Exchange Rates in the Short Run

Chapter 14: Exchange Rates and the Foreign
Exchange Market: An Asset Approach
Prepared by César R. Sobrino
Universidad del Turabo
June 20, 2018
1 / 39 Prepared by César R. Sobrino Chapter 14: Exchange Rates and the Foreign Exchang

Outline
1 The basics of exchange rates
2 Exchange rates and the prices of goods
3 Triangular condition
4 The foreign exchange markets
5 The demand of currency and other assets
6 A model of foreign exchange markets
role of interest rates on currency deposits
role of expectations of exchange rates

Deﬁnitions of Exchange Rates
Exchange rates are quoted as foreign currency per unit of
domestic currency or domestic currency per unit of foreign
currency.
How much can be exchanged for one dollar? ¥89.40/$
How much can be exchanged for one yen? $0.011185/¥
Exchange rates allow us to denominate the cost or price of
a good or service in a common currency.
How much does a Nissan cost? ¥2,500,000
Or, ¥2,500,000 × $0.011185/¥= $27,962.50

Table 14-1: Exchange Rate Quotations

Depreciation and Appreciation
Depreciation is a decrease in the value of a currency
relative to another currency.
A depreciated currency is less valuable (less expensive) and
therefore can be exchanged for (can buy) a smaller amount
of foreign currency.
$1/e ⇒ $1.20/e means that the dollar has depreciated
relative to the euro. It now takes $1.20 to buy one euro so
that the dollar is less valuable.
The euro has appreciated relative to the dollar: it is now
more valuable.

Appreciation is an increase in the value of a currency
relative to another currency.
An appreciated currency is more valuable (more expensive)
and therefore can be exchanged for (can buy) a larger
amount of foreign currency.
$1/e ⇒ $0.90/e means that the dollar has appreciated
relative to the euro. It now takes only $0.90 to buy one
euro, so that the dollar is more valuable.
The euro has depreciated relative to the dollar: it is now
less valuable

A depreciated currency is less valuable, and therefore it can
buy fewer foreign produced goods that are denominated in
foreign currency.
A Nissan costs ¥2,500,000 = $ 25,000 at $ 0.010/¥
becomes more expensive $ 27,962.50 at $ 0.011185/¥
A depreciated currency means that imports are more
expensive and domestically produced goods and exports are
less expensive.
A depreciated currency lowers the price of exports relative
to the price of imports.

An appreciated currency is more valuable, and therefore it
can buy more foreign produced goods that are denominated
in foreign currency.
A Nissan costs ¥2,500,000 = $ 27,962.50 at $ 0.011185/¥
becomes less expensive $ 25,000 at $ 0.010/¥
An appreciated currency means that imports are less
expensive and domestically produced goods and exports are
more expensive.
An appreciated currency raises the price of exports relative
to the price of imports.

Table 14-2: $/£ Exchange Rates and the Relative Price of
American Designer Jeans and British Sweaters
One sweater in terms of pairs of jeans
£50
$45 × 1.25 $/£ = 1.39 pairs of jeans per sweater.
£50
£50
When the pound is appreciating (US dollar is depreciating),
the goods in UK (US) are getting more expensive (cheaper)
than in US (UK).
Find the price of one pair of jeans in terms of sweaters

Triangular condition
Actually, exchanges rates are reported in US dollars
But, it is possible to get exchange rates in terms of other
currencies.
Let E$/£ be the price of the pound in US dollars, E$/e be
the price of the euro in US dollars, and, Ee/£ be the price of
the pound in euros.
The triangular condition is:
E$/£ = Ee/£ × E$/e
Suppose E$/£ = 1.6 $/£ and E$/e = 1.1 $/e
⇒ Ee/£ = 1.55 e/£
It takes 1.55 euros to buy one pound

Foreign Exchange Rates
The set of markets where foreign currencies and other
assets are exchanged for domestic ones.
Institutions buy and sell deposits of currencies or other
assets for investment purposes.
The daily volume of foreign exchange transactions was $4.0
trillion in April 2010
up from $500 billion in 1989.
Most transactions (85% in April 2010) exchange foreign
currencies for U.S. dollars.

