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Review of Exchange Rate Basics

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Review ofExchange Rate Basics

Key Points

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

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

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

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

Key Points

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

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

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

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

Key Points

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

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

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

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

Key Points (cont’d)

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

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

Prices and Interest Rates

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

Prices and Interest Rates

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

Today

Tomorrow

Goods/Services

Price Level

Nominal Interest Rate

Cash

Cash

Prices and Interest Rates

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

Today

Tomorrow

Goods/Services

Pt

R t, t+1

Cash

Cash

Prices and Interest Rates

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

Today

Tomorrow

Goods/Services

Goods/Services

Inflation Rate

Pt

Pt+1

R t, t+1

Cash

Cash

Prices and Interest Rates

…which we denote as Pi.

Today

Tomorrow

Goods/Services

Goods/Services

t

Pt

Pt+1

R t, t+1

Cash

Cash

Prices and Interest Rates

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

Today

Tomorrow

Real Interest Rate

Goods/Services

Goods/Services

t

Pt

Pt+1

R t, t+1

Cash

Cash

Prices and Interest Rates

As before, we denote the real interest rate as

r t, t+1.

Today

Tomorrow

r t, t+1

Goods/Services

Goods/Services

t

Pt

Pt+1

R t, t+1

Cash

Cash

The Fisher Effect

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

Today

Tomorrow

r t, t+1

Goods/Services

Goods/Services

t

Pt

Pt+1

R t, t+1

Cash

Cash

The Fisher Effect

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

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

Today

Tomorrow

r t, t+1

Goods/Services

Goods/Services

t

Pt

Pt+1

R t, t+1

Cash

Cash

An Exchange Rate is Just a Price

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

Why is there confusion?

- 1.68DM/$ is price of a Dollar in terms of Marks.
- $0.59/DM is price of a Mark in terms of Dollars.
No different from any other price.

- $0.5/Apple
- 2 Apples/$.

Exchange Rate Quotations

2 Ways:

1)Direct Terms or American Terms (S)

Units of home currency ($) for one unit of foreign currency: S = $0.59/DM

2)European Terms

Price of home currency ($) in terms of foreign currency: 1.68DM/$

Exchange Rate Quotations

2 Ways:

1)Direct Terms or American Terms (S)

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

2)European Terms

Price of home currency ($) in terms of foreign currency: 1.68DM/$

S = $0.59/DM

Unless noted otherwise, we will use this notation.

Definitions:

Spot Exchange Rates:

Quotes for immediate exchanges of one currency for another.

Forward Exchange Rates:

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

Cross Exchange Rates

Exchange rates between two currencies when neither is the domestic currency

Definitions:

No Triangular Arbitrage Condition:

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

Bid Price:

Price at which a dealer is willing to buy.

Ask Price:

Price at which a dealer is willing to sell.

Definitions:

Gross Return:

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

Net Return:

Gross Return - 1.

Compound Annual Return:

(Gross Return)1/N - 1

Investments Denominated in Foreign Currency:

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

Law of One Price

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

Pi = S P*i

TheLaw of One Priceholds perfectly for homogeneous goods with low transaction costs.

Why?

Examples: precious metals, wheat, oil

Purchasing Power Parity

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

P= S P*

Example:

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

2000 Swiss Francs

Relative Purchasing Power Parity

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

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

% P - % P* = % s

Or denoting inflation (% P) as

- * = % s

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

Relative Purchasing Power Parity

Example:

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

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

What should be the value of the Real today?

$0.402/Real

Relative Purchasing Power Parity

- * = % s

In general, how well does Relative PPP hold?

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

Why?

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

What frictions exist?

Traded vs. Non-traded goods.

Exchange Rate Changes

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

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

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

Real Exchange Rate

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

Real Exchange Rate

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

et = st

Pt*

Pt

Real Exchange Rate

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

et = st

Pt*

Pt

PPP (P= s P*) says: et = 1.

Real Exchange Rate

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

Pt*

Pt

PPP (P= s P*) says: et = 1

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

Calculating Real Exchange Rates

PIt*

et = st

PIt

Calculating Real Exchange Rates

PIt*

et = st

PIt

Year st PIt*PIt et

2001 0.13100100???

Calculating Real Exchange Rates

PIt*

et = st

PIt

Year st PIt*PIt et

2001 0.13100100 0.13

Calculating Real Exchange Rates

PIt*

et = st

PIt

Year st PIt*PIt et

2001 0.131001000.13

2002 0.125128102???

Calculating Real Exchange Rates

PIt*

et = st

PIt

Year st PIt*PIt et

2001 0.131001000.13

2002 0.1251281020.157

Calculating Real Exchange Rates

PIt*

et = st

PIt

Year st PIt*PIt et

2001 0.131001000.13

2002 0.1251281020.157

2003 0.121541040.178

etc...

Exchange Rate Risk

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

% e = % s - ( - *)

When is there exchange rate risk?

Only when % e is unpredictable.

Exchange Rate Risk

Real exchange rate changes:

% e = % s - ( - *)

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

% s = - *

Combining, we get:

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

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

Are RER Changes Predictable?

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

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

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