Equilibrium in the Foreign Exchange Market
We now use what we have learned about the demand for foreign currency assets to
describe how exchange rates are determined. We will show that the exchange rate at
which the market settles is the one that makes market participants content to hold existing
supplies of deposits of all currencies. When market participants willingly hold the
existing supplies of deposits of all currencies, we say that the foreign exchange market
is in equilibrium.
The description of exchange rate determination given in this section is only a first step:
A full explanation of the exchange rate’s current level can be given only after we examine
how participants in the foreign exchange market form their expectations about the
exchange rates they expect to prevail in the future. The next two chapters look at the factors
that influence expectations of future exchange rates. For now, however, we will take
expected future exchange rates as given.
Interest Parity: The Basic Equilibrium Condition
The foreign exchange market is in equilibrium when deposits of all currencies offer the
same expected rate of return. The condition that the expected returns on deposits of any
two currencies are equal when measured in the same currency is called the interest parity
condition. It implies that potential holders of foreign currency deposits view them all as
equally desirable assets, provided their expected rates of return are the same.
Let’s see why the foreign exchange market is in equilibrium only when the interest parity
condition holds. Suppose the dollar interest rate is 10 percent and the euro interest rate
is 6 percent, but that the dollar is expected to depreciate against the euro at an 8 percent
rate over a year. (This is case 3 in Table 14-3.) In the circumstances described, the
expected rate of return on euro deposits would be 4 percent per year higher than that on
dollar deposits. We assumed at the end of the last section that individuals always prefer to
hold deposits of currencies offering the highest expected return. This implies that if the
expected return on euro deposits is 4 percent greater than that on dollar deposits, no one
will be willing to continue holding dollar deposits, and holders of dollar deposits will be
trying to sell them for euro deposits. There will therefore be an excess supply of dollar
deposits and an excess demand for euro deposits in the foreign exchange market.
As a contrasting example, suppose that dollar deposits again offer a 10 percent interest
rate but euro deposits offer a 12 percent rate and the dollar is expected to appreciate
against the euro by 4 percent over the coming year. (This is case 4 in Table 14-3.) Now
the return on dollar deposits is 2 percent higher. In this case no one would demand euro
deposits, so they would be in excess supply and dollar deposits would be in excess
demand.
When, however, the dollar interest rate is 10 percent, the euro interest rate is 6 percent,
and the dollar’s expected depreciation rate against the euro is 4 percent, dollar and euro
338 PART THREE Exchange Rates and Open-Economy Macroeconomics
deposits offer the same rate of return and participants in the foreign exchange market are
equally willing to hold either. (This is case 2 in Table 14-3.)
Only when all expected rates of return are equal—that is, when the interest parity condition
holds—is there no excess supply of some type of deposit and no excess demand for
another. The foreign exchange market is in equilibrium when no type of deposit is in
excess demand or excess supply. We can therefore say that the foreign exchange market is
in equilibrium when, and only when, the interest parity condition holds.
To represent interest parity between dollar and euro deposits symbolically, we use
expression (14-1), which shows the difference between the two assets’ expected rates of
return measured in dollars. The expected rates of return are equal when
(14-2)
You probably suspect that when dollar deposits offer a higher return than euro deposits,
the dollar will appreciate against the euro as investors all try to shift their funds into dollars.
Conversely, the dollar should depreciate against the euro when it is euro deposits that
initially offer the higher return. This intuition is exactly correct. To understand the mechanism
at work, however, we must take a careful look at how exchange rate changes like
these help to maintain equilibrium in the foreign exchange market.
How Changes in the Current Exchange Rate
Affect Expected Returns
As a first step in understanding how the foreign exchange market finds its equilibrium, we
examine how changes in today’s exchange rate affect the expected return on a foreign currency
deposit when interest rates and expectations about the future exchange rate do not
change. Our analysis will show that, other things equal, depreciation of a country’s currency
today lowers the expected domestic currency return on foreign currency deposits.
Conversely, appreciation of the domestic currency today, all else equal, raises the domestic
currency return expected of foreign currency deposits.
