ESM chapter 7
MULTINATIONAL BUSINESS FINANCE
COURSE723G33
yinghong.chen@liu.se PhD in
Finance
International Parity Conditions
7-1
International Parity Conditions
Managers of multinational firms, international
investors, importers and exporters, and
government officials must deal with these
fundamental issues:
What are the relationship between exchange rate,
interest rate and inflation?
Are changes in exchange rates predictable?
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International Parity Conditions
 The economic theories that link exchange
rates, price levels, and interest rates together
are called international parity
conditions.
 These international parity conditions form
the core of the financial theory.
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International Parity Conditions
 The derivation of these conditions requires the
assumption of Perfect Capital Markets (PCM).
 no transaction costs
 no taxes
 complete certainty
 NOTE – Parity Conditions are expected to hold in
the long-run, but not always in the short run.
4
The Law of one price:
 If the identical product or service can be:
 sold in two different markets; and
 no restrictions exist on the sale; and
 transportation costs of moving the product between
markets do not exist, then
 the product’s price should be the same in both markets.
 This is called the law of one price.
A primary principle of competitive markets is
that prices will equalize across markets if
frictions (transportation costs) do not exist.
That is:
P$ x S = P¥ or S= P¥ / P$

Where the product price in US dollars is (P$),
the spot exchange rate is (S) and the price in
Yen is (P¥).
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



Law of one price should hold for a basket of
identical goods and services in different
currencies.
By comparing the prices of identical products
denominated in different currencies, we
could determine the PPP exchange rate that
should exist if markets were efficient.
S ¥/$= ∑P¥/ ∑P$
Note that Big Mac index is potentially misleading but fun to know.
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
If the exchange rate between two currencies
starts in equilibrium, then, we have what is
termed Relative purchasing power parity
(RPPP).
St  St 1  D   F

St 1
1 F

The relative change in prices between two
countries over a period of time determines
the change in the exchange rate over that
period.
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
More specifically, with regard to RPPP:
“If the spot exchange rate between two
countries starts in equilibrium, any change in
the differential rate of inflation between
them tends to be offset over the long run by
an equal but opposite change in the spot
exchange rate.”
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%∆S
%∆P
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
RPPP is not accurate in predicting future
exchange rates.

Two general conclusions can be made from
empirical tests:
 RPPP holds up well over the very long run but
poorly for shorter time periods;
 the theory holds better for countries with
relatively high rates of inflation and
underdeveloped capital markets.
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
The objective is to discover whether a
nation’s exchange rate is “overvalued” or
“undervalued” in terms of RPPP.

This problem is often dealt with through the
calculation of exchange rate indices such as
the nominal effective exchange rate index.
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Relative PPP Example
 Given inflation rates of 5% and 10% in Australia and
the UK respectively, what is the prediction of PPP
with regards to $A/£ exchange rate?
St  St 1  D   F

St 1
1 F
Relative PPP
= (0.05 – 0.10)/(1 + 0.10) = - 0.045 = - 4.5%
The general implication of relative PPP is that countries
with high rates of inflation will see their currencies
depreciate against those with low rates of inflation.
14
Forecasting Future Spot Rates
 Suppose the spot exchange rate and expected
inflation rates are:
S¥/$,t0  90 ¥ / $;  U .S .  5%;  Japan  2%
 What is the expected ¥/$ exchange rate if relative
PPP holds?
Answer:
1  ¥ 
PPP

S ¥ / $, t1  S ¥ / S ,t 0  

1


$ 

 1.02 
 90 ¥ / $  
  87.43 ¥ / $
 1.05 
15


Incomplete exchange rate pass-through is one
of the reasons that a country’s Real effective
exchange rate index can deviate from the
exchange rate
For example, a car manufacturer may or may
not adjust pricing of its cars sold in a foreign
country if exchange rates alter the
manufacturer’s cost structure in comparison to
the foreign market.
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

Price elasticity of demand is an important
factor when determining pass-through levels.
The price elasticity of demand for any good is
the percentage change in quantity of the good
demanded as a result of the percentage
change in the goods price.
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
The Fisher Effect states that nominal interest rates in each
country are equal to the required real rate of return plus
compensation for expected inflation.

