Chapter 18

Exchange Rate Determination I:

Prices and the Real Exchange Rate

Chapter 19

Exchange Rate Determination II:

Nominal Exchange Rates and Currency Crises

Exchange Rate Crises & Hong Kong

HK Dollars, as currency, is printed by money center banks Standard Chartered, HSBC, and, now, Bank of China.

During the 1970’s, the banks faced little limitation on money creation. In July of 1982, the HK dollar was depreciating at a rate of 7.7% per year.

In 1983, Britain and the People’s Republic were engaged in talks about the terms on which Hong Kong would be returned to China. Responding to news from these talks, currency traders unloaded there HK dollar positions.

As a response, the Hong Kong dollar depreciated rapidly. By September 1983, the HK dollar was depreciating at a rate of 65% per year.

Policy Response: Currency Board

The government announced that Hong Kong would switch to a currency board system.

A currency board is an arrangement whereby a country can only issue domestic currency if it backed up by central bank holdings of a specific foreign currency.

To give permission to a money center bank to print 7.8 HK dollars, the government would have to acquire US$1.

This has been the monetary policy of Hong Kong ever since.

Objectives

Define the real exchange rate and purchasing power parity.

Explain why inflation in Hong Kong differs from the US.

Demonstrate that the capital account is the negative of the current account.

Use interest differentials to price exchange rate futures.

Define uncovered interest parity and explain exchange rate fluctuations.

Bilateral Exchange Rate

Bilateral Exchange Rate is the exchange rate of one countries’ currency vs. another’s.

Exchange rates can be written in two ways which are inverses of each other.

St Definition 1 The price of

foreign currency in terms of domestic currency (the # of domestic currency units needed to purchase 1 unit of foreign currency)

St = HK$7.8 per 1 US$

Zt Definition 2 The price of

domestic currency in terms of foreign currency (the # of foreign currency units needed to purchase 1 unit of domestic currency).

Zt = US$.128 per 1 HK$

1t

t

ZS

Terminology Typically, a bilateral

exchange rate is reported as the # of units of the currency with the lower value per unit of the currency of the higher value.

Examples HK$7.8 per 1 US$ ¥120.14 per 1 US$ US1.53 per 1 ₤

An appreciation of a currency is an increase in the value of a currency.

A depreciation is a decrease in value.

A depreciation would increase the exchange rate, St, by Definition 1.

Ex. A movement of HK$7.8 to HK$10 per US is a depreciation.

A depreciation would decrease the exchange rate, Zt, by Definition 2.

Ex. A movement of US$.127 to US$.1 would be a depreciation of HK dollar.

Exchange Rate Regimes

HK has a fixed bilateral exchange rate with the US.

HK Exchange Fund (the currency board operated by HKMA) stands ready to buy or sell unlimited amounts of HK$ at a fixed exchange rate HK$7.8:US$1. This policy fixes the market rate at this level. No one will ever pay more for HK dollars than

it costs to buy from the exchange fund. No one will ever sell HK dollars for less than

they could get from the exchange fund.

Floating Exchange Rates

Most large, wealthy economies conduct monetary policy through open market operations and allow the exchange rate to be determined on a minute-by-minute basis in financial markets. These exchange rates are said to float. (Example: Canada, UK, USA, Euroland)

Many smaller economies allow the exchange rates to float but occasionally buy or sell foreign currency to directly affect the exchange rate. Such exchange rates are called managed floats. (These are sometimes called dirty floats).

Effective Exchange Rates

Effective Exchange Rate is a weighted average of a country’s bilateral exchange rates relative to some base year.

The weight on the exchange rate with country j is the share of trade with country j.

Effective exchange rates are usually quoted in the form of Definition 2.

1 1

1 21 2....

NEER t t tt N N

B B B

Z Z ZZ w w w

Z Z Z

j jB B

jB B

IM EXw

IM EX

HK Effective Exchange Rate

108

110

112

114

116

118

120

122

1998 1999 2000 2001 2002

Effective Exchange Rate HK

Ind

ex

(10

0 in

19

90

)

Real Exchange Rate

A foreigner compares the price of their foreign goods with the price of our domestic goods. To buy 1 foreign good, he

must pay PF foreign currency units where PF ≡ Foreign price level.

To buy 1 domestic good, he must pay P domestic currency units, but he must pay Z× P foreign currency units.

Real exchange rates are the price of domestic goods relative to the price of foreign goods. In other words, real exchange rates are the # of foreign goods that must be given up to obtain 1 domestic good.

Real exchange rate can be calculated on a bilateral basis or an index basis.

