of its pound revenue will be
either $1.50/£ × £12 million = $18 million or $1.90/£ × £12 million = $22.8 million. With $30
million of cash flow from its U.S. operations, the company will therefore only be able to pay off
its debt in the good state of the world. Bondholders will either receive $48 million = $18 million
+ $30 million, in which case equity will be worthless, or the firm will have enough to pay the
bondholders the full $50 million, in which case equity will be worth $2.8 million = $22.8 million
+ $30 million - $50 million. Since the two states of the world are equally likely, and assuming a
zero discount rate for simplicity, the debt will sell at
0.5 × $48 million + 0.5 × $50 million = $49 million
and the equity will sell for
0.5 × $0 + 0.5 × $2.8 million = $1.4 million
b. Suppose that U.S. Machine Tool has access to forward contracts at a price of $1.70/£.
What is the value of the firm’s debt and equity if it hedges its foreign exchange risk?
Would the shareholders want the management to hedge?
Answer: If the firm hedges its pound revenue, the dollar value is $1.70/£ × £12 million = $20.4
million. There would be no additional uncertainty associated with the firm, so its revenues
would be $50.4 million = $20.4 million + $30 million. Debt would be riskless and would sell for
$50 million, and equity would be the residual claimant to the $0.4 million. Shareholders would
therefore not want the firm to hedge as they would prefer the “high variance” project.
c. Suppose U.S. Machine Tool could invest $1 million today in a project that returns £1
million next period. Is this a good project for the firm?
Answer: If the firm invests $1 million and gets £1 million next period, the dollar value of the
pounds would be either $1.5 million or $1.9 million. So, the project is certainly a positive NPV
project for the firm.
d. Suppose that U.S. Machine Tool is unhedged, that its managers are trying to maximize
the value of the firm’s equity, and that the $1 million must be raised from current
shareholders. Will the managers accept the project?
Answer: If U.S. Machine Tool does not hedge, the dollar value of its pound revenue will be
either $1.50/£ × £13 million = $19.5 million or $1.90/£ × £13 million = $24.7 million. With $30
million of cash flow from its U.S. operations, the company will still only be able to pay off its
debt in the good state of the world. Bondholders will either receive $49.5 million = $19.5 million
+ $30 million, in which case equity will be worthless, or the firm will have enough to pay the
bondholders the full $50 million, in which case equity will be worth $4.7 million = $24.7 million
+ $30 million - $50 million. Since the two states of the world are equally likely, and assuming a
zero discount rate for simplicity, the debt will sell for
0.5 × $49.5 million + 0.5 × $50 million = $49.75 million
Chapter 17: Risk Management and the Foreign Currency Hedging Decision 87
and the equity will sell for
0.5 × $0 + 0.5 × $4.7 million = $2.35 million
Because the value of the equity increases from $1.4 million to $2.35 million, which is less than
the $1 million cost of the project, the shareholders would want the management to reject the
project.
e. If U.S. Machine Tool hedges its foreign exchange risk, would the firm accept the
project?
Answer: Yes, if the firm is hedged, the debt is riskless and the equity is worth $0.4 million. The
return on the positive NPV project would therefore accrue totally to the shareholders. They
would invest $1 million and get $1.7/£ × £1 million = $1.7 million in return. Thus, their equity
would increase in value by $0.7 million.