Parity Models and Foreign
Exchange Rates
Assessing the “Correctness” of the Current
Spot Rate and Estimating Future Spot
Rates with Parity Models:
(1) Purchasing Power Parity and
(2) International Fisher Effect
What are Parity Models?


Parity is defined as a state of equilibrium.
Foreign exchange parity models “estimate”
what the equilibrium spot exchange rate
should be (under the model’s assumptions):


Is today’s spot rate appropriate?
What might the spot rate be in the future
(forecasting).


Generally a long term forecasting horizon.
Parity models have an economic basis (i.e.,
theory) for their spot rate determination.
Why are Parity Models Important?

Testing the “correctness” of a spot rate.


Could be important for a trading strategy.
Is the currency overvalued or undervalued?



Overvalued: perhaps a sell short strategy.
Undervalued: perhaps a buy long strategy.
Establishing a future spot rate

Could be important for:

International capital budgeting decisions


Converting estimated foreign currency cash flows into MNC’s
home currency as part of the capital budgeting process.
Investment and Financing decisions

Converting estimated investment inflows into home currency
equivalents and converting estimated financing outflows into
home currency equivalents.
Two Major Spot FX Parity Models


Purchasing Power Parity (PPP)
 Model based on relative rates of inflation
between two countries as the
determinant of the spot exchange rate.
International Fisher Effect (IFE)
 Model based on relative rates of interest
between two countries as the
determinant of the spot exchange rate.
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.
The concept was fully developed by the Swedish
economists, Gustav Cassel, during the years after WW1
(1918 -) when countries in Europe were experiencing
hyperinflation.
Two Forms of PPP

Absolute PPP:
 In equilibrium, when adjusted for exchange rates,
the prices of similar goods in two different
countries should be equal.


This form of the PPP is used to test how appropriate the
current spot exchange rate is.
Relative PPP:
 Over time, 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.

This form of the PPP is used to forecast the equilibrium
spot exchange rate in the future.
Rationale Behind the PPP: The Law of
One Price

The Purchasing Power Parity model is 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 or cultural differences) a product’s price
should be the same in all markets.
Why will the product’s price be the same?

The principle of competitive markets assumes that
prices will equalize as consumers shift their purchases
to those markets (or countries) where prices are the
lowest.
Absolute PPP and Exchange Rates

The Absolute PPP states that, in equilibrium
after adjusting for exchange rates, the prices
for similar products should be the same.


Based on Law of One Price.
Example (Using the U.S. and Japan):



In equilibrium the price of a product in the U.S. in US
dollars (P$), adjusted by the spot exchange rate, should
equal the price of the same product in Japan in
Japanese yen (P¥), or:
P$  Spot rate = P¥
This formula is the Law of One Price formula.
Example: Law of One Price

Assume:



A Big Mac hamburger costs $2.00 in the United States
and
The current yen spot exchange rate (USD/JPY) is
¥120.00
According to the Law of One Price, the
“equilibrium” Big Mac hamburger price in Japan
is:

P$  Spot Rate = P¥

$2.00 x ¥120.00 = ¥240.00

At these two prices ($2.00 and ¥240) and given the
spot exchange rate (120) there is no difference in
exchange rate adjusted prices for the Big Mac
between the United States and Japan.
The Absolute PPP Spot Exchange Rate

We can arrange the Law of One Price formula, which is
P$  Spot Rate = P¥, to calculate the Absolute PPP Spot
Exchange Rate:

Absolute PPP Spot Rate = P¥ /P$

Note: The Absolute PPP is calculated by the ratio of the two
local currency prices

The Absolute PPP spot exchange rate is the “equilibrium”
spot exchange rate which will result in the prices of similar
goods in one country to be equal to the prices of those
goods in another country.
Example: Calculating the Absolute PPP
Spot Exchange Rate

Assuming a Big Mac hamburger cost $2.00 in the U.S. and
300 yen in Japan.

According to the Absolute PPP formula (Absolute PPP Spot
Rate = P¥ /P$), the Absolute PPP spot rate is equal to
¥300/$2 = 150 (USD/JPY)

The USD/JPY exchange rate of 150 is the equilibrium
exchange rate that would produce “similar prices” for Big
Macs (a similar product) in both the United States and
Japan.