The participants:
1 Commercial banks and other depository institutions:
transactions involve buying/selling of deposits in different
currencies for investment purposes.
2 Non-bank financial institutions (mutual funds, hedge funds,
securities firms, insurance companies, pension funds) may
buy/sell foreign assets for investment.
3 Non-financial businesses conduct foreign currency
transactions to buy/sell goods, services and assets.
4 Central banks: conduct official international reserves
transactions.

Buying and selling in the foreign exchange market are
dominated by commercial and investment banks.
Inter-bank transactions of deposits in foreign currencies
occur in amounts $1 million or more per transaction.
Central banks sometimes intervene, but the direct effects of
their transactions are small and transitory in many
countries.
Computer and telecommunications technology transmit
information rapidly and have integrated markets.
The integration of financial markets implies that there can
be no significant differences in exchange rates across
locations.
Arbitrage: buy at low price and sell at higher price for a
profit.
If the euro were to sell for $1.1 in New York and $1.2 in
London, could buy euros in New York (where cheaper) and
sell them in London at a profit.

Spot Rates and Forward Rates
Spot rates are exchange rates for currency exchanges “on
the spot” or when trading is executed in the present.
Forward rates are exchange rates for currency exchanges
that will occur at a future (“forward”) date.
Forward dates are typically 30, 90, 180, or 360 days in the
future.
Rates are negotiated between two parties in the present,
but the exchange occurs in the future.
Foreign exchange swaps: a combination of a spot sale with
a forward repurchase.
Swaps allow parties to meet each other’s needs for a
temporary amount of time and often cost less in fees than
separate transactions.
For example, suppose Toyota receives $1 million from
American sales, plans to use it to pay its California
suppliers in three months, but wants to invest the money in
euro bonds in the meantime.

Fig. 14-1: Dollar/Pound Spot and Forward Exchange Rates,
1983–2011
Source: Datastream. Rates shown are 90-day forward exchange
rates and spot exchange rates, at end of month

Spot Rates and Forward Rates
Futures contracts: a contract designed by a third party for
a standard amount of foreign currency delivered/received
on a standard date.
Contracts can be bought and sold in markets, and only the
current owner is obliged to fulﬁll the contract.
Options contracts: a contract designed by a third party for
a standard amount of foreign currency delivered/received
on or before a standard date.
Contracts can be bought and sold in markets.
A contract gives the owner the option, but not obligation,
of buying or selling currency if the need arises.

The Demand of Currency Deposits
What influences the demand of (willingness to buy)
deposits denominated in domestic or foreign currency?
Factors that influence the return on assets determine the
demand of those assets.
Rate of return: the percentage change in value that an
asset offers during a time period.
The annual return for $100 savings deposit with an interest
rate of 2% is $100 x 1.02 = $102, so that the rate of return
= ($102 – $100)/$100 = 2%.
Real rate of return: inflation-adjusted rate of return,
which represents the additional amount of goods & services
that can be purchased with earnings from the asset.
The real rate of return for the above savings deposit when
inflation is 1.5% is 2% – 1.5% = 0.5%. After accounting for
the rise in the prices of goods and services, the asset can
purchase 0.5% more goods and services after 1 year.

If prices are fixed, the inflation rate is 0
Because trading of deposits in different currencies occurs on
a daily basis, we often assume that prices do not change
from day to day.
A good assumption to make for the short run.
Risk of holding assets also influences decisions about
whether to buy them.
Liquidity of an asset, or ease of using the asset to buy
goods and services, also influences the willingness to buy
assets.

