The Demand for Foreign Currency Assets
We have now seen how banks, corporations, and other institutions trade foreign currency bank
deposits in a worldwide foreign exchange market that operates 24 hours a day. To understand
how exchange rates are determined by the foreign exchange market, we first must ask how the
major actors’ demands for different types of foreign currency deposits are determined.
$1
$1
$3.70
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 329
The demand for a foreign currency bank deposit is influenced by the same considerations
that influence the demand for any other asset. Chief among these considerations is
our view of what the deposit will be worth in the future. A foreign currency deposit’s
future value depends in turn on two factors: the interest rate it offers and the expected
change in the currency’s exchange rate against other currencies.
Assets and Asset Returns
As you will recall, people can hold wealth in many forms—stocks, bonds, cash, real estate,
rare wines, diamonds, and so on. The object of acquiring wealth—of saving—is to transfer
purchasing power into the future. We may do this to provide for our retirement years, for
our heirs, or simply because we earn more than we need to spend in a particular year and
prefer to save the balance for a rainy day.
Defining Asset Returns Because the object of saving is to provide for future consumption,
we judge the desirability of an asset largely on the basis of its rate of return, that is, the
percentage increase in value it offers over some time period. For example, suppose that at the
beginning of 2012 you pay for a share of stock issued by Financial Soothsayers, Inc. If
the stock pays you a dividend of $1 at the beginning of 2013, and if the stock’s price rises
from to per share over the year, then you have earned a rate of return of 10 percent
on the stock over 2012—that is, your initial investment has grown in value to , the
sum of the dividend and the you could get by selling your share. Had Financial
Soothsayers stock still paid out its dividend but dropped in price to per share, your
investment would be worth only by year’s end, giving a rate of return of negative
10 percent.
You often cannot know with certainty the return that an asset will actually pay after you
buy it. Both the dividend paid by a share of stock and the share’s resale price, for example,
may be hard to predict. Your decision therefore must be based on an expected rate of
return. To calculate an expected rate of return over some time period, you make your best
forecast of the asset’s total value at the period’s end. The percentage difference between
that expected future value and the price you pay for the asset today equals the asset’s
expected rate of return over the time period.
When we measure an asset’s rate of return, we compare how an investment in the asset
changes in total value between two dates. In the previous example, we compared how the
value of an investment in Financial Soothsayers stock changed between 2012 and
2013 to conclude that the rate of return on the stock was 10 percent per year. We
call this a dollar rate of return because the two values we compare are expressed in terms
of dollars. It is also possible, however, to compute different rates of return by expressing
the two values in terms of a foreign currency or a commodity such as gold.
The Real Rate of Return The expected rate of return that savers consider in deciding
which assets to hold is the expected real rate of return, that is, the rate of return
computed by measuring asset values in terms of some broad representative basket of
products that savers regularly purchase. It is the expected real return that matters because
the ultimate goal of saving is future consumption, and only the real return measures the
goods and services a saver can buy in the future in return for giving up some consumption
(that is, saving) today.
To continue our example, suppose that the dollar value of an investment in Financial
Soothsayers stock increases by 10 percent between 2012 and 2013 but that the dollar
prices of all goods and services also increase by 10 percent. Then in terms of output—that
is, in real terms—the investment would be worth no more in 2012 than in 2013. With a
real rate of return of zero, Financial Soothsayers stock would not be a very desirable asset.
($110)
($100)
$100 $90
$1 $89
$1 $109
$100 $110
$100 $109
$100
330 PART THREE Exchange Rates and Open-Economy Macroeconomics
In a standard forward exchange contract, two parties
agree to exchange two different currencies at an
agreed rate on a future date. The currencies of many
developing countries are, however, not fully
convertible, meaning that they cannot be freely
traded on international foreign exchange markets.
An important example of an inconvertible currency
is China’s renminbi, which can be traded within
China’s borders (by residents) but not freely outside
of them (because China’s government does not
allow nonresidents unrestricted ownership of renminbi
deposits in China). Thus, for currencies such
as the renminbi, the customary way of trading forward
exchange is not possible.
Developing countries with inconvertible currencies
such as China’s have entered the ranks of the world’s
largest participants in international trade and investment.
Usually, traders use the forward exchange market
to hedge their currency risks, but in cases such as
China’s, as we have seen, a standard forward market
cannot exist. Is there no way for foreigners to hedge
the currency risk they may take on when they trade
with inconvertible-currency countries?
Since the early 1990s, markets in nondeliverable
forward exchange have sprung up in centers such as
Hong Kong and Singapore to facilitate hedging in inconvertible
Asian currencies. Among the currencies
traded in offshore nondeliverable forward markets
are the Chinese renminbi, the Taiwan dollar, and the
Indian rupee. By using nondeliverable forward contracts,
traders can hedge currency risks without ever
actually having to trade inconvertible currencies.
Let’s look at a hypothetical example to see how
this hedging can be accomplished. General Motors
has just sold some car components to China. Its contract
with the Chinese importer states that in three
months, GM will receive the dollar equivalent of 10
million yuan in payment for its shipment. (The yuan
is the unit in which amounts of renminbi are measured,
just as British sterling is measured in pounds.)
The People’s Bank of China (PBC), the central bank,
tightly controls its currency’s exchange rate by trading
dollars that it holds for renminbi with domestic
residents.* Today, the PBC will buy or sell a U.S.
dollar for 6.8 yuan. But assume that the PBC has
been gradually allowing its currency to appreciate
against the dollar, and that the rate it will quote in
three months is uncertain: It could be anywhere
between, say, 6.7 and 6.5 yuan per dollar. GM would
like to lock in a forward exchange rate of 6.6 yuan
per dollar, which the company’s chief financial officer
might typically do simply by selling the expected
10 million yuan receipts forward for dollars at that
rate. Unfortunately, the renminbi’s inconvertibility
means that GM will actually receive, not renminbi
that it can sell forward, but the dollar equivalent of 10
million yuan, dollars that the importer can buy
through China’s banking system.