At the exchange rate of 150, the U.S. dollar equivalent price of
the Big Mac in Japan is $2.00.
Absolute PPP Spot Exchange Rate:
European Terms and American Terms

Given that the absolute PPP spot rate is simply the ratio
of the two prices of similar goods (or a basket of goods)
in two local currencies, we can solve for this equilibrium
exchange rate for either a European terms or an
American terms quoted currency as follow:



For European terms (ET):
 Absolute PPPET = Foreign price/U.S. price
For American terms (AT):
 Absolute PPPAT = U.S. price/Foreign price.
We then compare the calculated Absolute PPP
equilibrium spot rate to the actual spot rate to determine
if the currency is overvalued or undervalued.
European Terms Example




Big Mac: United States :
$3.71 (excluding taxes)
Big Mac: Japan:
¥330 (excluding taxes)
Calculate Absolute PPP European Terms as follows:
 Absolute PPP Spot Exchange Rate = Yen Price/Dollar Price
 Absolute PPP Spot Exchange Rate = ¥330/$3.71= ¥88.95
The Absolute PPP Spot rate is then compared to the actual rate,
to determine if the current spot rate is overvalued or undervalued.
 Rate on October 13, 2010: 81.85
 Question: What is this model telling us about the yen’s current
spot rate (i.e., is it overvalued or undervalued?)
 ANSWER:
 Overvalued, by about 9%
 (88.95 – 81.85)/88.95 = 0.087%
American Terms Example



Big Mac: United States: $3.71 (excluding taxes)
Big Mac: United Kingdom: £2.30 (excluding taxes)
Calculate Absolute PPP American Terms as follows:
 Absolute PPP Spot Exchange Rate = Dollar Price/Pound Price
 Absolute PPP Spot Exchange Rate = $3.71 / £2.30 = $1.6130
 Compare this Absolute PPP Spot rate to the actual rate:
 Rate on October 13, 2010: 1.5856
 Question: What is this model telling us about the pound’s
spot rate (i.e., is it overvalued or undervalued?)
 ANSWER:
 Undervalued (by about 2%)
 (1.5856 – 1.6130) /1.5856 = 0.017%
Rules for the Absolute PPP


The Absolute PPP can be used to “estimate” whether
a foreign currency’s spot rate is overvalued or
undervalued and by how much using the following:
Absolute PPP European Terms:



If PPP Spot < Current Spot, then the currency is undervalued.
 E.g.: PPP = 100; Current Spot = 110
If PPP Spot > Current Spot, then the currency is overvalued.
 E.g.: PPP = 100; Current Spot = 90
Absolute PPP American Terms:


If PPP Spot > Current Spot, then the currency is undervalued.
 E.g.: PPP = $1.20; Current Spot = $1.00
If PPP Spot < Current Spot, then the currency is overvalued.
 E.g.: PPP = $1.20 Current Spot = $1.40
Using the Absolute PPP

In theory, the “absolute” PPP Spot exchange
rate can be used to assess the “correctness”
of a current spot rate on the basis of similar
goods in different countries.


It suggests the possibility that a currency is
overvalued or undervalued, and by how much?
Where can we get data for the Absolute PPP
model?


The "Big Mac” index.
http://www.economist.com/markets/Bigmac/Index.
cfm
Big Mac Index
October 14, 2010
Interpreting the Data


In the United States, a Big Mac
costs $3.71.
In China, a Big Mac costs 14.5
yuan.



Given the current exchange rate
(USD/CNY) of 6.6514 a Big Mac
in China works out to $2.18
(14.5/6.6514). Note this is the Big
Mac price on the chart.
The Absolute PPP for the yuan
is the ratio of the yuan cost to
the dollar cost, or: 14.5/3.71 =
3.9084.
Comparing spot (6.6514) to PPP
(3.9084) reveals that the yuan is
undervalued by 41%

(6.6514-3.9084/6.6514 = .41%)
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 euro’s
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 have weakened
in the period ahead.
What Happened to the Euro? The Euro:
January 1, 1999 – December 31, 1999
Absolute PPP in Practice

In practice, use of the absolute PPP to test the
“correctness” of a spot exchange rate depends
on a number of factors:


Goods that are tradable; necessary for the assumption
of competitive markets.
Goods that are comparable. Are the goods really
similar in quality and quantity?