F

PE ×

P F

PZ

S P

HK: US Real Exchange Rate

.06

.08

.10

.12

.14

.16

.18

.20

.22

1980 1985 1990 1995 2000

Real Exchange Rate US$ per HK$

Law of One Price (LoOP)

Arbitrage should insure that identical goods should sell for the same price in different markets. This is called the Law of One Price.

For easily transportable, standardized goods sold in highly competitive markets (such as gold), LoOP holds.

For most goods, that consumers buy and sell, LoOP does not hold across countries. Example: A Big Mac cost PF = US$2.65 in New York. A Big

Mac cost P = HK$11.20 in HK. Given an exchange rate Z = .128, the cost of a HK Big Mac in US$ is Z∙P = US$1.44.

Big Macs Around the World

Why doesn’t LoOP hold for most goods?

1. Transport Costs – Large costs of moving goods may keep arbitrage from working.

2. Non-traded Goods – Some goods, such as real estate, have near infinite transport prices.

3. Pricing-to-Market – Firms with market power may find it optimizing to charge different prices in different markets.

4. Tariffs & Taxes – Imported goods may face additional taxes

Purchasing Power Parity (PPP)

PPP theory says LoOP applies to all markets. Define relative prices of foreign goods

Absolute PPP says that the real exchange rate is always E = 1 or Z = XP

Relative PPP says that the growth rate of the real exchange rate is zero

FPXP P

0E Z Fg g

Does PPP Hold?

Does Absolute or Relative PPP hold? In short run, NO. Exchange rates are much more

volatile than inflation rates. In long run for countries with similar levels of

development, relative PPP holds. Example. Twenty year averages for OECD countries.

Rapidly developing countries typically see long-term real exchange rate appreciations Hong Kong has had much faster inflation than the US

over the life of the exchange rate peg.

Long Run

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

-4.00 -2.00 0.00 2.00 4.00 6.00 8.00

Aver age Annual Depr eciation (%) Against the US $

Ave

rag

e A

nn

ual

In

flat

ion

Dif

fere

nti

al

wit

h t

he

US

J apan

NZ

Italy

Switz. Germany

NL

Denmark

UK

FranceCanada

Rich Countries are more expensive than poor countries. Many types of services have unchanging technology

(like haircuts) or inherently limited supply (like real estate).

Most technology advances occur in traded goods sector.

As a country grows wealthier and more technologically advanced, the countries residents will pay more for real estate or services.

If traded goods have roughly equal prices across countries, but a countries non-traded goods start to become more expensive as it develops, the overall relative price of its goods will increase.

XP vs. Exchange Rate

RealExchange ExchangeRate XP Rate

Hong Kong 0.128 0.150 0.858China 0.121 0.522 0.231Japan 0.009 0.006 1.448Macau 0.125 0.203 0.613Singapore 0.580 0.724 0.801Philippines 0.023 0.091 0.249Indonesia 0.022 0.130 0.171

Year 2000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Hong Kong

China

Japan

Macau

Singapore

Philippines

Indonesia

Real Exchange Rate w/ USA

Converting GDP into Equivalent Units

GDP in different countries are measured in local currency units. To compare, we convert to common currency units, US dollars.

Two methods

1. Exchange Rate Conversion – Multiply by Z

2. PPP Conversion – Multiply by XP

GDP per Capita Z XP US$ US$Local Currency Z XP Exchange Rate PPP

HK 192,776 0.128 0.150 $24,743 $28,846China 6,423 0.121 0.522 $776 $3,353

Why do poor countries appear richer when PPP conversion is used. Exchange rate conversion calculates the # of US

dollars needed to buy the number of domestic currency units needed to buy the country’s GDP.

PPP conversion values the domestic goods at US dollar prices.

Since non-traded goods are cheap in poor countries (when calculated by exchange rate conversion), valuing them at US prices increases their relative value.

For poor countries, their goods are cheaper than their currency, because non-traded goods are relatively cheap.

Current Account

The current account is, conceptually, the amount of income earned overseas less the amount of income earned by foreigners from the domestic economies.

Current Account =

Balance on Goods (Goods Exports-Goods Imports)

+ Balance on Services (Services Exports-Services Imports)

+ Net Investment Income

(Investment Income Earned Overseas – Investment Income Paid to Foreigners)

+Net Transfers (Donations from Overseas – Donations to Overseas)

Capital & Financial Account

The capital account (more accurately the capital & financial account) records capital inflows into the country. The account includes the financial account, the capital account, and change in reserve assets.

