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University of Oregon, Ali Emami 1

International Parity Conditions

International Finance and InvestmentTopic 4

Ali EmamiDepartment of Finance

Lundquist College of BusinessUniversity of Oregon


International Parity Conditions

• Definition: The parity conditions are equilibrium conditions that establish linkage between financial prices (P, i, S, F) in the absence of arbitrage.

• Implications: Provide guidelines for financial strategic decisions suggested by each side of parity condition. The parity conditions define international financial “break-even” points encompassing alternative strategies yielding identical financial outcomes suggested by each side (RHS and LHS) of parity condition.


Implications…Continued

• From private investors point of view, parity conditions help to make optimal (beneficial) financial decisions regarding the choice of currency for borrowing, location of plants in different countries, measuring currency risk exposure, etc.

• From public policy makers point of view, parity conditions help to evaluate the strength of national currencies, the efficiency of national capital markets, and the effectiveness of fiscal and monetary policies towards achieving macroeconomic policies.


Implications………..Continued

• The empirical evidence and tests on validity (invalidity) of parity conditions provide useful signals regarding the opportunity for making profits for private enterprise.

• When parity conditions hold, it implies that its almost impossible to make profit from arbitrage in goods, services, capital, etc.

• When parity conditions do not hold, it often implies the possibility of making profits doing arbitrage in goods, capital, etc.


Parity Conditions in Perfect Capital Markets

• Perfect Capital Markets Assumptions:No transaction costs (“price” differentials only

provokes arbitrage)No taxes, tariff or trade barriersComplete certainty (no risk)

Given these assumption, profit-maximizing enterprise will act to capitalize on arbitrage opportunities in trade of goods and services between countries, between spot and forward exchange rates, and between real and financial assets to the extent that eliminates any further arbitrage activity.


Purchasing Power Parity (PPP) Doctrine

• Purchasing power party doctrine was introduced by the Swedish economist Gustav Cassel in 1918 (Gustav Cassel, “Abnormal Deviations in International Exchanges,” Economic Journal, December 1918, pp.413-415).

• He proposed the PPP doctrine after WWI as a new method for measuring exchange rates among countries.


PPP Definition

• Definition: Purchasing power parity focuses on the parity condition at a specific time that links the price of a specific product in a country in terms of its currency (P$) to:

a) the price of the same product in another country denominated in its currency (P€ ), and

b) the spot exchange rate between the two currencies (S($/€)) . $ €

$(1)

€P S P


Types of PPP

• The PPP doctrine has two forms:

a) The absolute PPP (APPP) and,

a) the relative PPP (RPPP).


Absolute PPP (APPP)• The APPP relies on perfect capital market

(PCM) assumptions and the Law of One Price (LOOP).

• The Law of One Price states that under PCM assumptions, there are no opportunities for arbitrage based on the prices of a similar (homogenous) good in two countries.

• Hence, prices of the same good in two trading partner countries will become identical (after adjustments in the exchange rate). Thus,

$ €

$(1)

€P S P


APPP Continued

• APPP and Exchange RateSubstituting general price levels

(a weighted price for all products) for each country in equation (1), yields a measurement for exchange rate between Dollar and Euro currencies:

$,

€,t

$(2)

€t

t

PS

P


APPP & Exchange rate: Example

• Exchange Rate Gold Standard (1876-1913):One ounce of gold in the United States was priced at $20.67 while in U.K., one ounce of gold was priced at £4.247. According to APPP, what would be the S($/£)?

$

£

$ $20.67 $4.86695££ £4.247

PS

P


The Big Mac Index

• Definition: The APPP measure of the “true equilibrium value” of a currency based on one product, a MacDonald’s Big Mac.

$

Big MacBig Mac FCAPPP Big Mac

PS

P


The Big Mac Index: Example

CountryBig Mac Prices

(Local Currency)Implied

PPPActual Spot Rate, 4/25/00

Overvaluation(+)

Or Undervaluation(-)

Of local currency

United States

Brazil

China

Germany

Japan

Mexico

Switzerland

2.51

2.95

9.90

4.99

294

20.9

5.90

-

1.18

3.94

1.99

117

8.33

2.35

-

1.79

8.28

2.11

106

9.41

1.70

-

- 34%

- 52

- 6

+10

- 11

+ 38

Source: “Big Mac Currencies” The Economist, April 12, 1977, p. 71; “Big Mac Currencies,” The Economist, April 29, 2000, p. 75.


Relative Purchasing Power Parity (RPPP) Doctrine

• Relative purchasing power parity (RPPP) is concerned with the changes in spot rate over time. That is RPPP estimates percentage changes in the exchange rates over a given time period.