It is easiest to see why these relationships hold by looking at an example: How does
a change in today’s dollar/euro exchange rate, all else held constant, change the
expected return, measured in terms of dollars, on euro deposits? Suppose that today’s
dollar/euro rate is per euro and that the exchange rate you expect for this day
next year is per euro. Then the expected rate of dollar depreciation against the
euro is or 5 percent per year. This means that when you
buy a euro deposit, you not only earn the interest but also get a 5 percent “bonus”
in terms of dollars. Now suppose that today’s exchange rate suddenly jumps up to
per euro (a depreciation of the dollar and an appreciation of the euro) but that
the expected future rate is still per euro. What happens to the “bonus” you expected
to get from the euro’s increase in value in terms of dollars? The expected rate of
dollar depreciation is now only or 1.9 percent instead of
5 percent. Since has not changed, the dollar return on euro deposits, which is the
sum of and the expected rate of dollar depreciation, has fallen by 3.1 percentage
points per year (5 percent – 1.9 percent).
In Table 14-4 we work out the dollar return on euro deposits for various levels of today’s
dollar/euro exchange rate always assuming that the expected future exchange rate
remains fixed at per euro and the euro interest rate is 5 percent per year. As you can
see, a rise in today’s dollar/euro exchange rate (a depreciation of the dollar against the euro)
always lowers the expected dollar return on euro deposits (as in our example), while a fall
in today’s dollar/euro exchange rate (an appreciation of the dollar against the euro) always
raises this return.
$1.05
E$/€,
R€
R€
(1.05 - 1.03)/1.03 = 0.019,
$1.05
$1.03
R€
(1.05 - 1.00)/1.00 = 0.05,
$1.05
$1.00
R$ = R€ + (E$/€
e - E$/€)/E$/€.
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 339
It may run counter to your intuition that a depreciation of the dollar against the euro
makes euro deposits less attractive relative to dollar deposits (by lowering the expected
dollar return on euro deposits) while an appreciation of the dollar makes euro deposits
more attractive. This result will seem less surprising if you remember we have assumed
that the expected future dollar/euro rate and interest rates do not change. A dollar depreciation
today, for example, means the dollar now needs to depreciate by a smaller amount to
reach any given expected future level. If the expected future dollar/euro exchange rate
does not change when the dollar depreciates today, the dollar’s expected future depreciation
against the euro therefore falls, or, alternatively, the dollar’s expected future appreciation
rises. Since interest rates also are unchanged, today’s dollar depreciation thus makes
euro deposits less attractive compared with dollar deposits.
Put another way, a current dollar depreciation that affects neither exchange rate expectations
nor interest rates leaves the expected future dollar payoff of a euro deposit the same
but raises the deposit’s current dollar cost. This change naturally makes euro deposits less
attractive relative to dollar deposits.
It may also run counter to your intuition that today’s exchange rate can change while
the exchange rate expected for the future does not. We will indeed study cases later in this
book when both of these rates do change at once. We nonetheless hold the expected future
exchange rate constant in the present discussion because that is the clearest way to illustrate
the effect of today’s exchange rate on expected returns. If it helps, you can imagine
we are looking at the impact of a temporary change so brief that it has no effect on the
exchange rate expected for next year.
Figure 14-3 shows the calculations in Table 14-4 in a graphic form that will be helpful
in our analysis of exchange rate determination. The vertical axis in the figure measures
today’s dollar/euro exchange rate and the horizontal axis measures the expected dollar
return on euro deposits. For fixed values of the expected future dollar/euro exchange rate
and the euro interest rate, the relation between today’s dollar/euro exchange rate and the
expected dollar return on euro deposits defines a downward-sloping schedule.
The Equilibrium Exchange Rate
Now that we understand why the interest parity condition must hold for the foreign
exchange market to be in equilibrium and how today’s exchange rate affects the expected
return on foreign currency deposits, we can see how equilibrium exchange rates are determined.
