Lecture 9: Parity Models and Foreign Exchange Rates

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Lecture 9 Parity Models and Foreign Exchange
Rates

• Evaluating Current Spot Rates and Forecasting
  Rates with Parity Models
• International Fisher Effect

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Where is this Financial Center?
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Dubai, UAE, View From Top of Burj
(i.e.,Tower) Khalifa (2,717 feet, 162 floors)
Opened Jan 4, 2010
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Recall Two Major Spot FX Parity Forecasting
Models

• Purchasing Power Parity (PPP)
• Model assumes relative rates of inflation between
  two countries as the major determinant of the
  future spot exchange rate.
• International Fisher Effect (IFE)
• Model assumes relative rates of long term
  interest between two countries as the major
  determinant of the future spot exchange rate.
• This is the subject of this lecture.

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International Fisher Effect

• The International Fisher Effect (IFE) model uses
  market interest rates rather than inflation 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 (i.e., nominal) interest rate, and
• (2) The International Fisher Effect which is an
  explanation of the relationship of market
  interest rates to exchange rates.
• The model is attributed to the
• American economist, Irving Fisher.
• Born in upstate New York in 1867.
• Ph.D. in economics from Yale.
• - Quantity Theory of Money (MVPT)
• - Phillips Curve

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Explanation of Market Interest Rate

• Fisher market interest rate model developed in
  his book the Theory of Interest (1930)
• Fishers interest rate model states that the
  market rate of interest on a default free bond is
  the sum of
• (1) a real rate requirement.
• The real rate requirement reflects the reward
  that should accrue to a lender for lending to a
  productive economy.
• (2) the markets expected rate of inflation
  (i.e., an inflation premium which represents the
  markets expectation of future rates of
  inflation).
• This inflation premium protects investors against
  a loss of purchasing power.
• Market (nominal) interest rate on a default free
  bond real rate requirement inflation
  expectations.

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Fisher Real Rate Requirement

• Defined by Fisher as The reward for lending into
  a productive economy.
• Problem This real rate requirement is much
  easier to conceptualize than it is to actually
  measure.
• Conceptually, however, it is probably related to
  economic growth theory, with an economys growth
  dependent upon the productivity of its workforce,
  capital stock, and population.
• While the real rate requirement cannot be
  observed, different estimation methods relying on
  theoretical growth models have suggested
• A range of 2-3 for both the United States and
  the euro area.
• A rate of 3 for the United Kingdom
• Sources Manrique and Manuel Marques (2004),
  Laubach and Williams (2003), Giammarioli and
  Valla (2003), Larsen and McKeown (2004)

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Estimating the Real Rate Requirement for the
United States
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Relative Stability of Market Interest Rate
Components

• Given that the market interest rate on a default
  free bond consists of two components (1) real
  rate requirement and (2) inflationary
  expectations, the question arises as to the
  relative stability of these two components.
• Real rate requirement is assumed to be relatively
  (more) stable.
• Changes in real rate only occur slowly in
  response to technology changes, population
  growth, population skills, changes in the capital
  stock, etc.
• Inflationary expectations, however, are subject
  to potentially wide variations over short periods
  of time.

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The Relation of Inflation to Long Term U.S.
T-Bond Interest Rates 1965 2011
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The Relation of Inflation to Short Term U.S.
T-Bill Interest Rates 1965 2011
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International Assumptions of the Fisher Model

• On an international level, the Fisher Model
  assumes that the real rate requirement is similar
  across major industrial countries.
• Thus any observed market interest rate
  differences between counties according to this
  model is 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.

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The International Fisher Effect

• The second part of the Fisher model, the
  International Fisher (IFE) effect assumes that
• Changes in spot exchange rates are related to
  differences in market interest rates between
  countries.
• Reason Because differences in interest rates
  capture differences in expected inflation, and
  inflation is assumed to be the major determinant
  of future exchange rates.
• IFE relationship to Exchange Rates
• Currencies of high interest rate countries will
  weaken.
• Why These countries have high inflationary
  expectations
• The annual depreciation of the currency will be
  equal to the observed interest rate differential.
• Currencies of low interest rate countries will
  strengthen.
• Why These countries have low inflationary
  expectations.
• The annual appreciation of the currency will be
  equal to the observed interest rate differential.

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IFE Examples

• Assume the following
• I year Government bond rate in U.S. 5.00
• 1 year Government bond rate Japan 2.00
• Current spot rate (USD/JPY) 70.00
• According to the IFE, What should happen to the
  yen and what should the exchange rate be one year
  from now?
• Now assume the following
• I year Government bond rate in U.S. 1.00
• 1 year Government bond rate Japan 3.00
• Current spot rate (USD/JPY) 70.00
• According to the IFE, What should happen to the
  yen and what should the exchange rate be one year
  from now?

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IFE Examples

• Given
• I year Government bond rate in U.S. 5.00
• 1 year Government bond rate Japan 2.00
• Spot rate (USD/JPY) 70.00
• According to the IFE, the yen should appreciate
  3.0 per year against the U.S. dollar.
• Thus, 1 year from now the spot rate will equal
• 70 - (70 x .03) 70 2.1 67.90
• This represents a appreciation of 3 over the
  current spot rate, and is an amount which is
  equal to the interest rate differential.
• Second example (2 difference in interest rates)
• 70 (70 x .02) 70 1.4 71.40
• This represents a depreciation of 2 over the
  current spot rate, and is an amount which is
  equal to the interest rate differential.

