INBU 4200 INTERNATIONAL FINANCIAL MANAGEMENT

1
INBU 4200 INTERNATIONAL FINANCIAL MANAGEMENT

• Lecture 6 Part 2
• Topic Forecasting Exchange Rates With Parity
  Models
• (1) Purchasing Power Parity
• (2) International Fisher Effect Model

2
What are Parity Models all About?

• Parity can be defined as a state of equilibrium.
• Foreign exchange parity models are attempts to
  estimate what the equilibrium spot exchange
  rate should be at some date.
• The date could be today (i.e., is the current
  spot rate realistic?).
• Or the date could be some time in the future
  (what might the equilibrium spot rate be then).
• Parity models have an economic basis (or theory)
  for their spot rate determination.

3
Two Major Spot FX Parity Models

• Two important spot foreign exchange parity models
  in use today are
• Purchasing Power Parity (PPP)
• Assumes that relative rates of inflation between
  two countries determines the equilibrium spot
  exchange rate.
• International Fisher Effect (IFE)
• Assumes that relative rates of interest (long
  term interest rates) between two countries
  determines the equilibrium spot exchange rate.

4
Long Term Spot FX Parity Models

• Both the Purchasing Power Parity Model and the
  International Fisher Effect are regarded as
  longer term forecasting models.
• Thus they would appear to be helpful for
  companies involved in intermediate and long term
  location decisions (i.e., capital budgeting) and
  intermediate and long term financing decisions.
• Probably not that useful in assess very short
  term foreign currency exposure.
• And only limited usefulness as a short term
  trading strategy.

5
Purchasing Power Parity Theory

• The Purchasing Power Parity (PPP) explains and
  quantifies the relationship between inflation and
  spot exchange rates.
• The theory states that the spot exchange rate
  between two currencies should be equal to the
  ratio of the two countries price levels.
• Idea was first proposed by the classical
  economist, David Ricardo, in the 19th century.
• But the concept was fully developed by the
  Swedish economist, Gustav Cassel, during the
  years after WW1 when countries in Europe were
  experiencing hyperinflation.

6
Two Popular Forms of PPP

• There are two popular forms of the Purchasing
  Power Parity
• (1) The Absolute PPP Model and
• (2) The Relative PPP Model.
• Absolute PPP
• After adjusting for exchange rates, the prices of
  similar goods in two different countries should
  be equal.
• Relative PPP
• The change in the exchange rate between two
  currencies should be equal to the rate of change
  in the prices of similar goods between the two
  countries.

7
Rationale Behind the PPP The Law of One Price

• Both Purchasing Power Parity models are based on
  the Law of One Price
• The Law of One Price states that all else equal
  (i.e., no transaction costs or other frictions,
  like tariffs) a products price should be the
  same in all markets.
• Question Why should the products price be the
  same?
• Answer The principle of competitive markets
  assumes that prices will equalize as consumers
  and business firms shift their purchases to those
  markets (or countries) where prices are the
  lowest.

8
Law of One Price and Exchange Rates

• Law of One Price In equilibrium, after adjusting
  for exchange rates, prices should be the same for
  similar products in different countries.
• Using the U.S. and Japan as an example
• In equilibrium the price of product X in the
  U.S. in US dollars (P), adjusted by the spot
  exchange rate (S Yen per dollar), will equal
  the price of product X in Japan in Japanese yen
  (P), or
• P ? S P
• The formula above is the Law of One Price formula

9
Law of One Price Example

• Assume a Big Mac hamburger costs 2.00 in the
  United States and the current yen spot exchange
  rate is 120.00
• According to the Law of One Price, the
  equilibrium Big Mac hamburger price in Japan
  is
• P ? S P
• 2.00 x 120.00 240.00

10
The Absolute PPP Spot Exchange Rate

• The Law of One Price formula can be re-arranged
  to calculate the Absolute PPP Spot Exchange
  Rate
• P x S P
• Sppp P / P
• Where Sppp is the Absolute PPP Spot Exchange Rate
  
• Example If a Big Mac cost 2.00 in the U.S. and
  300 yen in Japan, the Absolute PPP spot rate is
• 300/2 150 (in European terms)
• Note The Absolute PPP exchange rate of 150 is
  the equilibrium spot exchange rate that would
  produce similar prices.
• How do we calculate the Absolute PPP Spot rate?
• We do so from local currency prices for similar
  goods in two different countries.