Our main conclusion will be that exchange rates always adjust to maintain interest
parity. We continue to assume that the dollar interest rate the euro interest rate and
the expected future dollar/euro exchange rate E$/€ are all given.
e
R€R$, ,
TABLE 14-4 Today’s Dollar/Euro Exchange Rate and the Expected Dollar Return
on Euro Deposits When E$/€ = $1.05 per Euro
e
Today’s Dollar/Euro
Exchange Rate
Interest Rate on
Euro Deposits
Expected Dollar
Depreciation Rate
Against Euro
Expected Dollar
Return on Euro
Deposits
E$/€ R€
1.05 E$/€
E$/€
R€
1.05 E$/€
E$/€
1.07 0.05 - 0.019 0.031
1.05 0.05 0.00 0.05
1.03 0.05 0.019 0.069
1.02 0.05 0.029 0.079
1.00 0.05 0.05 0.10
340 PART THREE Exchange Rates and Open-Economy Macroeconomics
Figure 14-4 illustrates how the equilibrium dollar/euro exchange rate is determined
under these assumptions. The vertical schedule in the graph indicates the given level of
the return on dollar deposits measured in terms of dollars. The downward-sloping schedule
shows how the expected return on euro deposits, measured in terms of dollars, depends
on the current dollar/euro exchange rate. This second schedule is derived in the same way
as the one shown in Figure 14-3.
The equilibrium dollar/euro rate is the one indicated by the intersection of the two
schedules at point 1, At this exchange rate, the returns on dollar and euro deposits
are equal, so that the interest parity condition (14-2),
is satisfied.
Let’s see why the exchange rate will tend to settle at point 1 in Figure 14-4 if it is initially
at a point such as 2 or 3. Suppose first that we are at point 2, with the exchange rate
equal to The downward-sloping schedule measuring the expected dollar return on
euro deposits tells us that at the exchange rate the rate of return on euro deposits is
less than the rate of return on dollar deposits, . In this situation anyone holding euro
deposits wishes to sell them for the more lucrative dollar deposits: The foreign exchange
market is out of equilibrium because participants such as banks and multinational corporations
are unwilling to hold euro deposits.
How does the exchange rate adjust? The unhappy owners of euro deposits attempt to
sell them for dollar deposits, but because the return on dollar deposits is higher than that
R$
E$/€
2 ,
E$/€
2 .
R$ = R€ + (E$/€
e - E$/€
1 )/E$/€
1 ,
E$/€
1 .
R$,
Today’s dollar/euro
exchange rate, E$/€
0.031 0.050 0.069 0.079 0.100
1.00
1.02
1.03
1.07
1.05
Expected dollar return on
euro deposits, R€ +
E$/€ – E$/€
E$/€
e
Figure 14-3
The Relation Between the Current
Dollar/Euro Exchange Rate and the
Expected Dollar Return on Euro
Deposits
Given and , an
appreciation of the dollar against the euro
raises the expected return on euro deposits,
measured in terms of dollars.
RE$/€ € = 0.05
e = 1.05
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 341
on euro deposits at the exchange rate , no holder of a dollar deposit is willing to sell it
for a euro deposit at that rate. As euro holders try to entice dollar holders to trade by offering
them a better price for dollars, the dollar/euro exchange rate falls toward that is,
euros become cheaper in terms of dollars. Once the exchange rate reaches euro and
dollar deposits offer equal returns, and holders of euro deposits no longer have an incentive
to try to sell them for dollars. The foreign exchange market is therefore in equilibrium.
In falling from to , the exchange rate equalizes the expected returns on the two
types of deposit by increasing the rate at which the dollar is expected to depreciate in the
future, thereby making euro deposits more attractive.
The same process works in reverse if we are initially at point 3 with an exchange rate of
. At point 3, the return on euro deposits exceeds that on dollar deposits, so there is
now an excess supply of the latter. As unwilling holders of dollar deposits bid for the more
attractive euro deposits, the price of euros in terms of dollars tends to rise; that is, the dollar
tends to depreciate against the euro. When the exchange rate has moved to rates
of return are equalized across currencies and the market is in equilibrium. The depreciation
of the dollar from to makes euro deposits less attractive relative to dollar
deposits by reducing the rate at which the dollar is expected to depreciate in the future.8
We now use what we have learned about the demand for foreign currency assets to
describe how exchange rates are determined. We will show that the exchange rate at
which the market settles is the one that makes market participants content to hold existing
supplies of deposits of all currencies. When market participants willingly hold the
existing supplies of deposits of all currencies, we say that the foreign exchange market
is in equilibrium.
