Review of Exchange Rate Basics

Review ofReview ofExchange Rate BasicsExchange Rate Basics

Key PointsKey Points

1. An economy’s price level captures the average rate at 1. An economy’s price level captures the average rate at which money is traded for goods - and inflation measures how which money is traded for goods - and inflation measures how this rate changes through time.this rate changes through time.

2. An economy’s nominal interest rate captures the price at 2. An economy’s nominal interest rate captures the price at which individuals are willing to trade money through time.which individuals are willing to trade money through time.

3. An economy’s real interest rate captures the price at which 3. An economy’s real interest rate captures the price at which individuals are willing to trade goods through time.individuals are willing to trade goods through time.

4. The Fisher Effect captures a relationship between each of 4. The Fisher Effect captures a relationship between each of these prices - which is enforced through risky arbitrage these prices - which is enforced through risky arbitrage activity.activity.


5. Prices and interest rates are determined by individuals’ 5. Prices and interest rates are determined by individuals’ demand for money (relative to that of goods or future money) demand for money (relative to that of goods or future money) and its supply.and its supply.

6. Central banks set the money supply via intervention in the 6. Central banks set the money supply via intervention in the money market and the foreign exchange market, as well as money market and the foreign exchange market, as well as through regulation.through regulation.

7. By adjusting the money supply, central banks can strongly 7. By adjusting the money supply, central banks can strongly influence inflation and interest rates.influence inflation and interest rates.

8. Exchange rate is a price, determined like any other price, by 8. Exchange rate is a price, determined like any other price, by buyers and sellers of currencies; relative supply and demand buyers and sellers of currencies; relative supply and demand for currencies.for currencies.


9. Since the exchange rate is determined by relative supply 9. Since the exchange rate is determined by relative supply and demand, other factors affecting supply and demand will and demand, other factors affecting supply and demand will impact the exchange rate: inflation, interest rate changes, impact the exchange rate: inflation, interest rate changes, government intervention.government intervention.

10. Law of One Price, Purchasing Power Parity, and Relative 10. Law of One Price, Purchasing Power Parity, and Relative Purchasing Power Parity describe the relation between prices Purchasing Power Parity describe the relation between prices and exchange rates.and exchange rates.

11. These relationships hold well where goods arbitrage is 11. These relationships hold well where goods arbitrage is possible - in ‘tradable goods’.possible - in ‘tradable goods’.

12. The important exchange rate to focus on to determine the 12. The important exchange rate to focus on to determine the real impact of exchange rate fluctuations is the Real real impact of exchange rate fluctuations is the Real Exchange Rate - the exchange rate adjusted for inflation.Exchange Rate - the exchange rate adjusted for inflation.

Key Points (cont’d)Key Points (cont’d)

13. Exchange rate risk involves, therefore, 13. Exchange rate risk involves, therefore, unpredictable change in the real exchange rate.unpredictable change in the real exchange rate.

14. Some 14. Some real exchange rate changesreal exchange rate changes are are predictable (i.e. in growing economies) but many predictable (i.e. in growing economies) but many perhaps most are not.perhaps most are not.

Prices and Interest RatesPrices and Interest Rates

Prices and interest rates are simply numbers which Prices and interest rates are simply numbers which reflect the values of cash today relative to goods and reflect the values of cash today relative to goods and services today and to notes promising cash in the services today and to notes promising cash in the future.future.


Prices and interest rates are simply numbers Prices and interest rates are simply numbers which reflect the values of cash today relative which reflect the values of cash today relative to goods and services today and to notes to goods and services today and to notes promising cash in the future.promising cash in the future.

TodayToday

CashCash

Price LevelPrice Level

CashCashNominal Interest RateNominal Interest Rate

Goods/ServicesGoods/Services

TomorrowTomorrow


We use PWe use Ptt and R and R t, t+1t, t+1 to denote the price level to denote the price level and one-period nominal interest rate at time t:and one-period nominal interest rate at time t:

TodayToday

CashCash

PPtt

CashCashR R t, t+1t, t+1

Goods/Services

TomorrowTomorrow


The percent change in the price level is the The percent change in the price level is the inflation rate...inflation rate...

TodayToday

CashCash

Pt


TomorrowTomorrow

CashCash

PPt+1t+1Inflation RateInflation Rate


R R t, t+1t, t+1


……which we denote as Pi.which we denote as Pi.