Nondeliverable forwards result in a “virtual” forward
market, however. They do this by allowing
non-Chinese traders to make bets on the renminbi’s
value that are payable in dollars. To lock in a nondeliverable
forward exchange rate of 6.6 yuan per
dollar, GM can sign a contract requiring it to pay the
difference between the number of dollars it actually
receives in three months and the amount it would
receive if the exchange rate were exactly 6.6 yuan per
dollar, equivalent to 1/6.6 dollars per yuan = $0.1515
per yuan (after rounding). Thus, if the exchange rate
turns out to be 6.5 yuan per dollar (which otherwise
would be good luck for GM), GM will have to pay
out on its contract (1/6.5 - 1/6.6 dollars per yuan) *
(10,000,000 yuan) = ($0.1538 - $0.1515 per yuan) *
(10,000,000 yuan) = $23,310.
On the other hand, by giving up the possibility of
good luck, GM also avoids the risk of bad luck. If the
Nondeliverable Forward Exchange Trading in Asia
*China’s currency regime is an example of a fixed exchange rate system, which we will study in greater detail
in Chapter 18.
Although savers care about expected real rates of return, rates of return expressed in terms
of a currency can still be used to compare real returns on different assets. Even if all dollar
prices rise by 10 percent between 2012 and 2013, a rare bottle of wine whose dollar price rises
by 25 percent is still a better investment than a bond whose dollar value rises by 20 percent.
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 331
exchange rate turns out instead to be 6.7 yuan per
dollar (which otherwise would be unfavorable for
GM), GM will pay the negative amount ($0.1493
$0.1515 per yuan) (10,000,000 yuan) $22,614,
that is, it will receive $22,614 from the other contracting
party. The nondeliverable forward contract allows
GM to immunize itself from exchange risk, even
though the parties to the contract need never actually
exchange Chinese currency.
The chart above shows daily data on nondeliverable
forward rates of yuan for dollars with value
dates one month, one year, and two years away. (Far
longer maturities are also quoted.) Changes in these
rates are more variable at the longer maturities
because the rates reflect expectations about China’s
future exchange rate policy and because the far future
is relatively more uncertain than the near future.
How have China’s exchange rate policies evolved?
From July 2005 until July 2008, China followed a
widely understood policy of gradually allowing its
currency to appreciate against the U.S. dollar. Because
of expectations during this period that the yuan/dollar
rate would fall over time, the forward rates at which
people were willing to trade to cover transactions two
years away are below the one-year-ahead forward
rates, which in turn are below the one-month-ahead
forward rates.
China changed its policy in the summer of 2008,
pegging the yuan rigidly to the dollar without any
announced end date for that policy. That action altered
the relationship among the three forward rates,
as you can see in the chart. Two years later, in June
2010, China announced its return to a supposedly
more flexible exchange rate for the yuan.
China’s exchange rate system and policies have
been a focus of international controversy in recent
years, and we will say more about them in later
chapters.
5.5
6
6.5
7
7.5
8
8.5
Exchange rate (yuan per U.S. Dollar)
One month forward
Two years forward
June 2006
September 2006
December 2006
March 2007
June 2007
September 2007
December 2007
March 2008
June 2008
September 2008
December 2008
March 2009
June 2009
September 2009
December 2009
March 2010
June 2010
One year forward
Nondeliverable Forward Exchange Rates, China Yuan per Dollar
Source: Datastream.
The real rate of return offered by the wine is 15 percent while
that offered by the bond is only 10 percent Notice that the difference
between the dollar returns of the two assets must equal the
difference between their real returns (15 percent - 10 percent). The reason for this equality is
(25 percent - 20 percent)
(= 20 percent - 10 percent).
(= 25 percent - 10 percent)
332 PART THREE Exchange Rates and Open-Economy Macroeconomics
that, given the two assets’ dollar returns, a change in the rate at which the dollar prices of
goods are rising changes both assets’ real returns by the same amount.
The distinction between real rates of return and dollar rates of return illustrates an
important concept in studying how savers evaluate different assets: The returns on two
assets cannot be compared unless they are measured in the same units. For example, it
makes no sense to compare directly the real return on the bottle of wine (15 percent in our
example) with the dollar return on the bond (20 percent) or to compare the dollar return on
old paintings with the euro return on gold. Only after the returns are expressed in terms of
a common unit of measure—for example, all in terms of dollars—can we tell which asset
offers the highest expected real rate of return.
Risk and Liquidity
All else equal, individuals prefer to hold those assets offering the highest expected real
rate of return. Our later discussions of particular assets will show, however, that “all else”
often is not equal. Some assets may be valued by savers for attributes other than the
expected real rate of return they offer. Savers care about two main characteristics of an
asset other than its return: its risk, the variability it contributes to savers’ wealth, and its
liquidity, the ease with which the asset can be sold or exchanged for goods.
1. Risk. An asset’s real return is usually unpredictable and may turn out to be quite different
from what savers expected when they purchased the asset. In our last example,
savers found the expected real rate of return on an investment in bonds (10 percent) by
subtracting from the expected rate of increase in the investment’s dollar value (20 percent)
the expected rate of increase in dollar prices (10 percent). But if expectations are wrong
and the bonds’ dollar value stays constant instead of rising by 20 percent, the saver ends
up with a real return of negative 10 percent Savers dislike
uncertainty and are reluctant to hold assets that make their wealth highly variable. An asset
with a high expected rate of return may thus appear undesirable to savers if its realized
rate of return fluctuates widely.
2. Liquidity. Assets also differ according to the cost and speed at which savers can
dispose of them. A house, for example, is not very liquid because its sale usually
requires time and the services of brokers and inspectors. To sell a house quickly, one
might have to sell at a relatively low price. In contrast, cash is the most liquid of all
assets: It is always acceptable at face value as payment for goods or other assets.
Savers prefer to hold some liquid assets as a precaution against unexpected pressing
expenses that might force them to sell less liquid assets at a loss. They will therefore
consider an asset’s liquidity as well as its expected return and risk in deciding how
much of it to hold.
Interest Rates
As in other asset markets, participants in the foreign exchange market base their demands
for deposits of different currencies on a comparison of these assets’ expected rates of
return. To compare returns on different deposits, market participants need two pieces of
information. First, they need to know how the money values of the deposits will change.
Second, they need to know how exchange rates will change so that they can translate rates
of return measured in different currencies into comparable terms.
