13 Introduction to Exchange Rates and the Foreign Exchange Market
Notes to the Instructor
Chapter Summary
This chapter introduces students to exchange rates, to the foreign exchange (forex)
market, to the way foreign currency is exchanged in private and government transactions,
and to arbitrage conditions in the forex market. The chapter begins with a discussion of
Comments
Although most students have heard of exchange rates (either in the media or in previous
economics classes), few will understand how the foreign exchange market works and
how arbitrage is important in financial markets. This chapter serves two functions: (1) to
provide information on how the foreign exchange market works in practice (Sections 1
through 3), and (2) to establish a foundation for model-building in subsequent chapters
(Sections 4 and 5).
The chapter contains a large amount of detailed information. Because much of it is
fundamental in the development of concepts and models throughout the text, it is worth
spending more time on this material than might otherwise be devoted to a typical
textbook chapter. There are optional advanced topics and case studies that the instructor
may elect to skip without compromising material in later chapters.
An outline of the chapter follows.
1. Exchange Rate Essentials
a. Defining the Exchange Rate
b. Appreciations and Depreciations
c. Multilateral Exchange Rates
d. Example: Using Exchange Rates to Compare Prices in a Common Currency
i. Scenario 1
ii. Scenario 2
iii. Scenario 3
iv. Scenario 4
v. Generalizing
2. Exchange Rates in Practice
a. Exchange Rate Regimes: Fixed Versus Floating
3. The Market for Foreign Exchange
a. The Spot Contract
b. Transaction Costs
c. Derivatives
d. Application: Foreign Exchange Derivatives
i. Forwards
ii. Swaps
iii. Futures
iv. Options
e. Private Actors
f. Government Actions
4. Arbitrage and Spot Exchange Rates
5. Arbitrage and Interest Rates
i. The Problem of Risk
a. Riskless Arbitrage: Covered Interest Parity
i. What Determines the Forward Rate?
b. Application: Evidence on Covered Interest Parity
c. Risky Arbitrage: Uncovered Interest Parity
i. Side Bar: Assets and Their Attributes
ii. What Determines the Spot Rate?
d. Application: Evidence on Uncovered Interest Parity
e. Uncovered Interest Parity: A Useful Approximation
6. Conclusions
Lecture Notes
The exchange rate affects both the price Americans pay for foreign goods and services
and the price foreigners pay for U.S. goods and services. The exchange rate also affects
the cost of investment across countries. For these reasons, policy makers are concerned
with the value of the domestic currency relative to the rest of the world. Before
examining how the exchange rate fits into the economy, this chapter begins with defining
the exchange rate and then describes the market for foreign exchange.
1 Exchange Rate Essentials
An exchange rate (E) is the price of a foreign currency expressed in terms of a home
currency. Because an exchange rate is the relative price of two currencies, it may be
quoted in either of two ways:
1. The number of home currency units that can be exchanged for one unit of foreign
2. The number of foreign currency units that can be exchanged for one unit of home
currency. For example, the $1.15/€ exchange rate can also be expressed as €0.87
per U.S. dollar (or 0.87 €/$). To buy one dollar, you would have to pay €0.87.
Defining the Exchange Rate
By convention, the exchange rate is defined as units of domestic currency per unit of
foreign currency. Thus, E1/2 is the number of units of country 1’s currency needed to buy
one unit of country 2’s currency.
Consider two countries: the United States and the United Kingdom. These regions use
the U.S. dollar ($) and the British pound (£), respectively.
The exchange rate above implies an American must pay $1.80 for each British pound.
We can use this exchange rate to determine how much a U.K. resident would pay for a
U.S. dollar:
Appreciations and Depreciations
Appreciation and depreciation are terms used to describe how the value of a currency
changes over time. Because we’ve defined the exchange rate as a bilateral exchange rate,
To measure the degrees to which the currency appreciates or depreciates, we can
calculate the percentage change in the exchange rate:
Using the American terms exchange rate, the dollar has appreciated 11.1% vis-à-vis the
pound.
However, there is an asymmetry. Calculating the percentage depreciation of the
pound using the European terms exchange rate, we get
When we use the European terms exchange rate, the pound has depreciated by 11.6% vis-
à-vis the dollar. But the pound’s depreciation should be equal to the dollar’s appreciation.
