Review of Exchange Rate Basics

1
Review ofExchange Rate Basics
2
Key Points

• 1. An economys price level captures the average
  rate at which money is traded for goods - and
  inflation measures how this rate changes through
  time.
• 2. An economys nominal interest rate captures
  the price at which individuals are willing to
  trade money through time.
• 3. An economys 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.

3
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.

4
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.

5
Key Points (contd)

• 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.

6
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.

7
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
8
Prices and Interest Rates

• We use Pt and R t, t1 to denote the price level
  and one-period nominal interest rate at time t

Today
Tomorrow
Goods/Services
Pt
R t, t1
Cash
Cash
9
Prices and Interest Rates

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

Today
Tomorrow
Goods/Services
Goods/Services
Inflation Rate
Pt
Pt1
R t, t1
Cash
Cash
10
Prices and Interest Rates

• which we denote as Pi.

Today
Tomorrow
Goods/Services
Goods/Services
? t
Pt
Pt1
R t, t1
Cash
Cash
11
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
Pt1
R t, t1
Cash
Cash
12
Prices and Interest Rates

• As before, we denote the real interest rate as
• r t, t1.

Today
Tomorrow
r t, t1
Goods/Services
Goods/Services
? t
Pt
Pt1
R t, t1
Cash
Cash
13
The Fisher Effect

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

Today
Tomorrow
r t, t1
Goods/Services
Goods/Services
? t
Pt
Pt1
R t, t1
Cash
Cash
14
The Fisher Effect

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

1R t, t1 (1 E(? t) r t, t1)
Today
Tomorrow
r t, t1
Goods/Services
Goods/Services
? t
Pt
Pt1
R t, t1
Cash
Cash
15
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/.

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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/

17
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.
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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

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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.

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Definitions

• Gross Return
• Current value of 1 invested originally Todays
  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)

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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 Pi
• The Law of One Price holds perfectly for
  homogeneous goods with low transaction costs.
• Why?
• Examples precious metals, wheat, oil

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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
23
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 Parity asserts 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.

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Relative Purchasing Power Parity

• Example
• A year ago, the Brazilian Real traded at
  0.417/Real.
• For the last year, Brazils inflation was 4.2
  and the U.S. inflation was 1.7.
• What should be the value of the Real today?

0.402/Real
25
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.

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Exchange Rate Changes

• This suggests that exchange rate changes which
  are a result of inflation differentials will have
  very different consequences for an economy than
  those that are not
• - a countrys ability to export will be enhanced
  if its exchange rate declines by more than its
  prices have inflated.
• - a tourists ability to travel abroad will be
  greater if her wage increases have not been
  offset by a depreciation in her countrys
  currency.

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Real Exchange Rate

• A currencys real, inflation-adjusted value can
  often be conveniently captured in a measure known
  as its real exchange rate (RER)

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Real Exchange Rate

• A currencys real, inflation-adjusted value can
  often be conveniently captured in a measure known
  as its real exchange rate (RER)
• et st

Pt
Pt
29
Real Exchange Rate

• A currencys real, inflation-adjusted value can
  often be conveniently captured in a measure known
  as its real exchange rate (RER)
• et st

Pt
Pt
PPP (P s P) says et 1.
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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.
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Calculating Real Exchange Rates
PIt
et st
PIt
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Calculating Real Exchange Rates
PIt
et st
PIt
Year st PIt PIt et 2001
0.13 100 100 ???
33
Calculating Real Exchange Rates
PIt
et st
PIt
Year st PIt PIt et 2001
0.13 100 100 0.13
34
Calculating Real Exchange Rates
PIt
et st
PIt
Year st PIt PIt et 2001
0.13 100 100 0.13 2002 0.125 128 102 ???
35
Calculating Real Exchange Rates
PIt
et st
PIt
Year st PIt PIt et 2001
0.13 100 100 0.13 2002 0.125 128 102 0.157
36
Calculating Real Exchange Rates
PIt
et st
PIt
Year st PIt PIt et 2001
0.13 100 100 0.13 2002 0.125 128 102 0.157
2003 0.12 154 104 0.178 etc...
37
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.

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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.

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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.