The first piece of information needed to compute the rate of return on a deposit of a
particular currency is the currency’s interest rate, the amount of that currency an individual
can earn by lending a unit of the currency for a year. At a dollar interest rate of
0.10 (quoted as 10 percent per year), the lender of $1 receives $1.10 at the end of the
(= 0 percent - 10 percent).
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 333
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2011
Interest rates (percent per year)
Dollar rate
Yen rate
0
3
6
9
12
15
18
21
Figure 14-2
Interest Rates on Dollar and Yen Deposits, 1978–2011
Since dollar and yen interest rates are not measured in comparable terms, they can move quite differently over time.
Source: Datastream. Three-month interest rates are shown.
5Chapter 6 defined real interest rates, which are simply real rates of return on loans, that is, interest rates
expressed in terms of a consumption basket. Interest rates expressed in terms of currencies are called nominal
interest rates. The connection between real and nominal interest rates is discussed in detail in Chapter 16.
year, of which is principal and 10 cents of which is interest. Looked at from the other
side of the transaction, the interest rate on dollars is also the amount that must be paid to
borrow for a year. When you buy a U.S. Treasury bill, you earn the interest rate on
dollars because you are lending dollars to the U.S. government.
Interest rates play an important role in the foreign exchange market because the large
deposits traded there pay interest, each at a rate reflecting its currency of denomination.
For example, when the interest rate on dollars is 10 percent per year, a deposit
is worth after a year; when the interest rate on euros is 5 percent per year, a
deposit is worth after a year. Deposits pay interest because they are
really loans from the depositor to the bank. When a corporation or a financial institution
deposits a currency in a bank, it is lending that currency to the bank rather than using it for
some current expenditure. In other words, the depositor is acquiring an asset denominated
in the currency it deposits.
The dollar interest rate is simply the dollar rate of return on dollar deposits. You “buy”
the deposit by lending a bank , and when you are paid back with 10 percent
interest at the end of the year, your asset is worth . This gives a rate of return of
or 10 percent per year. Similarly, a foreign currency’s
interest rate measures the foreign currency return on deposits of that currency.
Figure 14-2 shows the monthly behavior of interest rates on the dollar and the Japanese
yen from 1978 to 2010. These interest rates are not measured in comparable terms, so
there is no reason for them to be close to each other or to move in similar ways over time.5
(110,000 - 100,000)/100,000 = 0.10,
$110,000
$100,000
€100,000 €105,000
$110,000
$100,000
$1
$1
334 PART THREE Exchange Rates and Open-Economy Macroeconomics
Exchange Rates and Asset Returns
The interest rates offered by a dollar and a euro deposit tell us how their dollar and euro
values will change over a year. The other piece of information we need in order to compare
the rates of return offered by dollar and euro deposits is the expected change in the
dollar/euro exchange rate over the year. To see which deposit, euro or dollar, offers a
higher expected rate of return, you must ask the question: If I use dollars to buy a euro
deposit, how many dollars will I get back after a year? When you answer this question,
you are calculating the dollar rate of return on a euro deposit because you are comparing
its dollar price today with its dollar value a year from today.
To see how to approach this type of calculation, let’s look at the following situation:
Suppose that today’s exchange rate (quoted in American terms) is per euro, but that
you expect the rate to be per euro in a year (perhaps because you expect unfavorable
developments in the U.S. economy). Suppose also that the dollar interest rate is
10 percent per year while the euro interest rate is 5 percent per year. This means a deposit
of pays after a year while a deposit of pays after a year. Which of
these deposits offers the higher return?
The answer can be found in five steps.
Step 1. Use today’s dollar/euro exchange rate to figure out the dollar price of a euro
deposit of, say, . If the exchange rate today is per euro, the dollar price of a
deposit is just .
Step 2. Use the euro interest rate to find the amount of euros you will have a year
from now if you purchase a deposit today. You know that the interest rate on euro deposits
is 5 percent per year. So at the end of a year, your deposit will be worth .
Step 3. Use the exchange rate you expect to prevail a year from today to calculate the
expected dollar value of the euro amount determined in Step 2. Since you expect the dollar
to depreciate against the euro over the coming year so that the exchange rate 12 months
from today is per euro, you expect the dollar value of your euro deposit after a year
to be
Step 4. Now that you know the dollar price of a deposit today and can forecast
its value in a year , you can calculate the expected dollar rate of return on a euro
deposit as or 11 percent per year.
Step 5. Since the dollar rate of return on dollar deposits (the dollar interest rate) is
only 10 percent per year, you expect to do better by holding your wealth in the form of
euro deposits. Despite the fact that the dollar interest rate exceeds the euro interest rate by
5 percent per year, the euro’s expected appreciation against the dollar gives euro holders a
prospective capital gain that is large enough to make euro deposits the higher-yield asset.
A Simple Rule
A simple rule shortens this calculation. First, define the rate of depreciation of the dollar
against the euro as the percentage increase in the dollar/euro exchange rate over a year. In
the last example, the dollar’s expected depreciation rate is
or roughly 6 percent per year. Once you have calculated the rate of depreciation of the
dollar against the euro, our rule is this: The dollar rate of return on euro deposits is
approximately the euro interest rate plus the rate of depreciation of the dollar against
the euro. In other words, to translate the euro return on euro deposits into dollar terms,
you need to add the rate at which the euro’s dollar price rises over a year to the euro
interest rate.
In our example, the sum of the euro interest rate (5 percent) and the expected depreciation
rate of the dollar (roughly 6 percent) is about 11 percent, which is what we found to
be the expected dollar return on euro deposits in our first calculation.
(1.165 - 1.10)/1.10 = 0.059,
(1.223 - 1.10)/1.10 = 0.11,
($1.223)
€1 ($1.10)
$1.165 per euro * €1.05 = $1.223.
$1.165
€1 €1.05
€1
$1.10
€1 $1.10 €1
$1.00 $1.10 €1 €1.05
$1.165
$1.10
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 335
We summarize our discussion by introducing some notation:
(The superscript attached to this last exchange rate indicates that it is a forecast of the
future exchange rate based on what people know today.)
