INTERNATIONAL FINANCE

ECON 171, Ch.14 1

Ch.14 Exchange Rates as an Asset Price

I. What is exchange rate? 1. Nominal Exchange Rates

• The nominal exchange rate (E) measures the price of one currency in terms of another.

• It can be quoted in one of two ways:

i) As the price of the foreign currency in terms of the domestic currency: $1.65/£; $0.01027/¥ • Direct (or “American”) terms: dollars per unit of foreign currency

ii) As the price of domestic currency in terms of the foreign currency: £0.61/$; ¥97.385/$

• Indirect (or “European”) terms: foreign currency units per unit of dollar

Note: We treat the U.S. dollar ($) as the domestic currency all the time.

ECON 171, Ch.14 2

• If the current nominal exchange rate between the US$ and Japanese ¥ is $0.01027/¥, how

much $ can be exchanged for one yen?

• Nominal exchange rates allow us to translate different countries’ prices into comparable

terms (in a common currency): What is the dollar price of a Nissan that costs ¥2,500,000

when today’s exchange rate is $0.01027/¥? When today’s exchange rate is $0.011185/¥?

• From the example above, a depreciated currency means that imports are more expensive and

exports of domestic goods are cheaper, i.e., a depreciated currency lowers the price

of exports relative to the price of imports.

ECON 171, Ch.14 3

2. Appreciation vs. Depreciation of the Domestic Currency

• Appreciation is an increase in the value of a currency relative to another currency:

1/1/2016 1/1/2017

$1/€ → $0.9/€

• In the case above, the dollar has appreciated (more valuable) relative to the euro because it

now takes only $0.9 to buy one euro. In other words, each dollar can be exchanged for (can

buy) a larger amount of euro.

• On the other hand, the euro has depreciated relative to the dollar: it is now less valuable.

Note: Talking about an appreciation or depreciation of the domestic currency is meaningless

if the base currency is not indicated. For example, the U.S. dollar can appreciate against the

euro but depreciate against the Japanese yen.

ECON 171, Ch.14 4

3. Real Exchange Rates

• The real exchange rate (q) is defined as the relative price of foreign goods in terms of

domestic goods.

Example 1: Suppose both the U.K. and U.S. produce only one good: a Jaguar and Cadillac luxury sedan, respectively. A pound is worth two dollars, i.e., E = $2/£. How do we find the real exchange rate between the U.K. and U.S.?

£ price $ price Jaguar £30,000 $60,000 Cadillac $40,000

• Given the information above, the price of a Jaguar in terms of Cadillacs – that is, the real

exchange rate between the U.K. and U.S. – would be: 1.5 Cadillacs/Jaguar

• The above result means that to buy a Jaguar in the U.K., an American citizen will have to

give up an amount that could purchase 1.5 Cadillacs in the United States.

ECON 171, Ch.14 5

Generalization: Instead of using the price of a Jaguar and the price of a Cadillac, we must use a price index for ALL goods produced (i.e., the GDP deflator or Consumer Price Index) in the United Kingdom (𝑃∗) and in the United States (𝑃). Let 𝑃 be the domestic price level and 𝑃∗ be the foreign price level. The real exchange rate (q), the price of British goods in terms of the U.S. goods is thus given by

𝑞 = 𝐸 𝑃∗

𝑃

where E is the nominal exchange rate, denoted as dollar/pound rate (e.g. $1.5/ £).

• A real appreciation (depreciation) corresponds to a decrease (increase) in 𝑞, implying a rise

(fall) in a dollar’s purchasing power of foreign products relative to a dollar’s purchasing

power of U.S. products.

• When there is a real appreciation, what would happen to the foreign demand for the domestic

goods?

ECON 171, Ch.14 6

II. The Foreign Exchange Market • The market in which foreign currencies and other assets are exchanged for domestic ones is

called the foreign exchange market.

• The daily volume of foreign exchange transactions was $4.0 trillion in April 2010 (It was

$500 billion in 1989.). Most transactions (85% in April 2010) exchange foreign currencies

for U.S. dollars.

1. The Actors

• The major participants in the foreign exchange market are commercial banks, non-bank

financial institutions such as mutual funds and insurance companies, corporations that

engage in international trade, and central banks.

• Since the nominal exchange rate changes every minute and hence speculating (taking

advantage of arbitrage opportunities) in foreign exchange is a risky but potentially profitable

thing to do.

ECON 171, Ch.14 7

• Buying and selling in the foreign exchange market are dominated by commercial and

investment banks.