But we assume that risk and liquidity of currency deposits
in foreign exchange markets are essentially the same,
regardless of their currency denomination.
Risk and liquidity are only of secondary importance when
deciding to buy or sell currency deposits.
Importers and exporters may be concerned about risk and
liquidity, but they make up a small fraction of the market.
We therefore say that investors are primarily concerned
about the rates of return on currency deposits.
Rates of return that investors expect to earn are
determined by
interest rates that the assets will earn
expectations about appreciation or depreciation

A currency deposit’s interest rate is the amount of a
currency that an individual or institution can earn by
lending a unit of the currency for a year.
The rate of return for a deposit in domestic currency is the
interest rate that the deposit earns.
To compare the rate of return on a deposit in domestic
currency with one in foreign currency, consider
the interest rate for the foreign currency deposit
the expected rate of appreciation or depreciation of the
foreign currency relative to the domestic currency.

Fig. 14-2: Interest Rates on Dollar and Yen Deposits,
1978–2011

Suppose the interest rate on a dollar deposit is 2
Suppose the interest rate on a euro deposit is 4
Does a euro deposit yield a higher expected rate of return?
Suppose today the exchange rate is $1/e, and the expected
rate one year in the future is $0.97/e.
$100 can be exchanged today for e100.
These e100 will yield e104 after one year.
These e104 are expected to be worth $0.97/e × e104 =
$100.88 in one year.
The rate of return in terms of dollars from investing in euro
deposits is ($100.88 − $100)/$100 = 0.88%.
Let’s compare this rate of return with the rate of return
from a dollar deposit
The rate of return is simply the interest rate.
After 1 year the $100 is expected to yield $102:
($102 − $100)/$100 = 2%.

The euro deposit has a lower expected rate of return: thus,
all investors should be willing to dollar deposits and none
should be willing to hold euro deposits.
Note that the expected rate of appreciation of the euro was
($0.97 − $1)/$1 = -0.03 = -3%.
We simplify the analysis by saying that the dollar rate of
return on euro deposits approximately equals
the interest rate on euro deposits plus the expected rate of
appreciation of euro deposits
4% + -3% = 1% ≈ 0.88%
Re + (Ee
$/e
− E$/e)/E$/e

The diﬀerence in the rate of return on dollar deposits and
euro deposits is
R$ − (Re + (Ee
$/e
− E$/e)/E$/e)
R$: expected rate of return = interest rate on dollar
deposits
Re: interest rate on euro deposits.
Ee
$/e
: expected exchange rate.
E$/e: current exchange rate.
(Ee
$/e
− E$/e)/E$/e : expected rate of appreciation of the euro
Re + (Ee
$/e
− E$/e)/E$/e: expected rate of return on euro
deposits

Table 14-3: Comparing Dollar Rates of Return on Dollar and
Euro Deposits
Source: Datastream. Three-month interest rates are shown.

Model of Foreign Exchange Markets
We use the
demand of (rate of return on) dollar denominated deposits
and the demand of (rate of return on) foreign currency
denominated deposits
to construct a model of foreign exchange markets.
This model is in equilibrium when deposits of all currencies
oﬀer the same expected rate of return: interest parity.
Interest parity implies that deposits in all currencies are
equally desirable assets.
Interest parity implies that arbitrage in the foreign
exchange market is not possible.

Interest parity says:
R$ = (Re + (Ee
$/e
− E$/e)/E$/e)
Why should this condition hold? Suppose it didn’t.
R$ > (Re + (Ee
$/e
− E$/e)/E$/e)
Then no investor would want to hold euro deposits, driving
down the demand and price of euros.
Then all investors would want to hold dollar deposits,
driving up the demand and price of dollars.
The dollar would appreciate and the euro would depreciate,
increasing the right side until equality was achieved:
R$ > (↑)(Re + (↑)(E
e
$/e
− (↓)E$/e)/E$/e(↓))