Using these symbols, we write the expected rate of return on a euro deposit, measured
in terms of dollars, as the sum of (1) the euro interest rate and (2) the expected rate of
dollar depreciation against the euro:
This expected return is what must be compared with the interest rate on one-year dollar
deposits, in deciding whether dollar or euro deposits offer the higher expected rate of
return.6 The expected rate of return difference between dollar and euro deposits is therefore
equal to less the above expression,
(14-1)
When the difference above is positive, dollar deposits yield the higher expected rate of
return; when it is negative, euro deposits yield the higher expected rate of return.
Table 14-3 carries out some illustrative comparisons. In case 1, the interest difference
in favor of dollar deposits is 4 percent per year and no
change in the exchange rate is expected This means that the
expected annual real rate of return on dollar deposits is 4 percent higher than that on euro
deposits, so that, other things equal, you would prefer to hold your wealth as dollar rather
than euro deposits.
[(E$/€
e - E$/€)/E$/€ = 0.00].
(R$ - R€ = 0.10 - 0.06 = 0.04),
R$ - [R€ + (E$/€
e - E$/€)/E$/€] = R$ - R€ - (E$/€
e - E$/€)/E$/€.
R$
R$,
R€ + (E$/€
e - E$/€)/E$/€.
e
expected to prevail a year from today.
E$/€
e = dollar/euro exchange rate (number of dollars per euro)
E$/€ = today’s dollar/euro exchange rate (number of dollars per euro),
R€ = today’s interest rate on one-year euro deposits,
TABLE 14-3 Comparing Dollar Rates of Return on Dollar and Euro Deposits
Dollar
Interest
Rate
Euro
Interest
Rate
Expected Rate of
Dollar Depreciation
Against Euro
Rate of Return
Difference Between
Dollar and Euro Deposits
Case R$ R€
E$/€
e - E$/€
E$/€
R$ R€
(E$/€
e E$/€)
E$/€
1 0.10 0.06 0.00 0.04
2 0.10 0.06 0.04 0.00
3 0.10 0.06 0.08 – 0.04
4 0.10 0.12 – 0.04 0.02
6If you compute the expected dollar return on euro deposits using the exact five-step method we described before
introducing the simple rule, you’ll find that it actually equals
This exact formula can be rewritten, however, as
The expression above is very close to the formula derived from the simple rule when, as is usually the case, the
product R is a small number. € * (E$/€
e - E$/€)/E$/€
R€ + (E$/€
e - E$/€)/E$/€ + R€ * (E$/€
e - E$/€)/E$/€.
(1 + R€) (E$/€
e /E$/€) - 1.
336 PART THREE Exchange Rates and Open-Economy Macroeconomics
In case 2 the interest difference is the same (4 percent), but it is just offset by an
expected depreciation rate of the dollar of 4 percent. The two assets therefore have the
same expected rate of return.
Case 3 is similar to the one discussed earlier: A 4 percent interest difference in favor of
dollar deposits is more than offset by an 8 percent expected depreciation of the dollar, so
euro deposits are preferred by market participants.
In case 4, there is a 2 percent interest difference in favor of euro deposits, but the dollar
is expected to appreciate against the euro by 4 percent over the year. The expected rate of
return on dollar deposits is therefore 2 percent per year higher than that on euro deposits.
So far we have been translating all returns into dollar terms. But the rate of return differentials
we calculated would have been the same had we chosen to express returns in
terms of euros or in terms of some third currency. Suppose, for example, we wanted to
measure the return on dollar deposits in terms of euros. Following our simple rule, we
would add to the dollar interest rate the expected rate of depreciation of the euro
against the dollar. But the expected rate of depreciation of the euro against the dollar is
approximately the expected rate of appreciation of the dollar against the euro, that is, the
expected rate of depreciation of the dollar against the euro with a minus sign in front of it.
This means that in terms of euros, the return on a dollar deposit is
The difference between the expression above and is identical to expression (14-1).
Thus, it makes no difference to our comparison whether we measure returns in terms of
dollars or euros, as long as we measure them both in terms of the same currency.
Return, Risk, and Liquidity in the Foreign Exchange Market
We observed earlier that a saver deciding which assets to hold may care about the assets’
riskiness and liquidity in addition to their expected real rates of return. Similarly, the
demand for foreign currency assets depends not only on returns but also on risk and
liquidity. Even if the expected dollar return on euro deposits is higher than that on dollar
deposits, for example, people may be reluctant to hold euro deposits if the payoff to holding
them varies erratically.
There is no consensus among economists about the importance of risk in the foreign
exchange market. Even the definition of “foreign exchange risk” is a topic of debate. For
now we will avoid these complex questions by assuming that the real returns on all deposits
have equal riskiness, regardless of the currency of denomination. In other words, we
are assuming that risk differences do not influence the demand for foreign currency assets.
We discuss the role of foreign exchange risk in greater detail, however, in Chapter 18.7
Some market participants may be influenced by liquidity factors in deciding which currencies
to hold. Most of these participants are firms and individuals conducting international
trade. An American importer of French fashion products or wines, for example, may
find it convenient to hold euros for routine payments even if the expected rate of return on
euros is lower than that on dollars. Because payments connected with international trade
R€
R$ - (E$/€
e - E$/€)/E$/€.
R$
7In discussing spot and forward foreign exchange transactions, some textbooks make a distinction between foreign
exchange “speculators”—market participants who allegedly care only about expected returns—and “hedgers”—
market participants whose concern is to avoid risk. We depart from this textbook tradition because it can mislead the
unwary: While the speculative and hedging motives are both potentially important in exchange rate determination,
the same person can be both a speculator and a hedger if she cares about both return and risk. Our tentative assumption
that risk is unimportant in determining the demand for foreign currency assets means, in terms of the traditional
language, that the speculative motive for holding foreign currencies is far more important than the hedging motive.
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 337
make up a very small fraction of total foreign exchange transactions, we ignore the liquidity
motive for holding foreign currencies.
We are therefore assuming for now that participants in the foreign exchange market
base their demands for foreign currency assets exclusively on a comparison of those assets’
expected rates of return. The main reason for making this assumption is that it simplifies
our analysis of how exchange rates are determined in the foreign exchange market.
In addition, the risk and liquidity motives for holding foreign currencies appear to be of
secondary importance for many of the international macroeconomic issues discussed in
the next few chapters.
