FIN 40500: International
Finance
Purchasing Power Parity
The relationship between exchange rates and prices starts with a very
basic idea – ANY PRODUCT SHOULD COST THE SAME EVERYWHERE.
Suppose that a BMW sells for $40,000
in the United States and E 30,000 in
Germany. The current exchange rate is
$1.25 per Euro.
1
Borrow $37,500 and convert it to
Euros at $1.25/Euro.
2
Buy a BMW in Germany for
E30,000 and ship it back to the US.
3
Sell the car in the US for $40,000
$37,500
= E 30,000
$1.25
  P  eP*   ($40,000  $37,500)  $2,500
A 6.7% return
The act of arbitrage should eliminate the profit opportunity
Suppose that a BMW sells for $40,000
in the United States and E 30,000 in
Germany. The current exchange rate is
$1.25 per Euro.
1
Increased demand
for Euros should
increase the price of
a Euro.
  P  eP* 
3
2
Increased demand
for BMWs in
Germany should
increase the
German price .
Increased supply in US should
drive down US price
The Law of One Price (LOOP) states that, given a domestic and foreign
price, there is only one arbitrage free exchange rate
As in the previous example, if the Euro
is undervalued relative to LOOP, buy in
Europe and sell in the US
  P  eP* 
The arbitrage
free exchange
rate is given
by the ratio of
prices
$40, 000
= $1.33 per Euro
E30,000
Domestic Price
P
e *
P
if the Euro is overvalued relative to LOOP,
buy in US and sell in Europe
  eP*  P 
Foreign Price
Purchasing Power Parity (PPP) refers to the same concept as the Law of
One Price, with specific prices replaced by general price indices
PPP Exchange Rate
e=
USA
CPI = 199.8
(March 2006)
=
CPI (USA)
CPI (UK)
199.8
195.0
England
= $1.025/L
CPI = 195.0
(March 2006)
Currently, the British Pound is trading at $1.786
$1.786 – $1.025
$1.205
X 100 = 74%
Is the British pound really
overvalued by 74%?
One problem with this method had to do with how the CPI (in both the US
and Britain) are calculated:
Suppose that we have two goods: BMWs and Computers
2006
1992
PBMW  $40,000
PBMW  $30,000
PC  $3,000
PC  $2,250
A price index is defined
as a weighted average of
individual good’s prices
CPI  .5PBMW   .5PC 
CPI  .5$40,000  .5P$3,000  $21,500
2006
1992
CPI  .5$30,000  .5$2,250  $16,125
The prices are then normalized by a ‘base year’
CPI1992  100
 $21,500 
CPI 2006  
 100  133.3
 $16,125 
We can correct for this by looking at PPP in relative terms
%e    
USA
Inflation = 3.4%
(12 months)
*
 3.4  2.4
 1%
The dollar should depreciate
by 1% against the pound
England
Inflation = 2.4%
(12 months)
12 months ago, the British pound was trading at $1.904
$1.904 ( 1.01) = $1.923
$1.786 – $1.923
$1.923
X 100 = -7.1%
Now, it looks like the British
pound is undervalued
Its easy to calculate currency values with the PPP method. Just
compare inflation differentials with actual currency price changes!
What’s a better currency
predictor, Coffee or
Burgers?
The right answer is “neither!”
Overall, it turns out that inflation differentials alone provide a relatively
poor forecast of the exchange rate
Country
Exchange Inflation
PPP implied
Actual
Rate
Differential
exchange rate Exchange
(12/2003) (US-Foreign)
Rate (12/2004)
JPY/USD
.00928
3.5%
.00960
.00963
EUR/USD
1.23
-.5%
1.224
1.34
GBP/USD
1.75
1.5%
1.776
1.93
CAD/USD
.761
-.5%
.757
.820
CHF/USD
.791
1%
.799
.872
AUD/USD
.740
.5%
.7437
.768
The exception would be countries with notoriously high inflation rates –
Zimbabwe has a 585% annual inflation rate (2006). From 1998 to 2006,
the Zimbabwe dollar fell from 24 per US dollar to 96,000!!!
Alternatively, we could estimate a forecasting equation using inflation
differentials

%et      t  
Percentage change is
exchange rate (dollars
per foreign currency) –
an increase is a
depreciation
*
t

Parameters to be
estimated – PPP implies
that alpha is zero and
beta is one
Typically, estimated values for beta are close to
zero and statistically insignificant
The real exchange rate is the price level adjusted exchange rate. Its
meant to capture the relative value of goods and services across
countries
 P* 
RER  e 
 P
Foreign CPI
Nominal Exchange Rate
Domestic CPI
By definition, the PPP explanation of exchange rates assumes that
the real exchange rate is constant (and equal to one)
Empirically, real exchange rates are clearly not constant. In fact, the
correlation between real and nominal exchange rates is nearly one. This
casts some serious doubt on PPP.
300
250
200
150
100
50
Jan-85
Jan-89
Jan-93
Yen/$
Real
Jan-97
In reality, there are costs that will inhibit arbitrage of goods between
countries. Let’s take another look at our BMW example.