11
Absolute PPP Spot Exchange Rate European Terms
and American Terms

• Since the absolute PPP spot rate is simply the
  ratio of the two prices of similar goods in two
  local currencies, we can calculate this
  equilibrium exchange rate for either a European
  terms or an American terms quoted currency as
  follow
• For European terms, the Absolute PPP Spot is
• Absolute PPP Foreign price/U.S. price
• For American terms, the Absolute PPP Spot is
• Absolute PPP U.S. price/Foreign price.

12
European Terms Example

• Big Mac United States 3.08 (excluding
  taxes)
• Big Mac Japan 250 (excluding taxes)
• Calculate Absolute PPP European Terms as follows
• Absolute PPP Spot Exchange Rate Yen
  Price/Dollar Price
• Absolute PPP Spot Exchange Rate 250/3.08
  81.17
• Question How do we use this number?
• Answer Compare the Absolute PPP Spot rate to the
  actual spot rate, to determine if the current
  spot rate is overvalued or undervalued.
• Rate on June 20, 2007 was 123.61
• Question What is this model telling us about
  the yens current spot rate (i.e., is it
  overvalued or undervalued?)
• ANSWER Undervalued (by about 34).
• 123.61 81.17/123.61 34.33

13
American Terms Example

• Tall Starbucks Latte United States 2.80
  (excluding taxes)
• Tall Starbucks Latte France 2.90
  (excluding taxes)
• Calculate Absolute PPP American Terms as follows
• Absolute PPP Spot Exchange Rate Dollar
  Price/Euro Price
• Absolute PPP Spot Exchange Rate 2.80 / 2.90
  0.9655
• Compare this Absolute PPP Spot rate to the actual
  rate
• Rate on June 20, 2007 was 1.3409
• Question What is this model telling us about
  the euros spot rate (i.e., is it overvalued or
  undervalued?)
• ANSWER Overvalued (by about 28)
• 1.3409 - .9655/1.3409 27.99

14
Rules for the Absolute PPP

• As noted, the Absolute PPP can be used to
  estimate whether a foreign currencys spot rate
  is overvalued or undervalued and by how much.
• Absolute PPP European Terms
• If PPP Spot lt Current Spot, then the currency is
  undervalued.
• E.g. PPP 100 Current Spot 110
• If PPP Spot gt Current Spot, then the currency is
  overvalued.
• E.g. PPP 100 Current Spot 90
• Absolute PPP American Terms
• If PPP Spot gt Current Spot, then the currency is
  undervalued.
• E.g. PPP 1.20 Current Spot 1.00
• If PPP Spot lt Current Spot, then the currency is
  overvalued.
• E.g. PPP 1.20 Current Spot 1.40

15
Absolute PPP in Practice

• In practice, the absolute PPP Spot exchange
  rate is used to assess the correctness of a
  current spot rate on the basis of similar goods
  in different countries.
• It examines the possibility that a currency is
  overvalued or undervalued, and by how much?
• Where can we get data for the Absolute PPP model?
• The Economist magazines "Big Mac index.
• http//www.economist.com/markets/Bigmac/Index.cfm
• Go to this web-site an examine specific
  currencies.

16
One Test of the Big-Mac The Introduction of the
Euro

• The Euro was introduced on January 1, 1999. The
  first day trading price was 1.1874.
• According to the Big-Mac data, at the time of the
  euros introduction the Absolute PPP Spot rate
  could be calculated as follows
• Average price of a Big-Mac in the euro zone
  2.53
• Average price of a Big-Mac in the U.S. 2.63
• Absolute PPP Spot rate 2.63/2.53 1.04
• Comparing the actual spot (1.1874) to the
  Absolute PPP Spot (1.04) suggested the euro was
  overvalued by about 12.5 at the time it began
  trading.
• This would suggest the currency should weaken in
  the period ahead.

17
What Happened to the Euro? The Euro January 1,
1999 December 31, 1999
18
Relative Purchasing Power Parity

• The second PPP model, the relative Purchasing
  Power Parity model is concerned with the rate of
  change in the exchange rate.
• It is not assessing the correctness of the
  current spot rate.
• It is concerned with forecasting a future
  equilibrium rate.
• The relative PPP model suggests that spot
  exchange rates change (i.e., move) in a manner
  opposite to the inflation differential between
  the two countries.
• The Relative PPP model suggests that the percent
  change in a spot exchange rate over time should
  be equal to, but opposite in direction to, the
  difference in the rates of inflation between
  countries.