We have now seen how banks, corporations, and other institutions trade foreign currency bank
deposits in a worldwide foreign exchange market that operates 24 hours a day. To understand
how exchange rates are determined by the foreign exchange market, we first must ask how the
major actors’ demands for different types of foreign currency deposits are determined.
$1
$1
$3.70
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 329
The demand for a foreign currency bank deposit is influenced by the same considerations
that influence the demand for any other asset. Chief among these considerations is
our view of what the deposit will be worth in the future. A foreign currency deposit’s
future value depends in turn on two factors: the interest rate it offers and the expected
change in the currency’s exchange rate against other currencies.
Assets and Asset Returns
As you will recall, people can hold wealth in many forms—stocks, bonds, cash, real estate,
rare wines, diamonds, and so on. The object of acquiring wealth—of saving—is to transfer
purchasing power into the future. We may do this to provide for our retirement years, for
our heirs, or simply because we earn more than we need to spend in a particular year and
prefer to save the balance for a rainy day.
Defining Asset Returns Because the object of saving is to provide for future consumption,
we judge the desirability of an asset largely on the basis of its rate of return, that is, the
percentage increase in value it offers over some time period. For example, suppose that at the
beginning of 2012 you pay for a share of stock issued by Financial Soothsayers, Inc. If
the stock pays you a dividend of $1 at the beginning of 2013, and if the stock’s price rises
from to per share over the year, then you have earned a rate of return of 10 percent
on the stock over 2012—that is, your initial investment has grown in value to , the
sum of the dividend and the you could get by selling your share. Had Financial
Soothsayers stock still paid out its dividend but dropped in price to per share, your
investment would be worth only by year’s end, giving a rate of return of negative
10 percent.
You often cannot know with certainty the return that an asset will actually pay after you
buy it. Both the dividend paid by a share of stock and the share’s resale price, for example,
may be hard to predict. Your decision therefore must be based on an expected rate of
return. To calculate an expected rate of return over some time period, you make your best
forecast of the asset’s total value at the period’s end. The percentage difference between
that expected future value and the price you pay for the asset today equals the asset’s
expected rate of return over the time period.
When we measure an asset’s rate of return, we compare how an investment in the asset
changes in total value between two dates. In the previous example, we compared how the
value of an investment in Financial Soothsayers stock changed between 2012 and
2013 to conclude that the rate of return on the stock was 10 percent per year. We
call this a dollar rate of return because the two values we compare are expressed in terms
of dollars. It is also possible, however, to compute different rates of return by expressing
the two values in terms of a foreign currency or a commodity such as gold.
The Real Rate of Return The expected rate of return that savers consider in deciding
which assets to hold is the expected real rate of return, that is, the rate of return
computed by measuring asset values in terms of some broad representative basket of
products that savers regularly purchase. It is the expected real return that matters because
the ultimate goal of saving is future consumption, and only the real return measures the
goods and services a saver can buy in the future in return for giving up some consumption
(that is, saving) today.
To continue our example, suppose that the dollar value of an investment in Financial
Soothsayers stock increases by 10 percent between 2012 and 2013 but that the dollar
prices of all goods and services also increase by 10 percent. Then in terms of output—that
is, in real terms—the investment would be worth no more in 2012 than in 2013. With a
real rate of return of zero, Financial Soothsayers stock would not be a very desirable asset.
($110)
($100)
$100 $90
$1 $89
$1 $109
$100 $110
$100 $109
$100
330 PART THREE Exchange Rates and Open-Economy Macroeconomics
In a standard forward exchange contract, two parties
agree to exchange two different currencies at an
agreed rate on a future date. The currencies of many
developing countries are, however, not fully
convertible, meaning that they cannot be freely
traded on international foreign exchange markets.
An important example of an inconvertible currency
is China’s renminbi, which can be traded within
China’s borders (by residents) but not freely outside
of them (because China’s government does not
allow nonresidents unrestricted ownership of renminbi
deposits in China). Thus, for currencies such
as the renminbi, the customary way of trading forward
exchange is not possible.
Developing countries with inconvertible currencies
such as China’s have entered the ranks of the world’s
largest participants in international trade and investment.
Usually, traders use the forward exchange market
to hedge their currency risks, but in cases such as
China’s, as we have seen, a standard forward market
cannot exist. Is there no way for foreigners to hedge
the currency risk they may take on when they trade
with inconvertible-currency countries?
Since the early 1990s, markets in nondeliverable
forward exchange have sprung up in centers such as
Hong Kong and Singapore to facilitate hedging in inconvertible
Asian currencies. Among the currencies
traded in offshore nondeliverable forward markets
are the Chinese renminbi, the Taiwan dollar, and the
Indian rupee. By using nondeliverable forward contracts,
traders can hedge currency risks without ever
actually having to trade inconvertible currencies.
Let’s look at a hypothetical example to see how
this hedging can be accomplished. General Motors
has just sold some car components to China. Its contract
with the Chinese importer states that in three
months, GM will receive the dollar equivalent of 10
million yuan in payment for its shipment. (The yuan
is the unit in which amounts of renminbi are measured,
just as British sterling is measured in pounds.)
The People’s Bank of China (PBC), the central bank,
tightly controls its currency’s exchange rate by trading
dollars that it holds for renminbi with domestic
residents.* Today, the PBC will buy or sell a U.S.
dollar for 6.8 yuan. But assume that the PBC has
been gradually allowing its currency to appreciate
against the dollar, and that the rate it will quote in
three months is uncertain: It could be anywhere
between, say, 6.7 and 6.5 yuan per dollar. GM would
like to lock in a forward exchange rate of 6.6 yuan
per dollar, which the company’s chief financial officer
might typically do simply by selling the expected
10 million yuan receipts forward for dollars at that
rate. Unfortunately, the renminbi’s inconvertibility
means that GM will actually receive, not renminbi
that it can sell forward, but the dollar equivalent of 10
million yuan, dollars that the importer can buy
through China’s banking system.
