# Determinants of Exchange Rates

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```					Parity Conditions

Eiteman and Stonehill

Chapter 4

May 16, 2012        Parity Conditions   1
Big Mac index
 The Big Mac, in real terms, should cost the
same everywhere
 Prices increase with inflation
 prices of Big Macs in Canada increase by 1.9%
 prices of Big Macs in US increase by 2.3%
 If nothing real changes, exchange rates
should adjust for the difference
 CD appreciates

May 16, 2012           Parity Conditions              2
The Law of one price
 The Law of One Price does not hold -
given an exchange rate of 1.1254

Pcd equiv, BigMac          Pusd , BigMac  ecd ,usd       
1.005 cd
3.41 usd                                3.43 cd
usd
3.41             3.88
May 16, 2012           Parity Conditions                3
Example - the Law of One Price
 Price = 3.41 usd          in January 2007
 Expected inflation 2.7% in 2007
 Price = 3.50 usd in January 2008
 Price = 3.80 cd in January 2007
 Inflation 1.7% in 2007
 Price = 3.86 cd in January 2008
 Implied exchange rate
 3.80 cd / 3.41usd = 1.1144 cd / 1 usd   Jan 07
 3.86cd / 3.50 usd = 1.1029 cd / 1 usd   Jan 08

May 16, 2012          Parity Conditions                4
Purchasing Power Parity (PPP)
 Absolute PPP - the law of one price
 the price of any good is the same after
adjusting for exchange rate changes and
relative inflation rates
 Relative PPP
 exchange rates adjust to take into
account relative inflation rates

May 16, 2012        Parity Conditions       5
Purchasing Power Parity
 Absolute parity
P x , cd
P x , cd  e cd , usd  P x , usd                                         e cd , usd
P x , usd

 Relative parity                                                        n

n                                 n

i1
w i  Pi , cd
     w i  Pi , cd  e cd , usd   w i  Pi , usd                   n                      e cd , usd
i1                               i1

i1
w i  Pi , usd

May 16, 2012                                    Parity Conditions                                             6
Purchasing Power Parity
 The exchange rate changes to
accommodate differential rates of
inflation
 If this is so, then relative PPP holds

eT     1.1659
                        0.9895 
e0     1.1783
T
 1   cd 
                                1
1.021
                            0.9980
 1   usd          1.023 
May 16, 2012                        Parity Conditions       7
Theory behind relative PPP
 international competition in efficient
goods markets will cause arbitrage of
real prices of goods
 relative inflation will cause internal
prices to change
 exchange rates will adjust for relative
inflation so that real prices remain
unchanged

May 16, 2012     Parity Conditions      8
PPP for forecasting
 Known: forecasts of
 Expected cd inflation,
 Expected usd inflation
 Known: the current exchange rate
 Calculate the expected future spot
 Compare to the quoted future spot
1

1.017    12
eT                    1.0012        1.0004      1.0009
1.027 
May 16, 2012                 Parity Conditions                 9
Relative Purchasing Power Parity
% chg in spot
x

% chg in relative inflation

May 16, 2012       Parity Conditions                        10
Empirical does PPP hold ?
 international goods mkts not efficient
short run
 barriers to trade, transactions costs
 measurement problems
 indices measure changes in a market
basket of goods, not traded goods
 differences exist in tastes, level of
development, income
 approximately efficient in the long
run
May 16, 2012           Parity Conditions         11
Exchange Rate pass through
 exchange rate adjusts for relative
inflation
 relative inflation means
 some prices increase faster than inflation
 some slower
 some prices decrease
 relative real prices of goods may
change internationally

P   cd    P  ecd , usd
usd
May 16, 2012                 Parity Conditions          12
Real exchange rates

n


i1
w i  P i , usd
142.67
n                         e cd , usd                      11783
.      
171.20

i1
w i  P i , cd

0.9819             real exchange rate index

May 16, 2012                      Parity Conditions                        13
Real effective exchange rates

100

May 16, 2012   Parity Conditions   14
Differential Price movements
 Calculate the expected price of
buying US

P         cd    P  ecd , usd
usd

 Expected greater than actual price
 if you are selling this product, you may
face competitive pressures to lower price

P  Pcd
cd
May 16, 2012                  Parity Conditions   15
Price elasticity of demand
 How do the revenues of the firm react
to changes in price
d ln Q
%Qd
                        dt
%P                  d ln P
dt
 revenues decline if elasticity of own
demand is less than 1
  1
May 16, 2012      Parity Conditions              16
Inelastic own demand
P