19
Relative PPP Example

• Assume the following
• Annual rate of inflation in U.S. 2.0
• Annual rate of inflation in U.K. 3.0
• Question What should the pound do over time
  according to the Relative PPP?
• Answer The British pound should depreciate
  (i.e., weaken) 1 per year against the U.S.
  dollar.
• So, if the current spot rate is 1.80, then
• 1 year from now the spot rate should be 1.7820
  
• 1.80 (1.80 x. 01) 1.7820
• Note This represents a depreciation of 1 over
  the current spot rate, An amount which is equal
  to the inflation differential.
• Note See Appendix 1 for specific Relative PPP
  formulas for both American terms and European
  terms currencies.

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PPP Over the Long Term, 1980 - 2000
21
Where can we get Inflation Data?

• Historical and Current Data
• Visit Central Bank Web sites at
• http//www.bis.org/cbanks.htm
• For Forecasts of Inflation
• Visit The Economist Magazine.
• http//www.economist.com/index.html

22
The International Fisher Effect

• The second foreign exchange parity model is the
  International Fisher Effect (IFE).
• This model uses long term interest rates to
  explain why exchange rates change over time.
• The model consists of two parts
• (1) Fisher Effect which is an explanation of the
  market interest rate, and
• (2) The International Fisher Effect which is an
  explanation of the relationship of market
  interest rates to exchange rate changes.
• The model is attributed to the American
• economist, Irving Fisher
• (1895 - 1935).

23
Part 1 The Fisher Effect

• The IFE model begins with the Fisher interest
  rate model
• According to Irving Fisher the market interest
  rate is made up of two components
• Real rate requirement which relates to the real
  growth rate (e.g., real GDP) in the economy.
• U.S. Data Last 125 years 1.8 1973-2006 2.3
• Inflationary expectations premium which relates
  to the markets expectations regarding future
  rates of inflation.
• Or, simply put
• Market rate of interest real rate expected
  inflation
• Real rate requirement is assumed to be relatively
  stable.
• Changes only occur slowly in response to
  technology changes, population growth, population
  skills, etc.
• Inflationary expectations, however, are subject
  to potentially wide variations over short periods
  of time.

24
Evidence on the Fisher Effect, United States
1970-2007
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Fisher Effect International Assumptions

• On an international level, the Fisher Model
  assumes that the real rate requirement is similar
  across major industrial countries.
• If this is true, any observed market interest
  rate differences between counties will be
  accounted for on the basis of differences in
  inflation expectations.
• Example
• If the United States 1 year market interest rate
  is 5 and the United Kingdom 1 year market
  interest rate is 7, then
• The expected rate of inflation over the next 12
  months must be 2 higher in the U.K. compared to
  the U.S.

26
Part 2 International Fisher Effect

• The second part of the Fisher model, the
  International Fisher (IFE) effect assumes that
• Changes in spot exchange rates are determined by
  differences in market interest rates between
  countries.
• Why this assumption?
• Because differences in interest rates reflect
  differences in expected inflation, which in turn
  affect exchange rates.
• IFE relationship to Exchange Rates
• Currencies of high interest rate countries will
  weaken.
• Why These countries have high inflationary
  expectations
• Currencies of low interest rate countries will
  strengthen.
• Why These countries have low inflationary
  expectations.
• Note The IFE is a longer term model and its
  conclusions differ (they are opposite) from the
  short term asset choice model.

27
IFE Example

• Assume the following
• I year Government bond rate in U.S. 5.00
• 1 year Government bond rate Japan 2.00
• According to the IFE, the yen should appreciate
  3.0 per year against the U.S. dollar.
• Thus, if the current spot rate is 120, then
• 1 year from now the spot rate should be,
• 120 - (120 x .03) 116.40
• Note This represents a appreciation of 3 over
  the current spot rate.
• An amount which is equal to the interest rate
  differential.
• Note See Appendix 2 for specific IFE formulas.

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Problematic Issues Regarding the Two Parity Models

• PPP model issues
• User needs to forecast the future rates of
  inflation.
• How does one do this for very long periods of
  time?
• Perhaps it is easier for short time periods.
• IFE model issues
• User relies on market interest rate data to
  proxy for future inflation.
• However, are real rates similar across countries?
• And, do real rates change over time?
• And how stable are inflationary expectations over
  the period of the forecast?.

29
Appendix 1 Formulas for the Relative PPP

• The following slides cover the specific formulas
  to be used in calculated the Relative PPP spot
  rate for some future date. Note the formula for
  an American Terms quoted currency and for an
  European Terms quoted currency.

