parity conditions

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