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IFE Formula American Terms

• For American Term quoted currency
• IFE Spot RateAT Current Spot RateAT x (1
  INTUS)n/(1 INTFC)n
• Where
• IFE Spot RateAT forecasted spot rate quoted in
  American Terms.
• Current Spot RateAT is the American Terms spot
  rate.
• INTUS is the current annual market interest rate
  in the United States.
• INTFC is the current annual market interest rate
  in the foreign country.
• N is the number of years in the future (i.e., the
  forecast horizon).

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Example IFE American Terms Forecast

• Given data for October 7, 2011
• Current spot rate for British pounds
• GBP/USD 1.5560
• Annual rate of interest on 5 year Government
  bonds
• United States 1.07
• United Kingdom 1.37
• Use the IFE formula below to calculate the spot
  pound 5 years from now
• IFE Spot RateAT Current Spot RateAT x (1
  INTUS)n/(1 INTFC)n
• Insert data and solve.

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IFE American Terms Forecast

• Given data for October 7, 2011
• Current spot rate for British pounds GBP/USD
  1.5560
• Annual rate of interest on 5 year Government
  bonds
• United States 1.07
• United Kingdom 1.37
• Use the IFE formula to calculate the spot pound
  5 years from now
• IFE Spot RateAT Current Spot RateAT x (1
  INTUS)n/(1 INTFC)n
• IFE Spot RateAT 1.5560 x (1 0.0107)5/(1
  0.0137)5
• IFE Spot RateAT 1.5560 x (1.0107)5/(1.0137)5
• IFE Spot RateAT 1.5560 x (1.05466/1.0704)
• IFE Spot RateAT 1.5560 x .9853
• IFE Spot RateAT 1.5331 (This is the forecasted
  spot rate 5 years from now is the pound expected
  to appreciate or depreciate and why?)

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IFE Formula European Terms

• For European Term quoted currency
• IFE Spot RateET Current Spot RateET x (1
  INTFC)n/(1 INTUS)n
• Where
• IFE Spot RateET is the forecasted spot rate
  quoted in European Terms.
• Current spot rateET is the European terms spot
  rate.
• INTFC is the current annual market interest rate
  in the foreign country.
• INTUS is the current annual market interest rate
  in the United States.
• N is the number of years in the future (i.e., the
  forecast horizon).

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Example IFE European Terms Forecast

• Given data for October 7, 2011
• Current spot rate for Japanese yen
• USD/JPY 76.84
• Annual rate of interest on 2 year Government
  bonds
• United States 0.29
• Japan 0.14
• Use the IFE formula below to calculate the spot
  yen rate 2 years from now
• IFE Spot RateET Current Spot RateET x (1
  INTFC)n/(1 INTUS)n
• Insert data and solve.

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IFE European Terms Forecast

• Given data for October 7, 2011
• Current spot rate for Japanese yen USD/JPY
  76.84
• Annual rate of interest on 2 year Government
  bonds
• United States 0.29
• Japan 0.14
• Use the IFE formula to calculate the spot yen
  rate 2 years from now
• IFE Spot RateET Current Spot RateET x (1
  INTFC)n/(1 INTUS)n
• IFE Spot RateET 76.84 x (1 0.0014)2/(1
  0.0029)2
• IFE Spot RateET 76.84 x (1.0014)2/(1.0029)2
• IFE Spot RateET 76.84 x (1.0028)/(1.00581)
• IFE Spot RateET 76.84 x .9970
• IFE Spot RateET 76.61(This is the forecasted
  spot rate 2 years from now is the yen expected
  to appreciate or depreciate and why?)

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Empirical Tests of IFE

• Empirical tests lend some support to the
  relationship postulated by the international
  Fisher effect (i.e., currencies with high
  interest rates tend to depreciate over the long
  run and currencies with low interest rates tend
  to appreciate over the long run), although
  considerable short-run deviations occur.
• Emil Sundqvist, 2002 study of the 1993 2000
  period, correlating quarterly interest rate
  differentials to quarterly exchange rate changes
  found the following R-squares
• Swedish krona 11.5, Japanese yen 8.9,
  British pound 3.6, Canadian dollar 1.4,
  German mark 1.4

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Problematic Issues Regarding the PPP and IFE

• 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 shorter time periods
  (e.g., 1 year).
• IFE model issues
• User relies on market interest rate data to
  proxy for future inflation.
• However, are real rates similar across countries?
• Do real rates change over time?
• Inflationary expectations during the forecasted
  horizon are subject to change.

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Practical Use of PPP and IFE

• Neither model appears appropriate for short term
  forecasting (less than 1 year).
• Both models work better for the long term and in
  this regard appear to be good indicators of the
  long term trend in the exchange rate
• Relatively high (low) inflation currencies will
  exhibit long term depreciation (appreciation).
• Relatively high (low) interest rate currencies
  will exhibit long term depreciation
  (appreciation).