A rigorous test would involve a market basket of goods, not
just one.
Market basket PPP exchange rates are published by the
OECD and the World Bank.



http://stats.oecd.org/Index.aspx?datasetcode=SNA_TABLE4
See next slide
Are there government policies (tariffs and quotas) or
cultural differences which render such goods not
useful for absolute PPP calculations?
OECD PPP Exchange Rates by
Year
Cultural Differences and Government
Policy Impacts on Absolute PPP
Cultural Differences
Tariffs and Quotas
Testing your Understanding of the
Absolute PPP Model

Given:


Czech Republic Price of a Starbuck’s Venti Latte:
105 CZK (crown)
U.S. Price of a Starbuck’s Venti Latte: $3.45



Absolute PPP = 105/3.45 = 30.4 (USD/CZK)
Current spot rate = 17.5 (USD/CZK)
Estimate the correctness of the current spot rate
for the CZK. Is it overvalued or undervalued?
What trading strategy might you consider in light
of your findings?
Examining Discrepancies from
Absolute PPP


When a discrepancy from Absolute PPP is
identified, it is probably useful to examine reasons
for the discrepancy to determine if the spot rate will,
or will not, move towards the Absolute PPP.
Issues to consider:

Examine the exchange rate regime and the commitment of
the government for that exchange rate regime.

Does this account for the discrepancy between the Absolute PPP
and the spot rate?


Chinese yuan is undervalued by 41% (Big Mac)
Are there economic or financial conditions which could
account for the observed discrepancy and how long might
they dominate the spot rate?

Relative economic performance, interest rates, trade balances,
capital flows, etc.

Brazilian real is overvalued by 40% (Big Mac)
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.
The relative PPP model suggests that spot
exchange rates move in a manner opposite to the
inflation differential between the two countries.

Specifically, the Relative PPP model suggests that the
percent change in a spot exchange rate should be equal to,
but opposite in direction to, the difference in the rates of
inflation between countries.
Relative PPP Example

Assume the following:




Annual rate of inflation in U.S. = 2.0%
Annual rate of inflation in U.K. = 3.0%
According to the Relative PPP, the British pound
should depreciate 1% per year against the U.S.
dollar.
Thus, if the current spot rate is $1.80, then

1 year from now the spot rate should be: $1.7820


Note: This represents a depreciation of 1% over the current
spot rate.


$1.80 – (1.80 x. 01) = $1.7820
An amount which is equal to the inflation differential.
Note: See Appendix 1 for specific Relative PPP formulas.
PPP Over the Long Term, 1980 - 2000
The Relative PPP in Practice


While historical data tends to validate the
relative PPP (see last slide), the practical
issue for users is estimating future rates of
inflatio.
How can we do this?



Use recent historical data to estimate the future,
or for a benchmark starting point.
Combine historical data with likely outcomes
which might affect inflation (e.g., government
deficits, economic growth, monetary policy)
Use independent forecasts of inflation date
Historical Inflation Data

Historical and Current Data:
 Visit Central Bank Web sites at:
 http://www.bis.org/cbanks.htm
 Or visit the Economist
 http://www.economist.com/index.html
 Link to Economic and Financial Indicators
(go to output, prices and jobs data).
 See next slide
The Economist, Inflation Data
Where can we get Inflation
Forecasts?

For Forecasts of Inflation:
 Visit: The Economist Magazine (once a
month, they publish forecasts for
inflation).
 See Next Slide
The Economist: Monthly Forecasts for
Inflation (October 9th)
Does the Relative PPP Hold for
Short Time Periods

While many studies have validated the reliability
of the relative PPP model for “explaining” the
long term relationship between inflation and
exchange rate, studies which have examined
the short term relationship have proved much
less reliable.


See slides which follow.
This is generally explained on the basis of short
term potential factors which can move the
exchange rate away from PPP.

Safe haven effects, government intervention, carry
trade transactions, dirty floats, etc.
Tests of the PPP over the Short
Run
The Euro
The Canadian Dollar
Tests of the PPP over the Short
Run
The Mexican Peso
Conclusions
 In the short-run, relative
PPP will often miss the
spot rate. However, in the
long-run, it appears that
relative PPP can at least
get the trend right.
Relative PPP: MXN/USD
16
14
PPP
10
S(t)
8
6
4
2
20
07
20
05
20
03
20
01
19
99
19
97
19
95
19
93
19
91
0
19
89
MXN/USD
12
International Fisher Effect



The second major foreign exchange parity model is
the International Fisher Effect (IFE).
This model uses 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
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).
Part 1: The Fisher Effect

The IFE model begins with the Fisher interest rate
model:



Irving Fisher’s explanation of the market interest rate was
as follows:
Market interest rate is made up of two components:
 Real rate requirement; which relates to the real growth
rate in the economy.
 Inflationary expectations premium; which related 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.
Estimating the Real Rate
Requirement for the United States
The Fisher Effect and the U.S.
Fisher Effect: International Assumptions

On an international level, the Fisher Model assumes
that the real rate requirement is similar across major
industrial countries.