2. Standard Methods of Currency Exchange

1) Spot exchange rates: Exchange rates for currency exchanges “on the spot”, or when trading

is executed immediately

2) Forward exchange rates: Exchange rates for currency exchanges that will occur at a future

(“forward”) date (typically 30, 90, 180, or 360 days in the future).

ECON 171, Ch.14 8

Fig.1: Dollar/Pound Spot and Forward Exchange Rates, 1983-2013

ECON 171, Ch.14 9

III. The Demand for Foreign Currency Assets 1. What Influences the Demand for a Foreign Currency Bank Deposit?

• A foreign currency deposit’s future value depends on: i) the interest rate it offers and ii) the

expected change in the currency’s exchange rate against other currencies.

1) (expected) Asset Returns

• Rate of return: the percentage change in value that an asset offers over some time period

For example, the annual return for $100 savings deposit with an interest rate of 2% is

$100 × 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 and services that can be purchased with earnings from the assets (i.e., the

purchasing power of asset returns)

ECON 171, Ch.14 10

Question: What would be the real rate of return for the above savings deposit when inflation is expected to be 1.5%? Interpret your result.

• Therefore, in the short-run when prices are fixed,

(nominal) rates of return = real rates of return

2) Risk and Liquidity

• Holding an asset is risky because its real return is usually unpredictable and may turn out to

be quite different from what savers expected when they purchased the asset. In finance,

asset risk (≈ uncertainty) is often measured by the variance (or standard deviation) of

asset’s expected returns.

• Liquidity of an asset refers to how easily the asset can be transformed into the medium of

exchange in the economy. Certainly, cash is the most liquid of all assets.

ECON 171, Ch.14 11

• We assume that risk and liquidity of currency deposits in foreign exchange markets are

essentially the same, regardless of their currency denomination. In fact, risk and liquidity

are only of secondary importance when deciding to buy or sell currency deposits.

3) Interest Rates and Exchange Rates

• We therefore say that investors are primarily concerned about the rates of return on

currency deposits which consist of interest rates (in domestic currency) and expected

changes in exchange rates.

ECON 171, Ch.14 12

Fig.2: Interest Rates on Dollar and Yen Deposits, 1978-2013

• Note that two interest rates above are not measured in comparable terms, so no close co-

movement is observed.

ECON 171, Ch.14 13

Example 2: Suppose the interest rate on a dollar deposit (𝑅$) is 2% and on a euro deposit (𝑅€) is 4%. Today’s exchange rate :𝐸$/€; is $1/€ and the expected exchange rate one year in the future :𝐸$/€

< ; is $0.97/€. Compare the rate of return from two deposits.

Year t Year t + 1

Dollar deposit $1 → $(1 + 𝑅$) $1 $(1 + 𝑅€) × 𝐸$/€

<

↓ at 𝐸$/€ ↑ at 𝐸$/€ <

Euro deposit €1 := $1/𝐸$/€; → €(1 + 𝑅€)

• The rate of return in terms of dollars from investing in euro deposits is 0.88% (not 4%) and

the rate of return from a dollar deposit is 2%. Thus, all investors should be willing to hold

only dollar deposits.

ECON 171, Ch.14 14

Generalization: The rate of return in terms of dollars from investing euro deposits can be written by

$(1 + 𝑅€) 𝐸$/€

× 𝐸$/€ <

• If

$(1 + 𝑅$)?@@A@@B <CD<EF<G $ H<FIHJ KHLM N GLOONH G<DLPQF

≠ S $(1 + 𝑅€)

𝐸$/€ × 𝐸$/€

< T ?@@@@@@A@@@@@@B

<CD<EF<G $ H<FIHJ KHLM NJ <IHL G<DLPQF

there exists an arbitrage opportunity. Given the exchange rate markets move instantaneously,

this arbitrage opportunity will disappear immediately if all traders start taking advantage of

existing profit opportunity. In other words, the two returns must be equal in equilibrium.

ECON 171, Ch.14 15

• Equalizing the two returns (and cancelling the dollar signs),

(1 + 𝑅$) = (1 + 𝑅€) × U1 + 𝐸$/€ < − 𝐸$/€ 𝐸$/€

W

≈ 1 + 𝑅€ + 𝐸$/€ < − 𝐸$/€ 𝐸$/€

• Further simplifying, we eventually obtain the uncovered interest parity (UIP) condition:

𝐑$ = 𝐑€ + U 𝐄$/€ 𝐞 − 𝐄$/€ 𝐄$/€

W

where the \ 𝐄$/€ 𝐞 ]𝐄$/€ 𝐄$/€

^ on the right-hand-side can be called the expected appreciation rate

of the euro.