TodayToday

CashCash

PPtt


TomorrowTomorrow

CashCash

PPt+1t+1 tt


R R t, t+1t, t+1


The real interest rate - although not observed - can be The real interest rate - although not observed - can be thought of as the price at which individuals are willing to thought of as the price at which individuals are willing to exchange goods today for goods tomorrow…exchange goods today for goods tomorrow…

TodayToday

CashCash

PPtt


TomorrowTomorrow

CashCash

PPt+1t+1

Real Interest RateReal Interest RateGoods/ServicesGoods/Services

tt

R R t, t+1t, t+1


As before, we denote the real interest rate as As before, we denote the real interest rate as rr t, t+1 t, t+1..

TodayToday

CashCash

PPtt


TomorrowTomorrow

CashCash

PPt+1t+1

rr t, t+1 t, t+1Goods/ServicesGoods/Services

R R t, t+1t, t+1

tt

The Fisher EffectThe Fisher Effect

The Fisher Effect captures the relationship between The Fisher Effect captures the relationship between inflation, nominal interest rates, and real interest inflation, nominal interest rates, and real interest rates.rates.

TodayToday

CashCash

PPtt


TomorrowTomorrow

CashCash

PPt+1t+1


R R t, t+1t, t+1

tt

The Fisher EffectThe Fisher Effect

This relationship says quite simply that nominal This relationship says quite simply that nominal interest rates are a product of real interest and interest rates are a product of real interest and expected inflation.expected inflation.

TodayToday

CashCash

PPtt


TomorrowTomorrow

CashCash

PPt+1t+1


R R t, t+1t, t+1

1+R 1+R t, t+1 t, t+1 = (1+ E(= (1+ E( t t) + r) + r t, t+1 t, t+1))

tt

An Exchange Rate is Just a PriceAn Exchange Rate is Just a Price

An exchange rate is simply the price of one currency in terms An exchange rate is simply the price of one currency in terms of another.of another.

Why is there confusion?Why is there confusion?

• 1.68DM/$ is price of a Dollar in terms of Marks.1.68DM/$ is price of a Dollar in terms of Marks.

• $0.59/DM is price of a Mark in terms of Dollars.$0.59/DM is price of a Mark in terms of Dollars.

No different from any other price.No different from any other price.

• $0.5/Apple$0.5/Apple

• 2 Apples/$.2 Apples/$.

Exchange Rate QuotationsExchange Rate Quotations

1)1) Direct Terms or American TermsDirect Terms or American Terms (S) (S)

Units of home currency ($) for one unit of Units of home currency ($) for one unit of

foreign currency: S = $0.59/DM foreign currency: S = $0.59/DM

2)2) European TermsEuropean Terms

Price of home currency ($) in terms of Price of home currency ($) in terms of

foreign currency: 1.68DM/$foreign currency: 1.68DM/$

2 Ways:2 Ways:

Exchange Rate QuotationsExchange Rate Quotations

1)1) Direct Terms or American TermsDirect Terms or American Terms (S) (S)

Units of home currency ($) for one unit of Units of home currency ($) for one unit of

foreign currency:foreign currency:

2)2) European TermsEuropean Terms

Price of home currency ($) in terms of Price of home currency ($) in terms of

foreign currency: 1.68DM/$foreign currency: 1.68DM/$

2 Ways:2 Ways:

S = $0.59/DMS = $0.59/DM

Unless noted otherwise, Unless noted otherwise, we will use this notation.we will use this notation.

Definitions:Definitions:

Spot Exchange Rates: Spot Exchange Rates:

Quotes for immediate exchanges of one currency for Quotes for immediate exchanges of one currency for another.another.

Forward Exchange Rates:Forward Exchange Rates:

Quotes for transactions agreed upon now that will Quotes for transactions agreed upon now that will take place 30, 90, and 180 days into the future.take place 30, 90, and 180 days into the future.