How realistic is this assumption (see next slide)?
Thus any observed market interest rate differences
between counties 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.
Real Rate Requirements
Part 2: International Fisher Effect

The second part of the Fisher model, the International
Fisher (IFE) effect assumes that:


Why this assumption?


Because differences in interest rates capture differences in
expected inflation.
IFE relationship to Exchange Rates



Changes in spot exchange rates are related to differences in
market interest rates between countries.
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 that the IFE is a longer term model and its
conclusions differ from the short term asset choice model.
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,


Note: This represents a appreciation of 3% over the current
spot rate.


120 - (120 x .03) = 116.40
An amount which is equal to the interest rate differential.
Note: See Appendix 2 for specific IFE formulas.
Testing the IFE Model

Empirical tests of the IFE model have produced
similar results as the tests of the Relative PPP.


Over the long run, the results support an IFE effect,
however, over the short run, the model explains little
of the future spot rate.
1993 – 2000 data correlating quarterly interest rate
differentials to quarterly exchange rate changes (An
Empirical Investigation of the IFE, by Emil Sundqvist,
2002) 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%
Conclusion: Little of the short run variation in
exchange rates is explained by interest rate differential
IFE and the Short Term

Why does the IFE explain little variation in
short run moves in spot exchange rates?


As with the Relative PPP, short term factors can
move the spot rate away from the exchange rate
predicted by the IFE.
Interest rate asset choice might dominate in short
run.


Higher interest rates are expected to produce an
appreciating currency.
Central banks certainly operate under this assumption.
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.
Practical Use of PPP and IFE


Neither model appears appropriate for short
term forecasting.
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 inflation currencies will exhibit long
term depreciation.
Relatively high interest rate currencies will exhibit
long term depreciation.
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.
Relative PPP Formula: American Terms

For an American Term quoted currency:


PPP Spot Rate = Current Spot Rate x (1 + infUS)n/(1 + infF)n)
Where:





PPP Spot Rate is the expected spot rate sometime in the
future.
Current spot rate is expressed in American terms.
InfUS is the expected annual rate of inflation in the United
States.
InfF is the expected annual rate of inflation in the foreign
country.
N is the number of years in the future.
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 + infUS)n/(1 + infF)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
Relative PPP Formula: European Terms

For European Term quoted currency:


PPP Spot Rate = Current Spot Rate x (1 + infF)n/(1 + infUS)n)
Where:





PPP spot rate is the expected spot rate sometime in the future.
Current spot rate is expressed in European terms.
InfF is the expected annual rate of inflation in the foreign
country.
InfUS is the expected annual rate of inflation in the United
States.
N is the number of years in the future.
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 + infF)n/(1 + infUS)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
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.
IFE Formula: American Terms

For American Term quoted currency:



IFE Spot Rate = Current Spot Rate x (1 + intUS)n/(1 + intF)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.
IntUS is the current annual market interest rate in the United
States.
IntF is the current annual market interest rate in the foreign
country.
N is the number of years in the future.
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 + intUS)n/(1 + intF)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
IFE Formula: European Terms

For European Term quoted currency:



IFE Spot Rate = Current Spot Rate x (1 + intF)n/(1 + intUS)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.
IntF 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.
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 + intF)n/(1 + intUS)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
Appendix 3
The following two slides will help you
test your understanding of using the IFE
to forecast American Terms and
European Terms spot exchange rates
for periods greater than one year
Testing Your Understanding of the
IFE Model





Go to http://noir.bloomberg.com/
Go to market data, rates and bonds.
Look up 5 year Government bond rates for the
United States and the United Kingdom.
Using the most recent spot exchange rate
(GBP/USD), calculate the IFE determined spot
GBP/USD exchange rate five years from now.
Does you forecast call for the pound to weaken
or strengthen and why?
Another Test of Your
Understanding of the IFE Model





Go to http://noir.bloomberg.com/
Go to market data, rates and bonds.
Look up 5 year Government bond rates for the
United States and the Japan.
Using the most recent spot exchange rate
(USD/JPY), calculate the IFE determined spot
USD/JPY exchange rate five years from now.
Does you forecast call for the yen to weaken or
strengthen and why?