Financial Markets and Institutions (2-downloads)

F

in terms

of dollars is the interest rate on foreign assets i

F

plus the expected appreciation of

the foreign currency, equal to minus the expected appreciation of the dollar,

.

If the interest rate on euro assets is 5%, for example, and the dollar is

expected to appreciate by 3%, then the expected return on euro assets in terms

R

F

 in terms of dollars

⫽ i

F

⫺

E

e

t

⫹1

⫺ E

t

E

t

⫺1E

e

t

⫹1

⫺ E

t

2>E

t

Relative R

D

⫽ i

D

⫺ i

F

⫹

E

e

t

⫹1

⫺ E

t

E

t

R

D

 in terms of euros

⫽ i

D

⫹

E

e

t

⫹1

⫺ E

t

E

t

1E

e

t

⫹1

⫺ E

t

2>E

t

E

e

t

⫹1

Chapter 15 The Foreign Exchange Market

371

1

This expression is actually an approximation of the expected return in terms of euros, which can be

more precisely calculated by thinking how a foreigner invests in dollar assets. Suppose that François

decides to put one euro into dollar assets. First he buys 1/E

t

of U.S. dollar assets (recall that E

t

, the

exchange rate between dollar and euro assets, is quoted in euros per dollar), and at the end of the

period he is paid 

in dollars. To convert this amount into the number of euros he

expects to receive at the end of the period, he multiplies this quantity by 

François’ expected

return on his initial investment of one euro can thus be written as 

minus his initial

investment of one euro:

This expression can be rewritten as

which is approximately equal to the expression in the text because 

is typically close to 1. To see

this, consider the example in the text in which i

D

= 0.04; 

, so 

.

Then François’ expected return on dollar assets is 

, rather than

the 7% reported in the text.

0.04

⫻ 1.03 ⫹ 0.03 ⫽ 0.0712 ⫽ 7.12%

E

e

t

⫹1

>E

t

⫽ 1.03

1E

e

t

⫹1

⫺ E

t

2>E

t

⫽ 0.03

E

e

t

⫹1

>E

t

i

D

a

E

e

t

⫹1

E

t

b ⫹

E

e

et

⫹1

⫺ E

t

E

t

11 ⫹ i

D

2¢

E

e

t

⫹1

E

t

≤ ⫺ 1

11 ⫹ i

D

2 1E

e

t

⫹1

>E

t

2

E

e

t

⫹1

11 ⫹ i

D

2 11>E

t

2

---

of dollars is 2%. Al earns the 5% interest rate, but he expects to lose 3% because

he expects the euro to be worth 3% less in terms of dollars as a result of the

dollar’s appreciation.

Al’s expected return on the dollar assets R

D

in terms of dollars is just i

D

. Hence,

in terms of dollars, the relative expected return on dollar assets is calculated by

subtracting the expression just given from i

D

to obtain

This equation is the same as Equation A1 describing François’s relative expected

return on dollar assets (calculated in terms of euros). The key point here is that

the relative expected return on dollar assets is the same—whether it is calculated

by François in terms of euros or by Al in terms of dollars. Thus, as the relative

expected return on dollar assets increases, both foreigners and domestic residents

respond in exactly the same way—both will want to hold more dollar assets and fewer

foreign assets.

Interest Parity Condition

We currently live in a world in which there is capital mobility: Foreigners can eas-

ily purchase American assets, and Americans can easily purchase foreign assets. If

there are few impediments to capital mobility and we are looking at assets that have

similar risk and liquidity—say, foreign and American bank deposits—then it is rea-

sonable to assume that the assets are perfect substitutes (that is, equally desirable).

When capital is mobile and when assets are perfect substitutes, if the expected return

on dollar assets is above that on foreign assets, both foreigners and Americans will

want to hold only dollar assets and will be unwilling to hold foreign assets. Conversely,

if the expected return on foreign assets is higher than on dollar assets, both foreigners

and Americans will not want to hold any dollar assets and will want to hold only

foreign assets. For existing supplies of both dollar assets and foreign assets to be held,

it must therefore be true that there is no difference in their expected returns; that

is, the relative expected return in Equation A1 must equal zero. This condition can

be rewritten as

(A2)

This equation, which is called the interest parity condition, states that the

domestic interest rate equals the foreign interest rate minus the expected appre-

ciation of the domestic currency. Equivalently, this condition can be stated in a

more intuitive way: The domestic interest rate equals the foreign interest rate

plus the expected appreciation of the foreign currency. If the domestic interest

rate is higher than the foreign interest rate, there is a positive expected 

appreciation of the foreign currency, which compensates for the lower foreign

interest rate.

i

D

⫽ i

F

⫺

E

e

t

⫹1

⫺ E

t

E

t

Relative R

D

⫽ i

D

⫺ a i

F

⫺

E

e

t

⫹1

⫺ E

t

E

t

b ⫽ i

D

⫺ i

F

⫹

E

e

t

⫹1

⫺ E

t

E

t

372

Part 5 Financial Markets

---

There are several ways to look at the interest parity condition. First, recognize

that interest parity means simply that the expected returns are the same on both dol-

lar assets and foreign assets. To see this, note that the left side of the interest par-

ity condition (Equation A2) is the expected return on dollar assets, while the right

side is the expected return on foreign assets, both calculated in terms of a single cur-

rency, the U.S. dollar. Given our assumption that domestic and foreign assets are per-

fect substitutes (equally desirable), the interest parity condition is an equilibrium

condition for the foreign exchange market. Only when the exchange rate is such that

expected returns on domestic and foreign assets are equal—that is, when interest

parity holds—investors will be willing to hold both domestic and foreign assets.

With some algebraic manipulation, we can rewrite the interest parity condition

in Equation A2 as

This equation produces exactly the same results that we find in the supply and

demand analysis in the text: If i

D

rises, the denominator falls and so E

t

rises. If i

F

rises,

the denominator rises and so E

t

falls. If 

rises, the numerator rises and so E

t

rises.

E

e

t

⫹1

E

t

⫽

E

e

t

⫹1

i

F

⫺ i

D

⫹ 1

Chapter 15 The Foreign Exchange Market

373

If interest rates in the United States and Japan are 6% and 3%, respectively, what is the

expected rate of appreciation of the foreign (Japanese) currency?

Solution

The expected appreciation of the foreign currency is 3%.

where

i

D

=

interest rate on dollars 

= 6%

i

F

=

interest rate on foreign currency 

= 3%

Thus,

= rate of appreciation of the foreign currency

⫽ 6% ⫺ 3% ⫽ 3%

⫺

E

e

t

⫹1

⫺ E

t

E

t

6%

⫽ 3% ⫺

E

e

t

⫹1

⫺ E

t

E

t

i

D

⫽ i

F

⫺

E

e

t

⫹1

⫺ E

t

E

t

E X A M P L E   A 1 5 . 1 Interest Parity Condition

---

374

The International 

Financial System

Preview

Thanks to the growing interdependence between the U.S. economy and the

economies of the rest of the world, the international financial system now plays

a more prominent role in economic events in the United States. In this chapter

we see how fixed and managed exchange rate systems work and how they can

provide substantial profit opportunities for financial institutions. We also look at

the controversies over what role capital controls and the International

Monetary Fund should play in the international financial system.

16

C H A P T E R

Intervention in the Foreign Exchange Market

In Chapter 15 we analyzed the foreign exchange market as if it were a completely

free market that responds to all market pressures. Like many other markets, how-

ever, the foreign exchange market is not free of government intervention; central

banks regularly engage in international financial transactions called foreign