30
Relative PPP Formula American Terms

• For an American Term quoted currency
• PPP Spot Rate Current Spot Rate x (1
  infhome)n/(1 infforeign)n)
• Where
• PPP Spot Rate is the expected spot rate sometime
  in the future.
• Current spot rate is expressed in American terms.
• Infhome is the expected annual rate of inflation
  in the United States.
• Infforeign is the expected annual rate of
  inflation in the foreign country.
• N is the number of years in the future.

31
Relative PPP Formula American Terms

• Example
• Current spot rate for British pounds 1.80
• Expected annual rate of inflation in the U.S.
  2.0
• Expected annual rate of inflation in the U.K.
  3.0
• Then, the spot pound 2 years from now is equal
  to
• PPP Spot Rate Current Spot Rate x (1
  infhome)n/(1 infforeign)n)
• Spot rate in 2 years 1.80 (1.02)2/(1.03)2
• Spot rate in 2 years 1.80 (1.0404/1.0609)
• Spot rate in 2 years 1.80 (.9807)
• Spot rate in 2 years 1.7653

32
Relative PPP Formula European Terms

• For European Term quoted currency
• PPP Spot Rate Current Spot Rate x (1
  infhome)n/(1 infforeign)n)
• Where
• PPP spot rate is the expected spot rate sometime
  in the future.
• Current spot rate is expressed in European terms.
• Infhome is the expected annual rate of inflation
  in the foreign country.
• Infforeign is the expected annual rate of
  inflation in the United States.
• N is the number of years in the future.

33
Relative PPP Formula European Terms

• Example
• Current spot rate for Japanese yen 111.00
• Expected annual rate of inflation in the U.S.
  2.0
• Expected annual rate of inflation in Japan 1.0
  
• Then, the spot yen 2 years from now is equal to
• PPP Spot Rate Current Spot Rate x (1
  infhome)n/(1 infforeign)n)
• Spot rate in 2 years 111 (1.01)2/(1.02)2
• Spot rate in 2 years 111 (1.0201/1.0404)
• Spot rate in 2 years 111 (.9805)
• Spot rate in 2 years 108.84

34
Appendix 2 Formulas for the IFE

• The following slides cover the specific formulas
  to be used in calculated the IFE spot rate for
  some future date. Note the formula for an
  American Terms quoted currency and for an
  European Terms quoted currency.

35
IFE Formula American Terms

• For American Term quoted currency
• IFE Spot Rate Current Spot Rate x (1
  inthome)n/(1 intforeign)n)
• Note the similarity to the Relative PPP formula
• Where
• IFE spot rate is the expected spot rate sometime
  in the future.
• Current spot rate is expressed in American terms.
• Inthome is the current annual market interest
  rate in the United States.
• Intforeign is the current annual market interest
  rate in the foreign country.
• N is the number of years in the future.

36
IFE Formula American Terms

• Example
• Current spot rate for British pounds 1.80
• Annual rate of interest in the U.S. 5.0
• Annual rate of interest in the U.K. 6.0
• Then, the spot pound 2 years from now is equal
  to
• PPP Spot Rate Current Spot Rate x (1
  infhome)n/(1 infforeign)n)
• Spot rate in 2 years 1.80 (1.05)2/(1.06)2
• Spot rate in 2 years 1.80 (1.1025/1.1236)
• Spot rate in 2 years 1.80 (.9812)
• Spot rate in 2 years 1.7679

37
IFE Formula European Terms

• For European Term quoted currency
• IFE Spot Rate Current Spot Rate x (1
  inthome)n/(1 intforeign)n)
• Again, note the similarity to the Relative PPP
  formula
• Where
• IFE spot rate is the expected spot rate sometime
  in the future.
• Current spot rate is expressed in European terms
  quote.
• Inthome is the current annual market interest
  rate in the foreign country.
• Intforeign is the current annual market interest
  rate in the United States.
• N is the number of years in the future.

38
IFE Formula European Terms

• Example
• Current spot rate for Japanese yen 120.00
• Annual rate of interest in the U.S. 5.0
• Annual rate of interest in Japan 2.0
• Then, the spot yen 2 years from now is equal to
• PPP Spot Rate Current Spot Rate x (1
  infhome)n/(1 infforeign)n)
• Spot rate in 2 years 120 (1.02)2/(1.05)2
• Spot rate in 2 years 120 (1.0404/1.1025)
• Spot rate in 2 years 120 (.9436)
• Spot rate in 2 years 113.24