Parity Conditions
Eiteman and Stonehill
Chapter 4
July 17, 2016
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
July 17, 2016
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 
usd
3.41
July 17, 2016


3.43 cd
3.88
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
 3.86cd / 3.50 usd = 1.1029 cd / 1 usd
July 17, 2016
Parity Conditions
Jan 07
Jan 08
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
July 17, 2016
Parity Conditions
5
Purchasing Power Parity
 Absolute parity
P x , cd
P x , cd  e cd , usd  P x , usd
P x , usd
 Relative parity
n

i1
 e cd , usd
n
n
w i  Pi , cd  e cd , usd   w i  Pi , usd
i1

i1
Parity Conditions
 e cd , usd
n

i1
July 17, 2016
w i  Pi , cd
w i  Pi , usd
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
 1   cd 



1


usd



July 17, 2016
T
1
1.021 
 
 0.9980

1.023 
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
July 17, 2016
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
1.017 
eT  
1.027 

July 17, 2016
1
12
 1.0012
 1.0004
Parity Conditions
 1.0009
9
Relative Purchasing Power Parity
x
% chg in spot
% chg in relative inflation
July 17, 2016
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
July 17, 2016
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
July 17, 2016

cd
 Pusd  ecd , usd
Parity Conditions
12
Real exchange rates
n

i1
n

i1
w i  P i , usd

w i  P i , cd
0.9819
July 17, 2016

e cd , usd

142.67
 11783
.
171.20

real exchange rate index
Parity Conditions
13
Real effective exchange rates
100
July 17, 2016
Parity Conditions
14
Differential Price movements
 Calculate the expected price of
buying US
P

cd
 Pusd  ecd , usd
 Expected greater than actual price
 if you are selling this product, you may
face competitive pressures to lower price

cd
P  Pcd
July 17, 2016
Parity Conditions
15
Price elasticity of demand
 How do the revenues of the firm react
to changes in price
%Qd
 
%P
d ln Q
dt

d ln P
dt
 revenues decline if elasticity of own
demand is less than 1
  1
July 17, 2016
Parity Conditions
16
Inelastic own demand
P
Decrease in revenue
due to price decrease
P0
PT
Increase in revenue
due to increased sales
July 17, 2016
Q0 QT
Parity Conditions
Q
17
Elastic own demand
P
Decrease in revenue
due to price decrease
P0
Increase in revenue
due to increased sales
PT
July 17, 2016
Q0
QT
Parity Conditions
Q
18
The Fisher Effect
 The nominal interest rate

i  r 
 r 

 relative nominal interest rates are proportional
to relative inflation rates
1.0418  1  icd 


1.0533 1  iusd 
T
 1 
 
1  

cd

usd



T
1.021

1.023
0.9891  0.9980
July 17, 2016
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
July 17, 2016
Parity Conditions
20
International Fisher Effect
 expected future spot should
accommodate any interest rate
differentials

T
 1  icd 
1.1659 eT
1.0418 

 
 

1.1783 e0
1

i
1
.
0533


usd 

0.9895  0.9891
July 17, 2016
Parity Conditions
21
1
Interest Rate parity
 interest rate differentials are covered
by the forward rate
T
 1  icd 
1.1566 fT
1.0418 

 
 

1.1783 e0
1.0533 
 1  iusd 
0.9816  0.9891
July 17, 2016
Parity Conditions
22
1
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
July 17, 2016
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
July 17, 2016
 eT
Parity Conditions
24
Comparative statistics
*
 usd

*
 cd
2.5 %
US
T-bill
rates
Canadian
T-bill
rates
One
month
July 17, 2016

2.2 %
Canadian
forward
rates
1.1622
Three
month
5.13%
4.27%
1.1605
Six
month
5.21%
4.30%
1.1575
One
year
5.09%
4.34%
1.1520
Parity Conditions
25
Purchasing Power Parity
e T
e0
 1 
 
 1  
*
cd
*
usd



T
0.9987 
1
12
11622
.
. 
 1022
 
11637
.
. 
 1025
0.25
Three months
11605
.
. 
 1022
0.9973 
 
11637
.
. 
 1025
Six months
11575
.
. 
 1022
0.9947 
 
11637
.
. 
 1025
0.5
One year
11520
.
. 
 1022
0.9899 
 
11637
.
. 
 1025
July 17, 2016
Parity Conditions
 0.9998
 0.9993
 0.9985
1
 0.9970
26
Fisher Effect
 1  i cd

 1  i usd



T
*
 1   cd

*
 1   usd

.
 10427

09979
.
 

.
 10513
0.25
.
 10430

0.9957  

.
 10521
0.5
.
 10434

0.9929  

.
 10509
July 17, 2016
1



. 
 1022
 
. 
 1025
T
0.25
. 
 1022
 
. 
 1025
 09993
.
Three months
0.5
.
 1022

 

.
 1025
 0.9985
Six months
 0.9990
One year
1
Parity Conditions
27
Interest rate parity
International Fisher effect
fT
e0

e T
e0
 1  i cd
 
 1  i usd



T
11605
.
.
 10427

0.9973 
 
11637
.
 10513 
0.25
11575
.
.
 10430

0.9947 
 
11637
.
 10521 
0.5
11520
.
.
 10434

0.9899 
 
11637
.
 10509 
1
July 17, 2016
 0.9979
 0.9956
 0.9929
Parity Conditions
Three months
Six months
One year
28