The description of exchange rate determination given in this section is only a first step:
A full explanation of the exchange rate’s current level can be given only after we examine
how participants in the foreign exchange market form their expectations about the
exchange rates they expect to prevail in the future. The next two chapters look at the factors
that influence expectations of future exchange rates. For now, however, we will take
expected future exchange rates as given.
Interest Parity: The Basic Equilibrium Condition
The foreign exchange market is in equilibrium when deposits of all currencies offer the
same expected rate of return. The condition that the expected returns on deposits of any
two currencies are equal when measured in the same currency is called the interest parity
condition. It implies that potential holders of foreign currency deposits view them all as
equally desirable assets, provided their expected rates of return are the same.
Let’s see why the foreign exchange market is in equilibrium only when the interest parity
condition holds. Suppose the dollar interest rate is 10 percent and the euro interest rate
is 6 percent, but that the dollar is expected to depreciate against the euro at an 8 percent
rate over a year. (This is case 3 in Table 14-3.) In the circumstances described, the
expected rate of return on euro deposits would be 4 percent per year higher than that on
dollar deposits. We assumed at the end of the last section that individuals always prefer to
hold deposits of currencies offering the highest expected return. This implies that if the
expected return on euro deposits is 4 percent greater than that on dollar deposits, no one
will be willing to continue holding dollar deposits, and holders of dollar deposits will be
trying to sell them for euro deposits. There will therefore be an excess supply of dollar
deposits and an excess demand for euro deposits in the foreign exchange market.
As a contrasting example, suppose that dollar deposits again offer a 10 percent interest
rate but euro deposits offer a 12 percent rate and the dollar is expected to appreciate
against the euro by 4 percent over the coming year. (This is case 4 in Table 14-3.) Now
the return on dollar deposits is 2 percent higher. In this case no one would demand euro
deposits, so they would be in excess supply and dollar deposits would be in excess
demand.
When, however, the dollar interest rate is 10 percent, the euro interest rate is 6 percent,
and the dollar’s expected depreciation rate against the euro is 4 percent, dollar and euro
338 PART THREE Exchange Rates and Open-Economy Macroeconomics
deposits offer the same rate of return and participants in the foreign exchange market are
equally willing to hold either. (This is case 2 in Table 14-3.)
Only when all expected rates of return are equal—that is, when the interest parity condition
holds—is there no excess supply of some type of deposit and no excess demand for
another. The foreign exchange market is in equilibrium when no type of deposit is in
excess demand or excess supply. We can therefore say that the foreign exchange market is
in equilibrium when, and only when, the interest parity condition holds.
To represent interest parity between dollar and euro deposits symbolically, we use
expression (14-1), which shows the difference between the two assets’ expected rates of
return measured in dollars. The expected rates of return are equal when
(14-2)
You probably suspect that when dollar deposits offer a higher return than euro deposits,
the dollar will appreciate against the euro as investors all try to shift their funds into dollars.
Conversely, the dollar should depreciate against the euro when it is euro deposits that
initially offer the higher return. This intuition is exactly correct. To understand the mechanism
at work, however, we must take a careful look at how exchange rate changes like
these help to maintain equilibrium in the foreign exchange market.
How Changes in the Current Exchange Rate
Affect Expected Returns
As a first step in understanding how the foreign exchange market finds its equilibrium, we
examine how changes in today’s exchange rate affect the expected return on a foreign currency
deposit when interest rates and expectations about the future exchange rate do not
change. Our analysis will show that, other things equal, depreciation of a country’s currency
today lowers the expected domestic currency return on foreign currency deposits.
Conversely, appreciation of the domestic currency today, all else equal, raises the domestic
currency return expected of foreign currency deposits.