Capital &

Capital Account

(Debt Forgiveness, Patents)

Financial

+ Financial Account →

Direct Investment (FDI of Foreign Companies – FDI by Domestic Companies)

Account=

+ PortfolioInvestment

(Domestic Securities Purchases by Foreigners – Foreign Securities Purchases by Domestic Residents)

+ Other Investments (Deposits in Domestic Banks by Foreigners – Deposits in Foreign Banks by Domestic Residents)

+ Change in Reserve Assets

-Accumulation of Foreign Exchange Reserves

Hong Kong Current Account & Capital Account 2001

Capital Account -9155Into HK Abroad

Direct Investment 96948 185424 88476Foreign Holdings Holdings ofof Hong Kong Foreign AssetsAssets

Portfolio Investment -322045 -9054 312992Financial Derivatives 39640 -100507 -140147Other Investment 133783 -327414 -461197Change in Reserves -36530Capital &Financial -97359Account

Hong Kong had a 96 billion dollar current account surplus in 2001.

Hong Kong had a 97 billion dollar capital & financial account deficit.

The difference is statistical or measurement error.

Net Credit DebitGoods -64970 1488982 1553952Services 133468 323087 189619Income 41175 384595 343420Current Transfers -13878 4719 18597Current Account 95795 2201383 2105588

Net Savings = Net Exports

Capital Account = I – S Current Account = EX – IM S = Y – C – G Y = C + I + G + EX – IM → Y – C – G = I + EX-IM

S = I + EX – IM → S – I = EX - IM

Net Capital Outflows = Goods Outflows When an economy provides more goods to the world

economy than it receives in return it will have extra foreign funds. These will be used to acquire foreign assets.

Real Exchange Rate and Net Exports

An increase in the real exchange rate has counter-veiling effects on net exports.

1. The value/price of a given amount of export goods will rise relative to a given amount of import goods when domestic goods increase in relative price. An economy exports 100 apples at price of $1 each and

imports 100 oranges at price of $1. Net exports are zero. If price of apples goes to $2, then net exports will increase to 100.

2. When relative price of domestic goods increases, the domestic economy will export fewer goods and import more goods.

In very short run, the first effect will dominate. In medium to long run, the second effect tends to dominate.

J-Curve: The dynamics of an exchange rate depreciation

time

E

NX

x

Equilibrium Real Exchange Rates

NX

S-IE

E*

Real Exchange Rate Determination

The real exchange rate, in the medium run, is determined by the position of savings and investment.

Shortfalls in domestic savings result in high real exchange rates and low net exports.

High relative demand for domestic goods for reasons such as tariffs will result in high real exchange rates

Net Savings (S-I)

Net ExportDemand

Real Exchange Rate

Budget Deficit

← ↑

Productivity Boom

← ↑

Tariffs ↑ ↑

Budget Deficit/Productivity Boom

NX

S-IES-I’

E**

Tariffs

NX

S-IE

E*

NX’

E**

Nominal Exchange Rate

Quantities of funds exchanged in foreign currency markets far exceed the currency needed for goods trade. Most currency trading is for asset trading or portfolio holding purposes.

Exchange rates are more volatile than goods prices and quantities.

In the short run, currencies behave like financial assets with volatility like financial markets.

Spot vs. Forward Markets

Two basic markets for foreign exchange.

1. Spot Markets – In spot markets, traders agree on terms/rates for currency trades with immediate delivery (within 48 hours).

2. Forward Markets – In forward markets, traders agree on terms/rates for currency trades at some specified future date (usually 30, 90 or 180 days)

Define St as the (Definition 1) exchange rate for currency for immediate trade.

Define Ft as the exchange rate for delivery at a date on period in the future.

Covered Interest Parity

An investor has $1 for saving. Consider two investment strategies:

1. Invest $1 in a domestic bond with interest rate 1+i.

2. Use $1 to buy 1/St foreign dollars in spot markets. Invest 1/St in foreign bonds at interest rate 1+i*. Agree on a forward contract to sell (1+i*)/St foreign currency for domestic dollars.

Arbitrage implies that the two strategies will have the same pay-off.

This implies a forward price.

*(1 )tt

t

F iS

*1 (1 )tt t

t

Fi iS

*1

1t

t tt

iF Si

Forward Rates

We can price long term futures using long-term interest rates. Define

as the yield on a domestic bond that matures in T periods and as the yield on a similar foreign bond.

Example 1: The three month interest yield for HK is 1.18%. In Thailand, the 3 month yield is 1.5%. The current Baht-HK$ rate is 0.18263839.