How do changes in the current exchange rate aﬀect the
expected rate of return of foreign currency deposits?
Depreciation of the domestic currency today lowers the
expected rate of return on foreign currency deposits. Why?
When the domestic currency depreciates, the initial cost of
investing in foreign currency deposits increases, thereby
lowering the expected rate of return of foreign currency
deposits.
Dollar depreciation and Euro appreciation.
Appreciation of the domestic currency today raises the
expected return of deposits on foreign currency deposits.
Why?
When the domestic currency appreciates, the initial cost of
investing in foreign currency deposits decreases, thereby
increasing the expected rate of return of foreign currency
deposits.
Dollar appreciation and Euro depreciation,

Table 14-4: Today’s Dollar/Euro Exchange Rate and the
Expected Dollar Return on Euro Deposits When Ee
$/e
=
$1.05 per Euro

Fig. 14-3: The Relation Between the Current Dollar/Euro
Exchange Rate and the Expected Dollar Return on Euro
Deposits

Fig. 14-4: Determination of the Equilibrium Dollar/Euro
Exchange Rate

The eﬀects of changing interest rates:
an increase in the interest rate paid on deposits
denominated in a particular currency will increase the rate
of return on those deposits.
This leads to an appreciation of the currency.
Higher interest rates on dollar-denominated assets cause the
dollar to appreciate.
Higher interest rates on euro-denominated assets cause the
dollar to depreciate.

Fig. 14-5: Eﬀect of a Rise in the Dollar Interest Rate

Fig. 14-6: Eﬀect of a Rise in the Euro Interest Rate

If people expect the euro to appreciate in the future, then
euro-denominated assets will pay in valuable euros, so that
these future euros will be able to buy many dollars and
many dollar-denominated goods.
The expected rate of return on euros therefore increases.
An expected appreciation of a currency leads to an actual
appreciation (a self-fulﬁlling prophecy).
An expected depreciation of a currency leads to an actual
depreciation (a self-fulﬁlling prophecy).

Covered Interest Parity
Covered interest parity relates interest rates across
countries and the rate of change between forward exchange
rates and the spot exchange rate:
R$ = (Re + (F$/e − E$/e)/E$/e)
where F$/e is the forward exchange rate.
It says that rates of return on dollar deposits and “covered”
foreign currency deposits are the same.
How could you earn a risk-free return in the foreign
exchange markets if covered interest parity did not hold?
Covered positions using the forward rate involve little risk.

Summary
1 An exchange rate is the price of one country’s currency in
terms of another country’s currency.
It enables us to translate diﬀerent countries’ prices into
comparable terms.
2 Depreciation of a currency means that it becomes less
valuable and goods denominated in it are less expensive:
exports are cheaper and imports more expensive.
3 Appreciation of a currency means that it becomes more
valuable and goods denominated in it are more expensive:
exports are more expensive and imports cheaper.
4 Commercial and investment banks that invest in deposits of
diﬀerent currencies dominate the foreign exchange market.
Expected rates of return are most important in determining
the willingness to hold these deposits.

Summary
5 Rates of return on currency deposits in the foreign
exchange market are inﬂuenced by interest rates and
expected exchange rates.
6 Equilibrium in the foreign exchange market occurs when
rates of returns on deposits in domestic currency and in
foreign currency are equal: interest rate parity.
7 An increase in the interest rate on a currency’s deposit
leads to an increase in its expected rate of return and to an
appreciation of the currency.
8 An expected appreciation of a currency leads to an increase
in the expected rate of return for that currency, and leads
to an actual appreciation.
9 Covered interest parity says that rates of return on
domestic currency deposits and “covered” foreign currency
deposits using the forward exchange rate are the same.

Reference
Krugman, P., M. Obstfeld, and, M. Melitz (2010)
International Economics: Theory and Policy, 9/e Pearson,
Addison Wesley, ISBN-10: 0132146657
ISBN-13:9780132146654

Exchange Rates in the Short Run

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