Cross Exchange RatesCross Exchange Rates

Exchange rates between two currencies when Exchange rates between two currencies when neither is the domestic currencyneither is the domestic currency


No Triangular Arbitrage Condition: No Triangular Arbitrage Condition:

The amount of currency B received by exchanging A must The amount of currency B received by exchanging A must equal that obtained exchange A to C then C to B. i.e. Yen/$ equal that obtained exchange A to C then C to B. i.e. Yen/$ = (DM/$) x (Yen/DM) = (Yen x DM)/(DM x $) = Yen/$ = (DM/$) x (Yen/DM) = (Yen x DM)/(DM x $) = Yen/$

Bid Price:Bid Price:

Price at which a dealer is willing to buy.Price at which a dealer is willing to buy.

Ask Price:Ask Price:

Price at which a dealer is willing to sell.Price at which a dealer is willing to sell.


Gross Return:Gross Return:

Current value of $1 invested originally = Today’s Price / Original Current value of $1 invested originally = Today’s Price / Original Price.Price.

Net Return:Net Return:

Gross Return - 1.Gross Return - 1.

Compound Annual Return:Compound Annual Return:

(Gross Return)(Gross Return)1/N 1/N - 1- 1

Investments Denominated in Foreign Currency:Investments Denominated in Foreign Currency:

Gross Return in $ = (Gross Return in FC) x (S today / S original)Gross Return in $ = (Gross Return in FC) x (S today / S original)

Law of One PriceLaw of One Price

In the absence of shipping costs, tariffs, and other In the absence of shipping costs, tariffs, and other frictions, identical goods should trade for the same frictions, identical goods should trade for the same real real price in different economies:price in different economies:

PPi i = S P*= S P*ii

TheThe Law of One PriceLaw of One Price holds perfectly for homogeneous holds perfectly for homogeneous goods with low transaction costs. goods with low transaction costs.

Why?Why?

Examples: precious metals, wheat, oilExamples: precious metals, wheat, oil

Purchasing Power ParityPurchasing Power Parity

Purchasing Power Parity is simply the extension of the Law of Purchasing Power Parity is simply the extension of the Law of One Price to all products in two economies. It says that the overall One Price to all products in two economies. It says that the overall real price levels should be identical:real price levels should be identical:

PP = S P*= S P*

Example:Example:

Costs $1400 (Costs $1400 (PP) to purchase a certain basket of U.S. consumption ) to purchase a certain basket of U.S. consumption goods. If Swiss Franc trades at 0.7 ($ per Franc,goods. If Swiss Franc trades at 0.7 ($ per Franc, SS), how many ), how many Swiss Francs will the same basket cost in Geneva (Swiss Francs will the same basket cost in Geneva (P*P*)?)?

2000 Swiss Francs2000 Swiss Francs

Relative Purchasing Power ParityRelative Purchasing Power ParityBecause overall economy price levels consist of different Because overall economy price levels consist of different goods in different countries, a more appropriate form of PPP goods in different countries, a more appropriate form of PPP is the relative form.is the relative form.

Relative Purchasing Power ParityRelative Purchasing Power Parity asserts that relative changes asserts that relative changes in price levels will be offset by changes in exchange rates:in price levels will be offset by changes in exchange rates:

% % P - % P - % P* = % P* = % ss

Or denoting inflation (% Or denoting inflation (% P) as P) as

- - * = % * = % ss

RPPP asserts that differences in inflation rates will be offset RPPP asserts that differences in inflation rates will be offset by changes in the exchange rate.by changes in the exchange rate.

Relative Purchasing Power ParityRelative Purchasing Power Parity

Example:Example:

A year ago, the Brazilian Real traded at $0.417/Real. A year ago, the Brazilian Real traded at $0.417/Real.

For the last year, Brazil’s inflation was 4.2% and the For the last year, Brazil’s inflation was 4.2% and the U.S. inflation was 1.7%. U.S. inflation was 1.7%.

What should be the value of the Real today?What should be the value of the Real today?

$0.402/Real$0.402/Real

Relative Purchasing Power ParityRelative Purchasing Power Parity

In general, how well does Relative PPP hold?In general, how well does Relative PPP hold?

O.K. in the long run (over 5 years) and under O.K. in the long run (over 5 years) and under extreme conditions - not so well in the short run.extreme conditions - not so well in the short run.

Why?Why?

Arbitrage is not making all real prices the same Arbitrage is not making all real prices the same across countries.across countries.

What frictions exist?What frictions exist?

Traded vs. Non-traded goods.Traded vs. Non-traded goods.

