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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

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

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

v. Generalizing

2. Exchange Rates in Practice

a. Exchange Rate Regimes: Fixed Versus Floating

b. Application: Recent Exchange Rate Experiences

i. Evidence from Developed Countries

3. The Market for Foreign Exchange

a. The Spot Contract

b. Transaction Costs

c. Derivatives

d. Application: Foreign Exchange Derivatives

i. Forwards

e. Private Actors

f. Government Actions

4. Arbitrage and Spot Exchange Rates

a. Arbitrage with Two Currencies

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

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

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.

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,

an increase in the value of one currency (appreciation) implies a decrease in the value of

the other currency (depreciation). For example, if the dollar–pound exchange rate falls

from E$/£ = 1.80 to E$/£ = 1.60, Americans must pay fewer U.S. dollars for the same

British pound. Since it takes fewer dollars to buy one pound, the dollar has appreciated

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

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

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:

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

London

£2,000

Hong Kong

HK$ 30,000

New York

$4,000

Exchange rates

HK$/£

15

16

14

$/£

2

1.9

2.1

1.9

Cost of the

London

£2,000

tuxedo in

pounds

Hong Kong

£2,000

£1,875

£2,143

New York

£2,000

£2,105

£1,905

£2,105

• Scenario 1: The exchange rates make the pound price of the tuxedo the same in all

• Scenario 2: The pound has appreciated vis-à-vis the HKD but has depreciated vis–

• Scenario 3: This is the opposite of scenario 2. The pound depreciates vis-à-vis the

• Scenario 4: The pound has depreciated vis-à-vis both currencies. Bond might as

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

■ An appreciation in the home currency leads to an increase in the relative price

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 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

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.

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

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

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

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.

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

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

liquidity. Therefore, the spread reflects market friction. In the foreign exchange markets,

these frictions are generally very small (less than $0.0001 for large trades of major

currencies).

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 establish capital controls to restrict the movement of forex

operations either coming into the country or exiting the country. The government may

The government may intervene in the forex market, which is usually the central

bank’s responsibility. The central bank can use foreign exchange reserves to buy or sell

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.

generically.

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

Case 3: ENY$/peso = ETok$/peso

Regardless of whether the market begins in Case 1 or Case 2, we know that it will settle

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

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

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

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.

Cross Rates and Vehicle Currencies

The vast majority of currency pairs are exchanged through a third currency. This is