It is easiest to see why these relationships hold by looking at an example: How does
a change in today’s dollar/euro exchange rate, all else held constant, change the
expected return, measured in terms of dollars, on euro deposits? Suppose that today’s
dollar/euro rate is per euro and that the exchange rate you expect for this day
next year is per euro. Then the expected rate of dollar depreciation against the
euro is or 5 percent per year. This means that when you
buy a euro deposit, you not only earn the interest but also get a 5 percent “bonus”
in terms of dollars. Now suppose that today’s exchange rate suddenly jumps up to
per euro (a depreciation of the dollar and an appreciation of the euro) but that
the expected future rate is still per euro. What happens to the “bonus” you expected
to get from the euro’s increase in value in terms of dollars? The expected rate of
dollar depreciation is now only or 1.9 percent instead of
5 percent. Since has not changed, the dollar return on euro deposits, which is the
sum of and the expected rate of dollar depreciation, has fallen by 3.1 percentage
points per year (5 percent – 1.9 percent).
In Table 14-4 we work out the dollar return on euro deposits for various levels of today’s
dollar/euro exchange rate always assuming that the expected future exchange rate
remains fixed at per euro and the euro interest rate is 5 percent per year. As you can
see, a rise in today’s dollar/euro exchange rate (a depreciation of the dollar against the euro)
always lowers the expected dollar return on euro deposits (as in our example), while a fall
in today’s dollar/euro exchange rate (an appreciation of the dollar against the euro) always
raises this return.
$1.05
E$/€,
R€
R€
(1.05 - 1.03)/1.03 = 0.019,
$1.05
$1.03
R€
(1.05 - 1.00)/1.00 = 0.05,
$1.05
$1.00
R$ = R€ + (E$/€
e - E$/€)/E$/€.
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 339
It may run counter to your intuition that a depreciation of the dollar against the euro
makes euro deposits less attractive relative to dollar deposits (by lowering the expected
dollar return on euro deposits) while an appreciation of the dollar makes euro deposits
more attractive. This result will seem less surprising if you remember we have assumed
that the expected future dollar/euro rate and interest rates do not change. A dollar depreciation
today, for example, means the dollar now needs to depreciate by a smaller amount to
reach any given expected future level. If the expected future dollar/euro exchange rate
does not change when the dollar depreciates today, the dollar’s expected future depreciation
against the euro therefore falls, or, alternatively, the dollar’s expected future appreciation
rises. Since interest rates also are unchanged, today’s dollar depreciation thus makes
euro deposits less attractive compared with dollar deposits.
Put another way, a current dollar depreciation that affects neither exchange rate expectations
nor interest rates leaves the expected future dollar payoff of a euro deposit the same
but raises the deposit’s current dollar cost. This change naturally makes euro deposits less
attractive relative to dollar deposits.
It may also run counter to your intuition that today’s exchange rate can change while
the exchange rate expected for the future does not. We will indeed study cases later in this
book when both of these rates do change at once. We nonetheless hold the expected future
exchange rate constant in the present discussion because that is the clearest way to illustrate
the effect of today’s exchange rate on expected returns. If it helps, you can imagine
we are looking at the impact of a temporary change so brief that it has no effect on the
exchange rate expected for next year.
Figure 14-3 shows the calculations in Table 14-4 in a graphic form that will be helpful
in our analysis of exchange rate determination. The vertical axis in the figure measures
today’s dollar/euro exchange rate and the horizontal axis measures the expected dollar
return on euro deposits. For fixed values of the expected future dollar/euro exchange rate
and the euro interest rate, the relation between today’s dollar/euro exchange rate and the
expected dollar return on euro deposits defines a downward-sloping schedule.
The Equilibrium Exchange Rate
Now that we understand why the interest parity condition must hold for the foreign
exchange market to be in equilibrium and how today’s exchange rate affects the expected
return on foreign currency deposits, we can see how equilibrium exchange rates are determined.