Nondeliverable forwards result in a “virtual” forward
market, however. They do this by allowing
non-Chinese traders to make bets on the renminbi’s
value that are payable in dollars. To lock in a nondeliverable
forward exchange rate of 6.6 yuan per
dollar, GM can sign a contract requiring it to pay the
difference between the number of dollars it actually
receives in three months and the amount it would
receive if the exchange rate were exactly 6.6 yuan per
dollar, equivalent to 1/6.6 dollars per yuan = $0.1515
per yuan (after rounding). Thus, if the exchange rate
turns out to be 6.5 yuan per dollar (which otherwise
would be good luck for GM), GM will have to pay
out on its contract (1/6.5 - 1/6.6 dollars per yuan) *
(10,000,000 yuan) = ($0.1538 - $0.1515 per yuan) *
(10,000,000 yuan) = $23,310.
On the other hand, by giving up the possibility of
good luck, GM also avoids the risk of bad luck. If the
Nondeliverable Forward Exchange Trading in Asia
*China’s currency regime is an example of a fixed exchange rate system, which we will study in greater detail
in Chapter 18.
Although savers care about expected real rates of return, rates of return expressed in terms
of a currency can still be used to compare real returns on different assets. Even if all dollar
prices rise by 10 percent between 2012 and 2013, a rare bottle of wine whose dollar price rises
by 25 percent is still a better investment than a bond whose dollar value rises by 20 percent.
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 331
exchange rate turns out instead to be 6.7 yuan per
dollar (which otherwise would be unfavorable for
GM), GM will pay the negative amount ($0.1493
$0.1515 per yuan) (10,000,000 yuan) $22,614,
that is, it will receive $22,614 from the other contracting
party. The nondeliverable forward contract allows
GM to immunize itself from exchange risk, even
though the parties to the contract need never actually
exchange Chinese currency.
The chart above shows daily data on nondeliverable
forward rates of yuan for dollars with value
dates one month, one year, and two years away. (Far
longer maturities are also quoted.) Changes in these
rates are more variable at the longer maturities
because the rates reflect expectations about China’s
future exchange rate policy and because the far future
is relatively more uncertain than the near future.
How have China’s exchange rate policies evolved?
From July 2005 until July 2008, China followed a
widely understood policy of gradually allowing its
currency to appreciate against the U.S. dollar. Because
of expectations during this period that the yuan/dollar
rate would fall over time, the forward rates at which
people were willing to trade to cover transactions two
years away are below the one-year-ahead forward
rates, which in turn are below the one-month-ahead
forward rates.
China changed its policy in the summer of 2008,
pegging the yuan rigidly to the dollar without any
announced end date for that policy. That action altered
the relationship among the three forward rates,
as you can see in the chart. Two years later, in June
2010, China announced its return to a supposedly
more flexible exchange rate for the yuan.
China’s exchange rate system and policies have
been a focus of international controversy in recent
years, and we will say more about them in later
chapters.
5.5
6
6.5
7
7.5
8
8.5
Exchange rate (yuan per U.S. Dollar)
One month forward
Two years forward
June 2006
September 2006
December 2006
March 2007
June 2007
September 2007
December 2007
March 2008
June 2008
September 2008
December 2008
March 2009
June 2009
September 2009
December 2009
March 2010
June 2010
One year forward
Nondeliverable Forward Exchange Rates, China Yuan per Dollar
Source: Datastream.
The real rate of return offered by the wine is 15 percent while
that offered by the bond is only 10 percent Notice that the difference
between the dollar returns of the two assets must equal the
difference between their real returns (15 percent - 10 percent). The reason for this equality is
(25 percent - 20 percent)
(= 20 percent - 10 percent).
(= 25 percent - 10 percent)
332 PART THREE Exchange Rates and Open-Economy Macroeconomics
that, given the two assets’ dollar returns, a change in the rate at which the dollar prices of
goods are rising changes both assets’ real returns by the same amount.
The distinction between real rates of return and dollar rates of return illustrates an
important concept in studying how savers evaluate different assets: The returns on two
assets cannot be compared unless they are measured in the same units. For example, it
makes no sense to compare directly the real return on the bottle of wine (15 percent in our
example) with the dollar return on the bond (20 percent) or to compare the dollar return on
old paintings with the euro return on gold. Only after the returns are expressed in terms of
a common unit of measure—for example, all in terms of dollars—can we tell which asset
offers the highest expected real rate of return.
Risk and Liquidity
All else equal, individuals prefer to hold those assets offering the highest expected real
rate of return. Our later discussions of particular assets will show, however, that “all else”
often is not equal. Some assets may be valued by savers for attributes other than the
expected real rate of return they offer. Savers care about two main characteristics of an
asset other than its return: its risk, the variability it contributes to savers’ wealth, and its
liquidity, the ease with which the asset can be sold or exchanged for goods.
1. Risk. An asset’s real return is usually unpredictable and may turn out to be quite different
from what savers expected when they purchased the asset. In our last example,
savers found the expected real rate of return on an investment in bonds (10 percent) by
subtracting from the expected rate of increase in the investment’s dollar value (20 percent)
the expected rate of increase in dollar prices (10 percent). But if expectations are wrong
and the bonds’ dollar value stays constant instead of rising by 20 percent, the saver ends
up with a real return of negative 10 percent Savers dislike
uncertainty and are reluctant to hold assets that make their wealth highly variable. An asset
with a high expected rate of return may thus appear undesirable to savers if its realized
rate of return fluctuates widely.
2. Liquidity. Assets also differ according to the cost and speed at which savers can
dispose of them. A house, for example, is not very liquid because its sale usually
requires time and the services of brokers and inspectors. To sell a house quickly, one
might have to sell at a relatively low price. In contrast, cash is the most liquid of all
assets: It is always acceptable at face value as payment for goods or other assets.
Savers prefer to hold some liquid assets as a precaution against unexpected pressing
expenses that might force them to sell less liquid assets at a loss. They will therefore
consider an asset’s liquidity as well as its expected return and risk in deciding how
much of it to hold.
Interest Rates
As in other asset markets, participants in the foreign exchange market base their demands
for deposits of different currencies on a comparison of these assets’ expected rates of
return. To compare returns on different deposits, market participants need two pieces of
information. First, they need to know how the money values of the deposits will change.
Second, they need to know how exchange rates will change so that they can translate rates
of return measured in different currencies into comparable terms.