• Rewriting equation (2) for time period (t+1) yields:

• Dividing (3) by (2) gives the dynamics behavior of exchange rate:€$

€1+

P PS

P

$, 11

€,t+1

$(3)

€t

t

PS

P


Implications of RPPP

• 1

• 2$,1

0

€,1

1$ $

€ € 1

t

t

PS S

P

$ €$ $€ € $ €

€1

P PS S P P

P


Example: Consider the following information on U.S. and Japanese CPIs. What was the PPP implied exchange rate between the ¥ and the $ in 1989? Was the ¥ overvalued or under valued against the $? By how much?

Year

CPI (U.S.)

CPI (Japan)

Exchange Rate

1973

40.3

44.0

$0.003762/¥

1989

117.2

104.6

$0.006971


Answer: Dividing equation (3) by equation (2) yields:

$, 1 $, 11

¥,t+1 $,1

$, ¥, 1

¥,t ¥,

1989

$$ $¥

$ ¥ ¥¥

117.2$ 40.3$0.003762 $0.004602

¥ ¥104.6¥44.0

t tt

tt t

t tt

t

P PS

P PS S

P PS

P P

S

Thus, according to PPP, the yen is overvalued by

$0.006971 $0.004602 $0.004602 100 51.47% , and dollar is undervalued by -33.98%.


Example:Assume that inflation rate in U.S. and euro region are expected to be 6% and 4% respectively each year for the next four years, and the current spot rate is $1.2812 per euro. Calculate the PPP rate for euro in four years.

• Answer:

2008

1 0.06$1.2812 $1.285454€ €1 0.04

S


Example:Suppose the base period is year 1990. Assume that currently (in 2004), the U.S. CPI is 102 and the United Kingdom’s CPI is at 115 relative to 1990 base period. The exchange rate was $1.5 in 1990. Calculate the PPP exchange rate in 2004.

• Answer:

2004$ 102 $1.330435$1.5 ££ 115

S


Example:Given the following information, if PPP hold over 1979-1998, what would have been the S(DM/$) rate in 1998?

Answer:

98,

79,,98 79

98,$

79,$

120.5922.4

145.3$79.2

DM

DMNPPP

CPI

CPIDMS S DM

CPI

CPI

S(DM/$)

CPIDM

CPI$

1979

DM2.4/$

92.0

79.2

1998

DM2.50/$

120.5

145.3


Real Purchasing Power Parity Exchange Rates

• The Real Bilateral Exchange Rate Based on Absolute PPP

• The Real Exchange Rate Based on Relative Purchasing Power Parity

( )

,$

¥

$$ ¥¥

market Nt

RAPPP t

SS

CPI

CPI

( )

,

$,

$,( )

¥,

¥,

$

¥

market NR t nRPPP t n

t n

tmarket Nt

t n

t

SS

CPI

CPIS

CPI

CPI


Real Exchange Rate Based on the Market Exchange Rate

• Formula:

$

$

$$

$ $

nominal

treal

t

FC

real nominal

t t

FC

FCS

FCS

P

P

PFC FCS S

P


Interest Rate Parity (IRP) Theory and the Fisher

Parities • Interest rate parity focuses on the parity

condition that links the spot and forward (expected) exchange rates with international money and bond markets.

• The parity condition implied by this theory establishes the break-even condition where the return on a domestic currency investment is identical with the return on a foreign currency investment covered against exchange rate risk


CIRP Relations

• Invest $1 at Home at the rate of i$ and after one year get:

• Invest $1 in euro at the rate of and after one year get:

$$1 1 i

€i

1

€ 0

0

€ $

$1 $1

$ €€

yeari FS


CIRP Relations……….continued

• Where to invest (if you got the money)?

• If (LHS > RHS), then invest in $.• If (LHS < RHS), then invest in Euro.• If (LHS = RHS), then indifferent.

1

$ € 0

0

€ $

$1 $$1 1 1

$ €€

yeari i FS

¦


CIRP Relations……….continued

• Where to borrow and invest (if you don’t have money)?

• If (LHS > RHS), then borrow from euro and invest in $.

• If (LHS < RHS), then borrow from $ and invest in Euro.

• If (LHS = RHS), then indifferent.

1

$ € 0

0

€ $

$1 $$1 1 1

$ €€

yeari i FS

¦


Variations of Covered and Uncovered IRP Formula

• 1

• 2

• 3

• 4

$

€

1$ $

€ € 1

iF S

i

$

€

1$ $

€ € 1

iES S

i

$ €

€

$ $€ €

$ 1€

F Si i

iS

$ € €

$ $€ €

1$€

F Si i i

S


Uncovered IRP: Relationship Between PPP and IRP: Fisher’s “interest-open economy”

condition • 1

• 2

• 3

• 4

€$

€1+

P PS

P

$ €

€

$ $ $1

€ € €$ 1€

F ES

tS S Si i

iS

$ €

€

$

€ 1

i iS

i

$ €$ €

€ €1+ 1

i iP P

P i


Fisher’s “interest-open economy” condition

• 1

• 2

$ € $ €P P i i

$ €

$ $ € €

real reali i

i P i P


Market Forces and Covered Interest Parity

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