ECON 171, Ch.14 16

• What are the assumptions made to reach the above UIP condition?

i) risk-neutral investors; ii) rational expectations; iii) negligible transaction costs; iv) perfect

capital mobility; v) identical maturity of assets; vi) identical default risk of assets

• Let’s go back to Example 2 above. There we had 𝑅$ = 2% and 𝑅€ = 4%. The uncovered

interest parity (UIP) condition did not hold in that example because

𝐸$/€ < − 𝐸$/€ 𝐸$/€

= 0.97 − 1

1 = −0.03 = −3%

and

𝑅$ > 𝑅€ + U 𝐸$/€ < − 𝐸$/€ 𝐸$/€

W ↔ 2% > 1%(≈ 0.88%)

All investors would want to hold dollar deposits (and no demand for euros).

ECON 171, Ch.14 17

• What will happen? The dollar would appreciate and the euro would depreciate until the

equality was achieved.

• If the UIP holds, we expect the euro to depreciate against the U.S. dollar by 2%.

• Lesson: The UIP condition says that a country that pays the higher interest rate is expected to

have a currency depreciation.

• On the other hand, the covered interest parity (CIP) condition relates interest rates across

countries and the rate of change between forward exchange rate 𝐹$/€ and the spot exchange

rate 𝐸$/€:

𝑅$ = 𝑅€ + U 𝐹$/€ − 𝐸$/€

𝐸$/€ W

?@@@A@@@B KLHcNHG DH<MQIM LJ <IHLP

ECON 171, Ch.14 18

• CIP says that rates of return on domestic currency deposits and “covered” foreign currency

deposits using the forward exchange rate are the same. Note that covered positions using the

forward rate involve little risk.

IV. Equilibrium in the Foreign Exchange Market • The foreign exchange market is in equilibrium when deposits of all currencies offer the same

expected rate of return (so called interest parity). Therefore, arbitrage in the foreign

exchange market is not possible.

1. How Changes in the Current Exchange Rate Affect Expected Returns?

Question: Would depreciation of the domestic currency today lower or raise the expected rate of return on foreign currency deposits?

ECON 171, Ch.14 19

Table 1: Today’s Exchange Rate (𝐸$/€) and Expected $ Return on Euro Deposits

(Assume 𝐸$/€ < = $1.05/€)

ECON 171, Ch.14 20

Fig.3: The Relation between 𝐸$/€ and the Expected $ Return on Euro Deposits

ECON 171, Ch.14 21

2. The Equilibrium Exchange Rate

Fig.4: Determination of the Equilibrium Dollar/Euro Exchange Rate based on UIP

ECON 171, Ch.14 22

V. Interest Rates, Expectations, and Equilibrium 1. The Effect of Changing Interest Rates on the Current Exchange Rate

• All else equal, 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.

Question: But the UIP condition says that a country that pays the higher interest rate is expected to have a currency depreciation! Does it make sense to you?

Note: Assumption of a constant expected future exchange rate, in Table 1, Fig 3-6, is often unrealistic. While in normal UIP condition, 𝑬$/€

𝒆 is not assumed fixed.

1) Higher interest rates on dollar-denominated assets (including dollar deposits) cause the

dollar to appreciate.

2) Higher interest rates on euro-denominated assets (including euro deposits) cause the dollar

to depreciate (or the euro to appreciate).

ECON 171, Ch.14 23

• Look at the graphical presentations: Fig.5 and Fig.6

Fig.5: Effect of a Rise in the Dollar Interest Rate (𝑅$)

ECON 171, Ch.14 24

Fig.6: Effect of a Rise in the Euro Interest Rate (𝑅€)

ECON 171, Ch.14 25

2. The Effect of Changing Expectations on the Current Exchange 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.

• From the analysis using Fig.6, we conclude that there exists self-fulfilling prophecy:

An expected appreciation (depreciation) of a currency leads to an actual appreciation

(depreciation).

“All else equal, a rise (fall) in the expected future exchange rate causes a rise (fall) in the

current exchange rate.”

ECON 171, Ch.14 26

Question: Do you think the UIP condition would hold well in practice in the short-run?

Recall the assumptions made to reach the UIP condition.

A difference in the risk of domestic and foreign assets is one reason why expected rates of

return are not equal across countries:

𝑅$ = 𝑅€ + U 𝐸$/€ < − 𝐸$/€ 𝐸$/€

W + 𝜌

where r is called a risk premium.