The first piece of information needed to compute the rate of return on a deposit of a
particular currency is the currency’s interest rate, the amount of that currency an individual
can earn by lending a unit of the currency for a year. At a dollar interest rate of
0.10 (quoted as 10 percent per year), the lender of $1 receives $1.10 at the end of the
(= 0 percent - 10 percent).
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 333
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2011
Interest rates (percent per year)
Dollar rate
Yen rate
0
3
6
9
12
15
18
21
Figure 14-2
Interest Rates on Dollar and Yen Deposits, 1978–2011
Since dollar and yen interest rates are not measured in comparable terms, they can move quite differently over time.
Source: Datastream. Three-month interest rates are shown.
5Chapter 6 defined real interest rates, which are simply real rates of return on loans, that is, interest rates
expressed in terms of a consumption basket. Interest rates expressed in terms of currencies are called nominal
interest rates. The connection between real and nominal interest rates is discussed in detail in Chapter 16.
year, of which is principal and 10 cents of which is interest. Looked at from the other
side of the transaction, the interest rate on dollars is also the amount that must be paid to
borrow for a year. When you buy a U.S. Treasury bill, you earn the interest rate on
dollars because you are lending dollars to the U.S. government.
Interest rates play an important role in the foreign exchange market because the large
deposits traded there pay interest, each at a rate reflecting its currency of denomination.
For example, when the interest rate on dollars is 10 percent per year, a deposit
is worth after a year; when the interest rate on euros is 5 percent per year, a
deposit is worth after a year. Deposits pay interest because they are
really loans from the depositor to the bank. When a corporation or a financial institution
deposits a currency in a bank, it is lending that currency to the bank rather than using it for
some current expenditure. In other words, the depositor is acquiring an asset denominated
in the currency it deposits.
The dollar interest rate is simply the dollar rate of return on dollar deposits. You “buy”
the deposit by lending a bank , and when you are paid back with 10 percent
interest at the end of the year, your asset is worth . This gives a rate of return of
or 10 percent per year. Similarly, a foreign currency’s
interest rate measures the foreign currency return on deposits of that currency.
Figure 14-2 shows the monthly behavior of interest rates on the dollar and the Japanese
yen from 1978 to 2010. These interest rates are not measured in comparable terms, so
there is no reason for them to be close to each other or to move in similar ways over time.5
(110,000 - 100,000)/100,000 = 0.10,
$110,000
$100,000
€100,000 €105,000
$110,000
$100,000
$1
$1
334 PART THREE Exchange Rates and Open-Economy Macroeconomics
Exchange Rates and Asset Returns
The interest rates offered by a dollar and a euro deposit tell us how their dollar and euro
values will change over a year. The other piece of information we need in order to compare
the rates of return offered by dollar and euro deposits is the expected change in the
dollar/euro exchange rate over the year. To see which deposit, euro or dollar, offers a
higher expected rate of return, you must ask the question: If I use dollars to buy a euro
deposit, how many dollars will I get back after a year? When you answer this question,
you are calculating the dollar rate of return on a euro deposit because you are comparing
its dollar price today with its dollar value a year from today.
To see how to approach this type of calculation, let’s look at the following situation:
Suppose that today’s exchange rate (quoted in American terms) is per euro, but that
you expect the rate to be per euro in a year (perhaps because you expect unfavorable
developments in the U.S. economy). Suppose also that the dollar interest rate is
10 percent per year while the euro interest rate is 5 percent per year. This means a deposit
of pays after a year while a deposit of pays after a year. Which of
these deposits offers the higher return?
The answer can be found in five steps.
Step 1. Use today’s dollar/euro exchange rate to figure out the dollar price of a euro
deposit of, say, . If the exchange rate today is per euro, the dollar price of a
deposit is just .
Step 2. Use the euro interest rate to find the amount of euros you will have a year
from now if you purchase a deposit today. You know that the interest rate on euro deposits
is 5 percent per year. So at the end of a year, your deposit will be worth .
Step 3. Use the exchange rate you expect to prevail a year from today to calculate the
expected dollar value of the euro amount determined in Step 2. Since you expect the dollar
to depreciate against the euro over the coming year so that the exchange rate 12 months
from today is per euro, you expect the dollar value of your euro deposit after a year
to be
Step 4. Now that you know the dollar price of a deposit today and can forecast
its value in a year , you can calculate the expected dollar rate of return on a euro
deposit as or 11 percent per year.
Step 5. Since the dollar rate of return on dollar deposits (the dollar interest rate) is
only 10 percent per year, you expect to do better by holding your wealth in the form of
euro deposits. Despite the fact that the dollar interest rate exceeds the euro interest rate by
5 percent per year, the euro’s expected appreciation against the dollar gives euro holders a
prospective capital gain that is large enough to make euro deposits the higher-yield asset.
A Simple Rule
A simple rule shortens this calculation. First, define the rate of depreciation of the dollar
against the euro as the percentage increase in the dollar/euro exchange rate over a year. In
the last example, the dollar’s expected depreciation rate is
or roughly 6 percent per year. Once you have calculated the rate of depreciation of the
dollar against the euro, our rule is this: The dollar rate of return on euro deposits is
approximately the euro interest rate plus the rate of depreciation of the dollar against
the euro. In other words, to translate the euro return on euro deposits into dollar terms,
you need to add the rate at which the euro’s dollar price rises over a year to the euro
interest rate.
In our example, the sum of the euro interest rate (5 percent) and the expected depreciation
rate of the dollar (roughly 6 percent) is about 11 percent, which is what we found to
be the expected dollar return on euro deposits in our first calculation.
(1.165 - 1.10)/1.10 = 0.059,
(1.223 - 1.10)/1.10 = 0.11,
($1.223)
€1 ($1.10)
$1.165 per euro * €1.05 = $1.223.
$1.165
€1 €1.05
€1
$1.10
€1 $1.10 €1
$1.00 $1.10 €1 €1.05
$1.165
$1.10
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 335
We summarize our discussion by introducing some notation:
(The superscript attached to this last exchange rate indicates that it is a forecast of the
future exchange rate based on what people know today.)