Our main conclusion will be that exchange rates always adjust to maintain interest
parity. We continue to assume that the dollar interest rate the euro interest rate and
the expected future dollar/euro exchange rate E$/€ are all given.
e
R€R$, ,
TABLE 14-4 Today’s Dollar/Euro Exchange Rate and the Expected Dollar Return
on Euro Deposits When E$/€ = $1.05 per Euro
e
Today’s Dollar/Euro
Exchange Rate
Interest Rate on
Euro Deposits
Expected Dollar
Depreciation Rate
Against Euro
Expected Dollar
Return on Euro
Deposits
E$/€ R€
1.05 E$/€
E$/€
R€
1.05 E$/€
E$/€
1.07 0.05 - 0.019 0.031
1.05 0.05 0.00 0.05
1.03 0.05 0.019 0.069
1.02 0.05 0.029 0.079
1.00 0.05 0.05 0.10
340 PART THREE Exchange Rates and Open-Economy Macroeconomics
Figure 14-4 illustrates how the equilibrium dollar/euro exchange rate is determined
under these assumptions. The vertical schedule in the graph indicates the given level of
the return on dollar deposits measured in terms of dollars. The downward-sloping schedule
shows how the expected return on euro deposits, measured in terms of dollars, depends
on the current dollar/euro exchange rate. This second schedule is derived in the same way
as the one shown in Figure 14-3.
The equilibrium dollar/euro rate is the one indicated by the intersection of the two
schedules at point 1, At this exchange rate, the returns on dollar and euro deposits
are equal, so that the interest parity condition (14-2),
is satisfied.
Let’s see why the exchange rate will tend to settle at point 1 in Figure 14-4 if it is initially
at a point such as 2 or 3. Suppose first that we are at point 2, with the exchange rate
equal to The downward-sloping schedule measuring the expected dollar return on
euro deposits tells us that at the exchange rate the rate of return on euro deposits is
less than the rate of return on dollar deposits, . In this situation anyone holding euro
deposits wishes to sell them for the more lucrative dollar deposits: The foreign exchange
market is out of equilibrium because participants such as banks and multinational corporations
are unwilling to hold euro deposits.
How does the exchange rate adjust? The unhappy owners of euro deposits attempt to
sell them for dollar deposits, but because the return on dollar deposits is higher than that
R$
E$/€
2 ,
E$/€
2 .
R$ = R€ + (E$/€
e - E$/€
1 )/E$/€
1 ,
E$/€
1 .
R$,
Today’s dollar/euro
exchange rate, E$/€
0.031 0.050 0.069 0.079 0.100
1.00
1.02
1.03
1.07
1.05
Expected dollar return on
euro deposits, R€ +
E$/€ – E$/€
E$/€
e
Figure 14-3
The Relation Between the Current
Dollar/Euro Exchange Rate and the
Expected Dollar Return on Euro
Deposits
Given and , an
appreciation of the dollar against the euro
raises the expected return on euro deposits,
measured in terms of dollars.
RE$/€ € = 0.05
e = 1.05
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 341
on euro deposits at the exchange rate , no holder of a dollar deposit is willing to sell it
for a euro deposit at that rate. As euro holders try to entice dollar holders to trade by offering
them a better price for dollars, the dollar/euro exchange rate falls toward that is,
euros become cheaper in terms of dollars. Once the exchange rate reaches euro and
dollar deposits offer equal returns, and holders of euro deposits no longer have an incentive
to try to sell them for dollars. The foreign exchange market is therefore in equilibrium.
In falling from to , the exchange rate equalizes the expected returns on the two
types of deposit by increasing the rate at which the dollar is expected to depreciate in the
future, thereby making euro deposits more attractive.
The same process works in reverse if we are initially at point 3 with an exchange rate of
. At point 3, the return on euro deposits exceeds that on dollar deposits, so there is
now an excess supply of the latter. As unwilling holders of dollar deposits bid for the more
attractive euro deposits, the price of euros in terms of dollars tends to rise; that is, the dollar
tends to depreciate against the euro. When the exchange rate has moved to rates
of return are equalized across currencies and the market is in equilibrium. The depreciation
of the dollar from to makes euro deposits less attractive relative to dollar
deposits by reducing the rate at which the dollar is expected to depreciate in the future.8
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