Therefore, we adopt this convention when calculating percentage changes in exchange
rates:
Multilateral Exchange Rates
Because a currency may appreciate relative to some currencies while depreciating
relative to others, we need a measure of the exchange rate that accounts for these
changes. One such measure is the effective exchange rate, which uses the importance of
trade to weight appreciation/depreciation in different bilateral exchange rates. For
example, for simplicity, suppose that the United States trades only with three countries:
Canada (Canadian dollars, C$), Mexico (pesos), and Japan (yen). The percentage change
in the nominal effective exchange rate would be calculated as
We use the share of the foreign country’s trade in the total trade to “weight” the relative
importance of the appreciation/depreciation in the currency. If U.S. trade with Canada
accounts for a large share of total U.S. trade, then an appreciation/depreciation with
Example: Using Exchange Rates to Compare Prices in a Common Currency
This case study considers the price for a new tuxedo James Bond would pay in three
countries—Hong Kong, the United States, and the United Kingdom—in four different
scenarios.
Suppose James Bond is considering purchasing a tuxedo in three different markets.
The prices of a tuxedo in these three markets are:
London: £2,000
For comparison purposes, let’s convert all prices into British pounds. The table below
summarizes the calculations.
Scenario
1
2
3
4
Cost of the
tuxedo in local
currency
London
£2,000
£2,000
£2,000
£2,000
Hong Kong
HK$ 30,000
HK$ 30,000
HK$ 30,000
HK$ 30,000
New York
$4,000
$4,000
$4,000
$4,000
Exchange rates
15
16
14
14
$/£
2
1.9
2.1
1.9
tuxedo in
pounds
• Scenario 1: The exchange rates make the pound price of the tuxedo the same in all
three countries.
• Scenario 2: The pound has appreciated vis-à-vis the HKD but has depreciated vis–
à-vis the dollar. Thus, the tuxedo’s price has fallen in Hong Kong but is higher in
New York.
Generalizing The previous example highlights how changes in the exchange rate affect
the relative price of goods (in this case, James Bond’s tuxedo) across countries. There are
two important lessons from this example:
1. When comparing goods and services across countries, we can use the exchange
rate to compare prices in the same currency terms.
2. Changes in the exchange rate affect the relative prices of goods across countries
but do not affect the domestic price of the good in domestic currency terms:
2 Exchange Rates in Practice
Changes in the exchange rate affect the relative prices of a country’s exports to foreigners
and imports from abroad. These changes can be dramatic and difficult to predict. Why?
Exchange rates fluctuate over time. Some bilateral exchange rates can move as much as
10% or more over a year.
Exchange Rate Regimes: Fixed Versus Floating
Large changes in exchange rates have important implications for a country’s exports and
imports, prompting some governments to try to limit changes in the exchange rate. An
exchange rate regime refers to a government’s policy regarding the exchange rate. A
floating, or flexible, exchange rate regime is one in which the government allows the
value of the currency to change over time. A fixed, or pegged, exchange rate regime is
APPLICATION
Recent Exchange Rate Experiences
This case study highlights exchange rate regimes in practice across developed and
developing countries.
Evidence from Developed Countries Most currencies appear to float against each other.
This is known as a free float. A few European countries use an exchange rate band to
manage their domestic currency against the euro. Exchange rates can exhibit high short-
run volatility.
Evidence from Developing Countries Exchange rates in developing countries tend to be
more volatile. Some countries tried adopting fixed exchange rate regimes but were forced
to abandon them after coming under “speculative attack”. For example, Thailand and
Korea experienced an exchange rate crisis, or a sudden depreciation in their currencies
Currency Unions and Dollarization A currency union is a group of countries that
agrees to adopt a common currency. The euro is, of course, the most recent example of
such a monetary union. Dollarization occurs when a country gives up its independent
currency and uses another country’s money as its medium of exchange. The example
given in the text is the Pitcairn Islands, whose 50 residents use the New Zealand dollar as
their currency. As noted earlier, Ecuador and Zimbabwe have both resorted to
dollarization in response to crises. (Note that this policy is called dollarization even if the
currency being used is not the dollar.)
Exchange Rate Regimes of the World There are official and unofficial exchange rate
regimes. The difference occurs because some countries that adopt one regime follow
another in practice. Some countries have no currency of their own. Others have a strict
Looking Ahead The data on exchange rates in practice have important implications for
the models and analysis in the remainder of the textbook. First, the world is divided into
3 The Market for Foreign Exchange
The market for foreign exchange (forex market, or FX market) is where currencies are
traded and the exchange rate is determined. Like any market, participants include
individuals, businesses, governments, central banks, and nongovernmental organizations.
The Spot Contract
Spot contracts are contracts for immediate (“on–the-spot”) delivery. In terms of volume,
most spot contracts are executed by banks and other large financial intermediaries.
Naturally, when a tourist exchanges euros for dollars, that trade is executed in the spot
market. Those transactions are a very small fraction of the total volume of spot trades.