Decrease in revenue
due to price decrease
P0

PT

Increase in revenue
due to increased sales

Q0 QT                               Q
May 16, 2012           Parity Conditions                  17
Elastic own demand
P

Decrease in revenue
due to price decrease
P0
Increase in revenue
PT                                   due to increased sales

Q0     QT                                Q
May 16, 2012           Parity Conditions                            18
The Fisher Effect
 The nominal interest rate

i  r  
 r        

 relative nominal interest rates are proportional
to relative inflation rates
T                        T
1.0418  1  icd             1    
         1.021
                          cd
       
1  

1.0533 1  iusd                    usd            1.023

0.9891  0.9980
May 16, 2012         Parity Conditions                      19
Empirical evidence
 capital market integration
 real returns are equal across economies
 efficient capital markets will arbitrage
differences
 capital market segmentation
 investor preferences may lead to real
interest rate differentials
 each economy is a separate market

May 16, 2012        Parity Conditions            20
International Fisher Effect
 expected future spot should
accommodate any interest rate
differentials
                       T
 1  icd 
1
1.1659 eT                1.0418 
                     
1.1783 e0   1  iusd   1.0533 

0.9895  0.9891
May 16, 2012         Parity Conditions       21
Interest Rate parity
 interest rate differentials are covered
by the forward rate
T
 1  icd 
1
1.1566 fT                 1.0418 
                      
1.1783 e0    1  iusd   1.0533

0.9816  0.9891
May 16, 2012        Parity Conditions       22
Covered Interest Arbitrage
 If US interest rates are higher than
interest rate parity would forecast
 Buy usd denominated bonds
 100,000 cd*0.8485 =84,846 usd
 receive 84,846 * 1.0533 = 89,369 usd in
one year
 Forward contract at deliver of 104,195 cd in
one year @ 1.1659 cd/usd in one year
 Invest in Canada 100,000 cd * 1.0418 =
104,180
May 16, 2012            Parity Conditions            23
Unbiased forward expectations
 forward rate is the best predictor of
the expected future spot
 market determined
 it is the best predictor?
 it is not unbiased predictor?


fT     eT
May 16, 2012         Parity Conditions    24
Comparative statistics

 usd
*
    25 %
.                               cd
*
   2.2 %

US           Canadian          Canadian
T-bill          T-bill           forward
rates           rates              rates
One
1.1622
month
Three
5.13%            4.27%           1.1605
month
Six
5.21%            4.30%           1.1575
month
One
5.09%            4.34%           1.1520
year
May 16, 2012                       Parity Conditions                          25
Purchasing Power Parity
T

eT        1     *
                                            1

 
cd
                       .
11622      1022 
.       12
0.9987                                   0.9998
 1                                            1025 
*
e0               usd   
                       .
11637        . 

0.25
11605
.       1022 
.
Three months                  0.9973                                    0.9993
.
11637    1025 
. 
0.5
Six months                           .
11575    1022 
.
0.9947                                   0.9985
.
11637    1025 
. 
1
One year                            .
11520    1022 
.
0.9899                                   0.9970
.
11637    1025 
. 

May 16, 2012                      Parity Conditions                             26
Fisher Effect
T                             T
 1  i cd                    1   cd
*

                                        
 1  i usd                    1   usd
*
             
                            

0.25                      0.25
 10427 
.                           1022 
.
09979  
.                                                          09993
.
 10513 
.                          1025 
.                             Three months

0.5                       0.5
 10430 
.                           1022 
.
09957  
.                                                          09985
.
 10521                       1025 
Six months
.                            . 
1                         1
 10434 
.                         1022 
.                               One year
0.9929                                                   0.9990
 10509 
.                        1025 
.   

May 16, 2012                               Parity Conditions                         27
Interest rate parity
International Fisher effect
T
fT           
eT      1  i cd    
                         
e0           e0      1  i usd
             

0.25
11605
.       10427 
.
0.9973                                                0.9979
 10513 
Three months
11637
.              

0.5
11575
.       10430 
.
09947 
.                                                     09956
.        Six months
.
11637    10521 

1
11520
.       10434 
.
09899 
.                                                 09929
.             One year
.
11637    10509 


May 16, 2012                                Parity Conditions                      28

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