- - * = % * = % ss

Exchange Rate ChangesExchange Rate Changes

This suggests thatThis suggests that exchange rate changes which are a exchange rate changes which are a result of inflation differentials will have very result of inflation differentials will have very different consequences for an economy than those different consequences for an economy than those that are not:that are not:

-- a country’s ability to export will be enhanced if its a country’s ability to export will be enhanced if its exchange rate declines by more than its prices have exchange rate declines by more than its prices have inflated. inflated.

-- a tourist’s ability to travel abroad will be greater if her a tourist’s ability to travel abroad will be greater if her wage increases have not been offset by a depreciation wage increases have not been offset by a depreciation in her country’s currency. in her country’s currency.

Real Exchange Rate

A currency’s real, inflation-adjusted value A currency’s real, inflation-adjusted value can often be conveniently captured in a can often be conveniently captured in a measure known as it’s real exchange rate measure known as it’s real exchange rate (RER):(RER):

Real Exchange Rate

Pt*Pt


eett = s = stt

Real Exchange Rate

Pt*Pt


eett = s = stt

PPP (PPPP (P = s P*) says: e= s P*) says: ett = 1. = 1.

Real Exchange Rate

Pt*Pt

This suggests that firms should primarily be This suggests that firms should primarily be concerned with changes in the real value of concerned with changes in the real value of their dollar in foreign country. That is, the their dollar in foreign country. That is, the inflation-adjusted, or inflation-adjusted, or real, real, exchange rate: exchange rate:

eett = s = stt

PPP (PPPP (P = s P*) says: e= s P*) says: ett = 1 = 1

RPPP (% RPPP (% PI - % PI - % PI* = % PI* = % s) says: es) says: et t is is constant.constant.

eett = s = stt

Calculating Real Exchange RatesCalculating Real Exchange Rates

PIPItt**

PIPItt

eett = s = stt


PIPItt**

PIPItt

YearYear s stt PIPItt** PIPItt e ett

20012001 0.13 0.13 100100 100100 ??????

eett = s = stt


PIPItt**

PIPItt


20012001 0.13 0.13 100100 100100 0.130.13

eett = s = stt


PIPItt**

PIPItt


20012001 0.13 0.13 100100 100100 0.130.13

20022002 0.125 0.125 128128 102102 ??????

eett = s = stt


PIPItt**

PIPItt


20012001 0.13 0.13 100100 100100 0.130.13

20022002 0.125 0.125 128128 102102 0.1570.157

eett = s = stt


PIPItt**

PIPItt


20012001 0.13 0.13 100100 100100 0.130.13

20022002 0.125 0.125 128128 102102 0.1570.157

20032003 0.12 0.12 154154 104104 0.1780.178

etc...etc...

Exchange Rate RiskExchange Rate Risk

Changes in the real exchange rate can be expressed as Changes in the real exchange rate can be expressed as changes in the nominal exchange rate that are not changes in the nominal exchange rate that are not accounted for by inflation differentials:accounted for by inflation differentials:

% % e = % e = % s - ( s - ( - - *) *)

When is there exchange rate risk?When is there exchange rate risk?

Only when % Only when % e is unpredictable. e is unpredictable.

Exchange Rate RiskExchange Rate Risk

Real exchange rate changes:Real exchange rate changes:

% % e = % e = % s - ( s - ( - - *) *)

Remember that % Remember that % s only holds well for traded- s only holds well for traded-goods:goods:

% % s = s = - - * *

Combining, we get:Combining, we get:

% % e = ( e = ( - - ) - ( ) - ( * - * - *) *)

Real exchange rate changes are differences in Real exchange rate changes are differences in relative inflation rates of traded and non-traded relative inflation rates of traded and non-traded goods in two economiesgoods in two economies..

Are RER Changes Predictable? Are RER Changes Predictable?

When are changes in relative prices of tradables to When are changes in relative prices of tradables to non-tradables predictable?non-tradables predictable?

Predictable: Growing economies (i.e. China) Predictable: Growing economies (i.e. China) commonly experience higher inflation in service (non-commonly experience higher inflation in service (non-tradables) sector.tradables) sector.

Unpredictable: Government intervention - can never Unpredictable: Government intervention - can never be sure when intervention will take place.be sure when intervention will take place.

Review of Exchange Rate Basics

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