The spot market price is called the spot exchange rate. Throughout the rest of the
Transaction Costs
Like most financial markets, there are huge economies of scale in the forex market. When
a French tourist on vacation at Yosemite uses euros to buy dollars, the exchange rate will
not be the same as the rate offered for the high-volume transactions mentioned earlier.
Instead, the tourist will pay the retail price (exchange rate). Small transactions carry
higher costs, meaning the bank will charge a higher price for those transactions. The
spread is the difference between the “buy” and “sell” prices. To add that the banks try to
buy low and sell high would be superfluous. However, it’s generally true that buying and
For example, suppose the “wholesale” exchange rate is 0.80 euro per dollar (E$/€ =
$1.250). If our French tourist wants to buy dollars with euros, the bank is likely to charge
slightly more than this, say, 0.81 euros per dollar. (This is called the ask price.) Thus, our
If a currency is not heavily traded in the foreign exchange market, then banks may
require a higher spread to compensate themselves for exchanging an asset with less
Derivatives
Derivatives are financial instruments that derive (i.e., are created from) a spot rate. There
are many different foreign exchange rate derivatives discussed further in the following
application. Derivatives are designed to increase flexibility, both in the exchange of
goods and services across countries and in investor hedging and speculation.
APPLICATION
Foreign Exchange Derivatives
This application discusses four foreign exchange derivatives: forwards, swaps, futures,
and options. Forwards and swaps are most often used as a hedge for foreign currency
traders and for businesses engaged in high-volume transactions. Futures and options are
primarily used for foreign currency speculation and comprise a very small share of the
foreign currency market.
Private Actors
There are three types of private actors in the foreign exchange markets: commercial
banks, large corporations, and non–bank financial institutions. It is important to note
that individuals do not directly engage in foreign exchange transactions—they go through
banks or non-bank institutions to exchange currency.
Commercial banks account for the largest share of foreign currency operations. Many
Government Actions
The government may participate in the forex market in a number of ways: capital
controls, official market (with fixed rates), and intervention.
The government may establish capital controls to restrict the movement of forex
operations either coming into the country or exiting the country. The government may
establish an official market with fixed exchange rates, making it illegal to trade at any
other exchange rate. This often gives rise to black markets (or parallel markets) as private
parties seek to exchange foreign currency at a free market rate.
4 Arbitrage and Spot Exchange Rates
The market equilibrium is determined by a no–arbitrage condition. Arbitrage is a
strategy that exploits profit opportunities arising from differences in prices among
markets. The equilibrium is defined as the price at which these opportunities are
exhausted so that there is no tendency for change.
Arbitrage with Two Currencies Consider the exchange rate between the U.S. dollar and
the Mexican peso. These currencies are traded in both Tokyo and New York.
Case 1: ENY$/peso > ETok$/peso
Suppose ENY$/peso = $0.095 and ETok$/peso = $0.085. An arbitrager James can sell 10,000
Case 2: ENY$/peso < ETok$/peso
Suppose ENY$/peso = $0.095 and ETok$/peso = $0.100. James can buy 10,000 Mexican pesos
at a price of $0.095 per peso in New York (costing $950), then sell 10,000 pesos in
Case 3: ENY$/peso = ETok$/peso
Regardless of whether the market begins in Case 1 or Case 2, we know that it will settle
here, where the exchange rates in both markets are the same. When the New York price
Arbitrage with Three Currencies This occurs when an arbitrager seeks to gain a profit
from the triangular trade of three currencies. Consider two exchange rates. The first rate
is between the U.S. dollar and the Mexican peso. The second is between the U.S. dollar
Case 1: E$/peso > E$/C$ EC$/peso
Suppose E$/peso = $0.015, E$/C$ = $0.80, and EC$/peso = $0.0125. An arbitrager Ava has
$400. She can sell her 400 U.S. dollars for 500 Canadian dollars (C$500) at the rate
E$/C$ = $0.80. Ava then sells her 500 Canadian dollars for 40,000 pesos at the rate EC$/peso
Case 2: E$/peso < E$/C$ EC$/peso
Suppose E$/peso = $0.01, E$/C$ = $0.80, and EC$/peso = $0.015. In this case, Ava can sell her
400 U.S. dollars for 40,000 pesos at the rate E$/peso = $0.01. Ava then sells her 40,000
Case 3: E$/peso = E$/C$ EC$/peso
Suppose E$/peso = $0.01, E$/C$ = $0.80, and EC$/peso = $0.0125. In this case, arbitragers
such as Ava will be unable to turn a profit from arbitrage.
In studying arbitrage among three currencies, we see that we can use ratios of
exchange rates to convert between several different currencies:
Cross Rates and Vehicle Currencies
The vast majority of currency pairs are exchanged through a third currency. This is