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April 20, 2023 Parity Conditions 1
Eiteman and Stonehill
Chapter 4
Parity Conditions
April 20, 2023 Parity Conditions 2
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
April 20, 2023 Parity Conditions 3
The Law of one price The Law of One Price does not hold -
given an exchange rate of 1.1254
usdcdBigMacusdBigMacequivcd ePP ,,,
cdusd
cdusd 43.3
005.141.3
88.341.3
April 20, 2023 Parity Conditions 4
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
April 20, 2023 Parity Conditions 5
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
April 20, 2023 Parity Conditions 6
Purchasing Power Parity
Absolute parity
Relative parity
P e Px cd cd usd x usd, , , P
Pe
x cd
x usdcd usd
,
,,
w P e w Pii
n
i cd cd usd i i u sdi
n
1 1, , ,
w P
w P
ei
i
n
i cd
i i u sdi
n cd usd
1
1
,
,
,
April 20, 2023 Parity Conditions 7
Purchasing Power Parity
The exchange rate changes to accommodate differential rates of inflation If this is so, then relative PPP holds
9895.01783.1
1659.1
0e
eT
9980.0023.1
021.1
1
11
T
usd
cd
April 20, 2023 Parity Conditions 8
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
April 20, 2023 Parity Conditions 9
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
0009.10004.10012.1027.1
017.1 12
1
Te
April 20, 2023 Parity Conditions 10
Relative Purchasing Power Parity% chg in spot
% chg in relative inflation
x
April 20, 2023 Parity Conditions 11
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
April 20, 2023 Parity Conditions 12
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
usdcdusdcd ePP ,
April 20, 2023 Parity Conditions 13
Real exchange rates
w P
w P
e
rea l exchange ra te index
ii
n
i u sd
i i cdi
n cd usd
1
1
1 4 2 6 7
1 7 1 2 01 1 7 8 3
0 9 8 1 9
,
,
,
.
..
.
April 20, 2023 Parity Conditions 14
Real effective exchange rates
100
April 20, 2023 Parity Conditions 15
Differential Price movements
Calculate the expected price of buying US
Expected greater than actual price if you are selling this product, you may
face competitive pressures to lower price
usdcdusdcd ePP ,
cdcd PP
April 20, 2023 Parity Conditions 16
Price elasticity of demand
How do the revenues of the firm react to changes in price
revenues decline if elasticity of own demand is less than 1
dtPd
dtQd
P
Qdln
ln
%
%
1
April 20, 2023 Parity Conditions 17
Inelastic own demand
P
Q
Decrease in revenuedue to price decrease
Increase in revenuedue to increased sales
P0
PT
Q0 QT
April 20, 2023 Parity Conditions 18
Elastic own demand
P
Q
Decrease in revenuedue to price decrease
Increase in revenuedue to increased sales
P0
PT
Q0 QT
April 20, 2023 Parity Conditions 19
The Fisher Effect The nominal interest rate
relative nominal interest rates are proportional to relative inflation rates
rri
023.1
021.1
1
1
1
1
0533.1
0418.1
T
usd
cd
T
usd
cd
i
i
9980.09891.0
April 20, 2023 Parity Conditions 20
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
April 20, 2023 Parity Conditions 21
International Fisher Effect
expected future spot should accommodate any interest rate differentials
1
0 0533.1
0418.1
1
1
1783.1
1659.1
T
usd
cdT
i
i
e
e
9891.09895.0
April 20, 2023 Parity Conditions 22
Interest Rate parity
interest rate differentials are covered by the forward rate
1
0 0533.1
0418.1
1
1
1783.1
1566.1
T
usd
cdT
i
i
e
f
9891.09816.0
April 20, 2023 Parity Conditions 23
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
April 20, 2023 Parity Conditions 24
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?
TT ef
Comparative statistics
April 20, 2023 Parity Conditions 25
US T-bill rates
Canadian T-bill rates
Canadian forward
rates
One month
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
u sd* . % 2 5 cd
* . % 2 2
Purchasing Power Parity
April 20, 2023 Parity Conditions 26
*
*
e
eT cd
u sd
T
0
1
1
0 9 9 8 7
11 6 2 2
11 6 3 7
1 0 2 2
1 0 2 50 9 9 9 8
1
1 2.
.
.
.
..
0 9 9 7 311 6 0 5
11 6 3 7
1 0 2 2
1 0 2 50 9 9 9 3
0 2 5
..
.
.
..
.
0 9 9 4 711 5 7 5
11 6 3 7
1 0 2 2
1 0 2 50 9 9 8 5
0 5
..
.
.
..
.
0 9 8 9 911 5 2 0
11 6 3 7
1 0 2 2
1 0 2 50 9 9 7 0
1
..
.
.
..
Three months
Six months
One year
Fisher Effect
April 20, 2023 Parity Conditions 27
1
1
1
1
i
icd
u sd
T
cd
u sd
T
*
*
0 9 9 7 91 0 4 2 7
1 0 5 1 3
1 0 2 2
1 0 2 50 9 9 9 3
0 2 5 0 2 5
..
.
.
..
. .
0 9 9 5 71 0 4 3 0
1 0 5 2 1
1 0 2 2
1 0 2 50 9 9 8 5
0 5 0 5
..
.
.
..
. .
0 9 9 2 91 0 4 3 4
1 0 5 0 9
1 0 2 2
1 0 2 50 9 9 9 0
1 1
..
.
.
..
Three months
Six months
One year
Interest rate parityInternational Fisher effect
April 20, 2023 Parity Conditions 28
f
e
e
e
i
iT T cd
u sd
T
0 0
1
1
0 9 9 7 311 6 0 5
11 6 3 7
1 0 4 2 7
1 0 5 1 30 9 9 7 9
0 2 5
..
.
..
.
0 9 9 4 711 5 7 5
11 6 3 7
1 0 4 3 0
1 0 5 2 10 9 9 5 6
0 5
..
.
..
.
0 9 8 9 911 5 2 0
11 6 3 7
1 0 4 3 4
1 0 5 0 90 9 9 2 9
1
..
.
..
Three months
Six months
One year