This implies a 3 month forward rate of

Example 2: The 10 year interest yield in Thailand is 3.3352 while the 10 year yield in HK is 4.310. This implies a

,t Ti

,Ft Ti

( ),

,

(1 )

(1 )

TTt TtF T

t t T

iF

S i

.25(.25)

.25

(1.018)0.18263839=0.1824942722

(1.015)tF

10(10)

10

(1.0431)0.18263839=0.200291575

(1.03352)tF

Uncovered Interest Parity

Forward prices should equal the market’s expectation of future spot rate. If traders think the price of foreign currency >

Ft, then why agree to deliver it at that price. If traders think the price of foreign currency < Ft, why agree to pay that price.

This should imply a term for exchange rate parity

11

1E t

Ft t tt

iS F Si

Implications

We observe that different countries have different interest rates.

UIRP suggests that countries with high interest rates are expected to have their currency depreciate. One reason not to buy bonds in a high interest

economy is that you expect the value of the currency to drop.

Interest rate differentials, by this logic, are the market’s prediction of future exchange rate growth:

1 1

1

Et t

Ft t

S i

S i

Exchange Rate Determination

UIRP Creates a financial market theory of exchange rate determination

Graph expected returns from investing in domestic and foreign currency.

Exchange Rate equalizes the two returns.

Domestic Currency Payoff From Domestic Bonds

Expected Domestic Currency Payoff from Foreign Bonds

1+it1 (1 )E

Ftt

t

S iS

Equilibrium Exchange Rate

1+i

Return

St

S*

1 (1 )E

Ftt

t

S iS

Exchange Rate Determination Implications:1. Given future exchange

rates, a rise in domestic interest rates or a fall in interest rates will lead to an appreciation.

• A temporary increase in domestic interest rates will lead to appreciation.

2. A rise in the future value of the currency will increase the current value.

• Current exchange rate depends on whole path of future interest rates.

Event Exchange Rate

Temporaryi→

St ↓

TemporaryiF →

St ↑

St+1 ↑ St ↑

Rise in Domestic Interest Rates

1+i

Return

St

S*

1 (1 )E

Ftt

t

S iS

1+i’

S**

Contradiction and Dynamics

If domestic bond yields are higher than foreign yields, we should expect a depreciation of domestic currency over the life of bond.

A temporary increase in domestic yields leads to a domestic currency appreciation.

Is this a contradiction? No, the domestic

currency will immediately appreciate and subsequently depreciate back to the original position.

Time Path: Temporary Rise in Domestic Interest Rates

S

i

timeX

Rise in Foreign Interest Rates or Future Depreciation

1+i

Return

St

S*

1 (1 )E

Ftt

t

S iS

S***

Time Path: Temporary Rise in Foreign Interest Rates

S

iF

time

Long-term Interest Differentials

Why might long-term nominal interest rates differ. If relative PPP holds in the long-run, then a countries

average expected depreciation rate over the long run should be a function of its inflation differential.

A country with higher average inflation should have a depreciating currency and higher average interest rates.

If long-term interest rates are the average of expected future interest rates, then countries with faster long-term inflation should have higher long-term interest rates.

UIRP & Exchange Rate Volatility

Using UIRP we can write the exchange rate as a function of the future series of exchange rate differentials.

Since forecasts of future variables may be volatile and subject to optimism and pessimism, this may explain a large degree of exchange rate volatility.

22 3

2

1,...

1

Ft

t tt

iS S

i

1

1,

1

Ft

t tt

iS S

i

11 2

1

1

1

Ft

t tt

iS S

i

1 2 3

1 2 3

1 1 1 1..... ,

1 1 1 1

F F F Ft t t t

t tLRt t t t

i i i iS S

i i i i

Is UIRP true

On average, UIRP does not hold. High interest rate countries do not see their countries currencies deteriorate.

On average, buying bonds in high interest rate countries generates high average returns.

Why don’t investors take advantage of these opportunities? Investors perceive these countries as having

some risk of an exchange rate depreciation and investors are risk averse.

Risk Adjusted UIRP

We might assume that there is a risk premium (either positive or negative) for investing in foreign bonds relative to investing in domestic bonds.

A temporary increase in the risk premium on foreign asset will lead to an appreciation of the domestic currency.

11 (1 )tt t t

t

Si rp i

S

Thai Interest Rates and the Dollar/Baht Rate

0

4

8

12

16

.12

.16

.20

.24

.28

.32

1990 1992 1994 1996 1998 2000

HK$: BahtThai Baht Time Deposit Rate - 1YearHK$ Time Deposits - 1 year

Costs of Exchange Rate Volatility

Volatile exchange rates generate income risk for firms that export goods. This may eliminate some benefits of international trade.

