Lecture 9: Parity Models and
Foreign Exchange Rates
Evaluating Current Spot Rates
and Forecasting Rates with
Parity Models:
International Fisher Effect
Where is this Financial Center?
Dubai, UAE, View From Top of Burj
(i.e.,“Tower”) Khalifa (2,717 feet, 162
floors): Opened Jan 4, 2010
Recall: Two Major Spot FX Parity
Forecasting Models
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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.
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This is the subject of this lecture.
International Fisher Effect
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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:
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(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 (MV=PT)
-
Phillips Curve
Explanation of Market Interest Rate
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Fisher market interest rate model developed in his
book the Theory of Interest (1930)
Fisher’s interest rate model states that the market
rate of interest on a default free bond is the sum of:
(1) a real rate requirement.
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(2) the market’s expected rate of inflation (i.e., an
inflation premium which represents the markets’
expectation of future rates of inflation).
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The real rate requirement reflects the reward that should
accrue to a lender for “lending to a productive economy.”
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.
Fisher Real Rate Requirement
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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.
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Conceptually, however, it is probably related to economic growth
theory, with an economy’s 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:
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A range of 2-3% for both the United States and the euro area.
A rate of 3% for the United Kingdom
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Sources: Manrique and Manuel Marques (2004), Laubach and Williams
(2003), Giammarioli and Valla (2003), Larsen and McKeown (2004)
Estimating the Real Rate
Requirement for the United States
Relative Stability of Market Interest
Rate Components
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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.
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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.
The Relation of Inflation to Long Term
U.S. T-Bond Interest Rates: 1965 – 2011
The Relation of Inflation to Short Term
U.S. T-Bill Interest Rates: 1965 – 2011
International Assumptions of the Fisher
Model
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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:
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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.
The International Fisher Effect
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The second part of the Fisher model, the International
Fisher (IFE) effect assumes that:
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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
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Currencies of high interest rate countries will weaken.
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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.
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Why: These countries have low inflationary expectations.
The annual appreciation of the currency will be equal to the
observed interest rate differential.
IFE Examples
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Assume the following:
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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:
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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
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?
IFE Examples
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Given:
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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:
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I year Government bond rate in U.S. = 5.00%
1 year Government bond rate Japan = 2.00%
Spot rate (USD/JPY) = 70.00
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)
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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.
IFE Formula: American Terms
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For American Term quoted currency:
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IFE Spot RateAT = Current Spot RateAT x (1 + INTUS)n/(1 + INTFC)n
Where:
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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).
Example: IFE American Terms
Forecast
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Given data for October 7, 2011:
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Current spot rate for British pounds:
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Annual rate of interest on 5 year Government bonds:
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GBP/USD 1.5560
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
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Insert data and solve.
IFE American Terms Forecast
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Given data for October 7, 2011:
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Current spot rate for British pounds: GBP/USD 1.5560
Annual rate of interest on 5 year Government bonds:
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United States = 1.07%
United Kingdom = 1.37%
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Use the IFE formula to calculate the spot pound 5
years from now:
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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
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For European Term quoted currency:
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IFE Spot RateET = Current Spot RateET x (1 + INTFC)n/(1 + INTUS)n
Where:
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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).
Example: IFE European Terms
Forecast
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Given data for October 7, 2011:
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Current spot rate for Japanese yen:
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Annual rate of interest on 2 year Government bonds:
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USD/JPY 76.84
United States = 0.29%
Japan = 0.14%
Use the IFE formula below to calculate the spot
yen rate 2 years from now:
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IFE Spot RateET = Current Spot RateET x (1 + INTFC)n/(1 + INTUS)n
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Insert data and solve.
IFE European Terms Forecast
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Given data for October 7, 2011:
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Current spot rate for Japanese yen: USD/JPY 76.84
Annual rate of interest on 2 year Government bonds:
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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?)
Empirical Tests of IFE
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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:
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Swedish krona: 11.5%, Japanese yen: 8.9%, British
pound: 3.6%, Canadian dollar: 1.4%, German mark:
1.4%
Problematic Issues Regarding the PPP
and IFE
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PPP model issues:
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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:
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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.
Practical Use of PPP and IFE
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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:
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Relatively high (low) inflation currencies will
exhibit long term depreciation (appreciation).
Relatively high (low) interest rate currencies will
exhibit long term depreciation (appreciation).