Using these symbols, we write the expected rate of return on a euro deposit, measured
in terms of dollars, as the sum of (1) the euro interest rate and (2) the expected rate of
dollar depreciation against the euro:
This expected return is what must be compared with the interest rate on one-year dollar
deposits, in deciding whether dollar or euro deposits offer the higher expected rate of
return.6 The expected rate of return difference between dollar and euro deposits is therefore
equal to less the above expression,
(14-1)
When the difference above is positive, dollar deposits yield the higher expected rate of
return; when it is negative, euro deposits yield the higher expected rate of return.
Table 14-3 carries out some illustrative comparisons. In case 1, the interest difference
in favor of dollar deposits is 4 percent per year and no
change in the exchange rate is expected This means that the
expected annual real rate of return on dollar deposits is 4 percent higher than that on euro
deposits, so that, other things equal, you would prefer to hold your wealth as dollar rather
than euro deposits.
[(E$/€
e - E$/€)/E$/€ = 0.00].
(R$ - R€ = 0.10 - 0.06 = 0.04),
R$ - [R€ + (E$/€
e - E$/€)/E$/€] = R$ - R€ - (E$/€
e - E$/€)/E$/€.
R$
R$,
R€ + (E$/€
e - E$/€)/E$/€.
e
expected to prevail a year from today.
E$/€
e = dollar/euro exchange rate (number of dollars per euro)
E$/€ = today’s dollar/euro exchange rate (number of dollars per euro),
R€ = today’s interest rate on one-year euro deposits,
TABLE 14-3 Comparing Dollar Rates of Return on Dollar and Euro Deposits
Dollar
Interest
Rate
Euro
Interest
Rate
Expected Rate of
Dollar Depreciation
Against Euro
Rate of Return
Difference Between
Dollar and Euro Deposits
Case R$ R€
E$/€
e - E$/€
E$/€
R$ R€
(E$/€
e E$/€)
E$/€
1 0.10 0.06 0.00 0.04
2 0.10 0.06 0.04 0.00
3 0.10 0.06 0.08 – 0.04
4 0.10 0.12 – 0.04 0.02
6If you compute the expected dollar return on euro deposits using the exact five-step method we described before
introducing the simple rule, you’ll find that it actually equals
This exact formula can be rewritten, however, as
The expression above is very close to the formula derived from the simple rule when, as is usually the case, the
product R is a small number. € * (E$/€
e - E$/€)/E$/€
R€ + (E$/€
e - E$/€)/E$/€ + R€ * (E$/€
e - E$/€)/E$/€.
(1 + R€) (E$/€
e /E$/€) - 1.
336 PART THREE Exchange Rates and Open-Economy Macroeconomics
In case 2 the interest difference is the same (4 percent), but it is just offset by an
expected depreciation rate of the dollar of 4 percent. The two assets therefore have the
same expected rate of return.
Case 3 is similar to the one discussed earlier: A 4 percent interest difference in favor of
dollar deposits is more than offset by an 8 percent expected depreciation of the dollar, so
euro deposits are preferred by market participants.
In case 4, there is a 2 percent interest difference in favor of euro deposits, but the dollar
is expected to appreciate against the euro by 4 percent over the year. The expected rate of
return on dollar deposits is therefore 2 percent per year higher than that on euro deposits.
So far we have been translating all returns into dollar terms. But the rate of return differentials
we calculated would have been the same had we chosen to express returns in
terms of euros or in terms of some third currency. Suppose, for example, we wanted to
measure the return on dollar deposits in terms of euros. Following our simple rule, we
would add to the dollar interest rate the expected rate of depreciation of the euro
against the dollar. But the expected rate of depreciation of the euro against the dollar is
approximately the expected rate of appreciation of the dollar against the euro, that is, the
expected rate of depreciation of the dollar against the euro with a minus sign in front of it.
This means that in terms of euros, the return on a dollar deposit is
The difference between the expression above and is identical to expression (14-1).
Thus, it makes no difference to our comparison whether we measure returns in terms of
dollars or euros, as long as we measure them both in terms of the same currency.
Return, Risk, and Liquidity in the Foreign Exchange Market
We observed earlier that a saver deciding which assets to hold may care about the assets’
riskiness and liquidity in addition to their expected real rates of return. Similarly, the
demand for foreign currency assets depends not only on returns but also on risk and
liquidity. Even if the expected dollar return on euro deposits is higher than that on dollar
deposits, for example, people may be reluctant to hold euro deposits if the payoff to holding
them varies erratically.
There is no consensus among economists about the importance of risk in the foreign
exchange market. Even the definition of “foreign exchange risk” is a topic of debate. For
now we will avoid these complex questions by assuming that the real returns on all deposits
have equal riskiness, regardless of the currency of denomination. In other words, we
are assuming that risk differences do not influence the demand for foreign currency assets.
We discuss the role of foreign exchange risk in greater detail, however, in Chapter 18.7
Some market participants may be influenced by liquidity factors in deciding which currencies
to hold. Most of these participants are firms and individuals conducting international
trade. An American importer of French fashion products or wines, for example, may
find it convenient to hold euros for routine payments even if the expected rate of return on
euros is lower than that on dollars. Because payments connected with international trade
R€
R$ - (E$/€
e - E$/€)/E$/€.
R$
7In discussing spot and forward foreign exchange transactions, some textbooks make a distinction between foreign
exchange “speculators”—market participants who allegedly care only about expected returns—and “hedgers”—
market participants whose concern is to avoid risk. We depart from this textbook tradition because it can mislead the
unwary: While the speculative and hedging motives are both potentially important in exchange rate determination,
the same person can be both a speculator and a hedger if she cares about both return and risk. Our tentative assumption
that risk is unimportant in determining the demand for foreign currency assets means, in terms of the traditional
language, that the speculative motive for holding foreign currencies is far more important than the hedging motive.
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 337
make up a very small fraction of total foreign exchange transactions, we ignore the liquidity
motive for holding foreign currencies.
We are therefore assuming for now that participants in the foreign exchange market
base their demands for foreign currency assets exclusively on a comparison of those assets’
expected rates of return. The main reason for making this assumption is that it simplifies
our analysis of how exchange rates are determined in the foreign exchange market.
In addition, the risk and liquidity motives for holding foreign currencies appear to be of
secondary importance for many of the international macroeconomic issues discussed in
the next few chapters.
No comments:
Post a Comment