P  $40,000
P*  E 30,000
Let’s assume that it costs
$5,000 to ship a BMW from
Germany to the US (12.5%
of the purchase price)
For arbitrage to occur, it must be profitable
  P  eP   $5,000  0
*
Buy in Germany,
Sell in the US
Insert the appropriate prices and solve for the exchange rate
40,000  e30,000  $5,000  0
e  $1.17
In reality, there are costs that will inhibit arbitrage of goods between
countries. Let’s take another look at our BMW example.
P  $40,000
P*  E 30,000
Let’s assume that it costs
$5,000 to ship a BMW from
Germany to the US (12.5%
of the purchase price)
We also have to consider the alternative strategy
  eP  P   $5,000  0
*
Buy US, Sell in
Germany
Insert the appropriate prices and solve for the exchange rate
e30,000  40,000  $5,000  0
e  $1.50
In reality, there are costs that will inhibit arbitrage of goods between
countries. Let’s take another look at our BMW example.
P  $40,000
P*  E 30,000
Let’s assume that it costs
$5,000 to ship a BMW from
Germany to the US (12.5%
of the purchase price)
The shipping cost provides a range within which arbitrage can’t occur
e
Buy in US, Sell in Germany
$1.50
No Arbitrage Possible
$1.17
This range
represents a 24%
change in the value
of the dollar !!
Buy in Germany, Sell in US
Time
A 24% band encompasses much of the EUR/USD
movement!
Suppose that there are two goods in each country;
haircuts and beer. Note that haircuts are a nontraded good.
Price indices in Europe and the US are defined equally (50% Beer, 50%
Haircut)
Europe
United States
PB*  E10
P  $12
PH*  E 20
P  $24
P*  .5(E10 )  .5(E 20 )  E15
P  .5( $12 )  .5( $24 )  $18
At an exchange rate of $1.20 per Euro, LOOP holds for each individual good
and PPP holds for the index – the real exchange rate equals 1
PB PH
 *  $1.20
*
PB PH
eP*
 15 
RER 
 1.20   1
P
 18 
Now, suppose that the price of a haircut rises in
Europe to E30 – because a haircut is not traded, there
is no need for the exchange rate to adjust
Europe
United States
PB*  E10
P  $12
PH*  E 30
P  $24
P *  .5(E10 )  .5(E 30 )  E 20
P  .5( $12 )  .5( $24 )  $18
The 25% inflation should cause a 25% depreciation of the Euro (i.e. a fall in
the EUR/USD to $.90, but this doesn’t happen.
eP*
 20 
RER 
 1.20   1.33
P
 18 
Instead, the Euro
appreciates in real
terms by 33%!!
The previous example
represented an increase
in the relative price of a
non-traded good. This
causes a real
appreciation of a
country’s currency
US CPI
Personal Care
4%
Tobacco &
Smoking Products
1%
Food & Beverage
16%
Education &
Communication
5%
Housing
40%
Recreation
6%
Medical
6%
When you consider that over
50% of the US CPI is non-traded,
these relative price changes are
important!!
Transportation
17%
Apparel
5%
Now, suppose that the two goods are beer and peanuts
– assume that more beer is consumed in Europe than in
the US
Europe
United States
PB*  E10
P  $12
Pp*  E 5
P  $6
P*  .80(E10 )  .20(E 5 )  E 9
P  .20( $12 )  .80( $6 )  $7.2
At an exchange rate of $1.20 per Euro, LOOP holds for each individual good,
but PPP does not hold!
PB Pp
 *  $1.20
*
PB Pp
eP*
 9 
RER 
 1.20
  1.50
P
 7.20 
Now, suppose that the price of beer in increases by 50%
worldwide
Europe
United States
PB*  E15
P  $18
Pp*  E 5
P  $6
P*  .80(E15 )  .20(E 5 )  E13
P  .20( $18 )  .80( $6 )  $8.40
Europe experiences a 36% inflation rate while the US experiences a 15%
inflation rate. The nominal exchange rate is constant, LOOP still holds for
each individual good but the Euro experiences a real appreciation
PB Pp
 *  $1.20
*
PB Pp
eP*
 13 
RER 
 1.20
  1.85
P
 8.40 
Given the importance of relative prices (real exchange rate
movements), we can use a modified version of PPP.
% Change in
Nominal
Exchange Rate
=
% Change in
Real Exchange
Rate
Inflation
+ Differential
Relative Price Movements
The two major relative price movements are:
Relative price of non-traded goods (causes a real currency
appreciation)
Terms of Trade (relative price of imports) – an increase in the
relative price of imports (worsening of the terms of trade) causes a
real depreciation
The competing alternative explanation deals with differing adjustment
speeds across different markets.
 P* 
RER  e 
 P
Exchange rates are determined in
asset markets – new information is
incorporated rapidly into prices
Prices are determined in commodity
markets – new information is
incorporated slowly into prices.
Therefore any nominal movement will be reflected in the real
exchange rate until commodity prices can “catch up”
How can we tell the difference between “sticky prices” and relative price
movements?
RER
If the “sticky price”
story is correct, then
the real exchange rate
should be mean
stationary
1
RER
Time
1
Time
If the “relative price”
story is correct, then
the real exchange rate
will not be mean
stationary – i.e. real
exchange rates are
unpredictable!