Volatile exchange rates generate liability risk for firms that borrow foreign currency to finance investment projects. This is especially significant for firms in emerging markets.

Means to Fix Exchange Rate

Currency Board: Government/central bank commit to buy or sell foreign currency at a fixed exchange rate. This fixes the exchange rate at that level (example: Hong Kong).

Dollarization: The economy abandons a national currency and uses some foreign currency for all transactions (example: Panama).

Currency Area: A number of countries choose to jointly adopt the same currency (example: Euroland).

Exchange Rate Peg: Central bank buys and sells foreign currency in foreign currency markets to manipulate exchange rate.

Exchange Rate Systems

Impossible Trinity: There are a menu of three policy goals, among which a government can choose at most two.

1. Free International Capital Flows

2. Fixed Exchange Rates

3. Free Interest Rate/Monetary Policy If a country, like HK, chooses 1) and 2) then

domestic interest rates must equal foreign interest rates.

Fixed Exchange Rates/Free Capital Movements If there are free capital flows, then UIRP

holds. A permanent fixed exchange rate St = St+1

implies i = iF. If currencies have constant relative value

over time, then investing in bonds denominated in either one should be equivalent so interest rates should be equivalent.

HK vs. US Interest Rates

0

2

4

6

8

10

12

1992 1994 1996 1998 2000 2002

Exchange Fund Yields US Treasury Bill Yields

Foreign Reserves & Fixed Exchange Rates To maintain a fixed exchange rate the central bank

must agree to buy or sell as much domestic currency as the marketplace wants at that level.

The central bank can always sell an infinite amount of domestic currency simply by printing new currency.

The central bank can only buy foreign currency if it has sufficient foreign reserves. When a central bank runs out of foreign reserves, the exchange rate regime must fail.

Type 1 Currency Crises: Lack of reserves When a government is unable to raise revenue

through taxation or selling bonds, it will often raise revenue through seignorage.

Under a flexible exchange rate, this would lead to high inflation and an exchange rate depreciation.

Under a fixed exchange rate, the central bank would buy the excess domestic currency which would drain its foreign reserves.

When the foreign reserves are lost the peg must go as well.

Type 2: Currency Crises (a self-fulfilling prophecy) If people lose confidence in the peg, then the

domestic interest rate will rise, reducing investment by domestic firms.

If the economic demand from domestic sources drops, then their will be political pressure to devalue the currency in order to increase net exports

Conclusion

The nominal exchange rate is the price of one currency with respect to another, which along with domestic and foreign price levels determines the relative price of foreign goods.

In a world with perfect arbitrage, all goods would have the same price in every country, but due to transport costs, tariffs and market power goods have different prices.

In the long run, countries at the same level of development will tend to have zero average growth in the real exchange rate, so a country’s currency will tend to depreciate on average if it has high relative inflation.

Conclusion, Pt. II

In the short run, a rise in the relative price of a country’s goods may increase net exports, but in all but the shortest run, a rise in the relative price of a country’s goods will induce expenditure switching and a fall in net exports.

It is an accounting identity that a country’s net capital outflows (the negative of the capital account) are equal to a country’s net goods outflows (the current account).

In equilibrium, the real exchange rate will adjust to set the trade balance (NX) equal to net capital outflow (S – I). Thus, a country’s trade balance is determined by the adequacy of domestic savings to finance domestic investment.

Conclusion Pt. III

Most, foreign currency trades are for capital flows. Equalizing risk-free returns across country’s bond

markets implies a formula for forward currency prices (at all maturities) as a function of nominal interest rate differentials and spot rates called covered interest parity.

If forward prices are the markets predictions of future spot rate, we can predict future exchange rate depreciations (at all future dates) as a function of interest differentials.

Conclusion Pt.IV

The equilibrium nominal exchange rate will equalize the expected returns of investing in foreign and domestic bonds given domestic and foreign interest rates and expected future interest rates.

Information that a currency will depreciate in the future would reduce the returns for investing in that country and lead in equilibrium to immediate pressure on the exchange rate. In the short run, exchange rates have a volatility and unpredictability similar to asset prices.

Conclusion Pt. V

Uncovered Interest Rate Parity may not hold on average because investors are risk averse. A rise in the risk of investing in a given country will put downward pressure on the interest rate.

A country may want to peg its exchange rate to avoid the negative impact of exchange volatility. However, central bank must either apply capital controls or give up an independent interest rate policy.