This equation reduces to:
i=r+ 
Where i is nominal interest rate, r is real interest
rate and
 is expected inflation.
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The relationship between the percentage
change in the spot exchange rate over time and
the differential between comparable interest
rates in different national capital markets.

Also called “Fisher-open”.
The spot exchange rate should change in an
equal amount but in the opposite direction to
the difference in interest rates between two
countries.
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
approximately: S – S
1
2
S2
= i$ - i¥

Where i$ and i¥ are the respective national interest rates
and S1 is the spot exchange rate (¥/$) at t=1, S2 is the
expected future spot rate at t=2.

Justification for the International Fisher effect is that
investors must offset the expected change in
exchange rates.
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
A forward exchange agreement between
currencies states the rate of exchange at
which a foreign currency will be bought or
sold forward at a specific date in the future.

A forward rate is an exchange rate quoted for
settlement at some future date. For 1, 2, 3, 6,
12 month.

Forward rate over 2 years is called swap rate.
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
The forward rate is calculated for any specific maturity by
adjusting the current spot exchange rate by the ratio of
Eurocurrency interest rates of the same maturity for the
two subject currencies.

For example, the 90-day forward rate for the Swiss Franc/US
dollar exchange rate
(FSF/$90) = the current spot rate (SSF/$) times the ratio of the 90day euro-Swiss franc deposit rate (iSF) over the 90-day
Eurodollar deposit rate (i$).
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
Formal representation of the forward rate:
FSF/$90 = SSF/$ x [1 + (iSF x 90/360)]
[1 + (i$ x 90/360)]
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
The forward premium or discount (of SF) is
the percentage difference between forward
exchange rate and spot rate, stated in annual
percentage terms.
f SF = Spot – Forward
x
Forward
360
days
x

Note that here SF/$ is used.

If use $/SF, then it is (F-S)/S instead.
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The theory of Interest Rate Parity (IRP) provides
the linkage between the foreign exchange markets
and the international money markets.

The theory states: The difference in the national
interest rates for securities of similar risk and
maturity (i$ -i€) should be equal to, but with an
opposite sign, the forward rate discount or
premium for the foreign currency (F-S)/S. we use
the quotation $/€ here. (i$ -i€) = (F-S)/S
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i$
isf
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Exchange market
Exchange market
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
The spot and forward exchange rates are not constantly in
the state of equilibrium described by interest rate parity.

When the market is not in equilibrium, the potential for riskfree arbitrage profit exists.

The arbitrager will exploit the imbalance by investing in the
currency that offers higher return and sell forward and
realize a risk free arbitrage profit.

This is known as covered interest arbitrage (CIA).
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Uncovered interest arbitrage (UIA) is a deviation
from covered interest arbitrage .
In UIA, investors borrow in currencies that have relatively
low interest rates and convert the proceed into currencies
that offer higher interest rates.
The transaction is “uncovered” because the investor does
not sell the higher yielding currency proceeds forward,
choosing to remain uncovered and accept the exchange
rate risk at the end of the period.
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In the yen carry trade, the investor borrows Japanese yen at relatively low interest rates, converts the proceeds to another currency
such as the U.S. dollar where the funds are invested at a higher interest rate for a term period. At the end of the period, the investor
exchanges the dollars back to yen to repay the loan, pocketing the difference as arbitrage profit. If the spot rate at the end of the
period is roughly the same as at the start, or the yen has fallen in value against the dollar, the investor profits. If, however, the yen
were to appreciate versus the dollar over the period, the investment may result in significant loss.
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
The following exhibit (7,9) illustrates the equilibrium
conditions between interest rates and exchange rates.

The disequilibrium situation, denoted by point U, is located
off the interest rate parity line.

However, the situation represented by point U is unstable
because all investors have an incentive to execute the same
covered interest arbitrage, which will close this gap in no
time.
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Exhibit 7.9 Interest Rate Parity
(IRP) and Equilibrium
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
Forward exchange rates are unbiased
predictors of future spot exchange rates.

Intuitively this means that the distribution of
possible actual spot rates in the future is
centered on the forward rate.

Unbiased prediction simply means that the
forward rate will, on average, overestimate
and underestimate the actual future spot
rate in equal frequency and degree.
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Fundamental parity conditions (using dollar and yen).
The forcasted inflation for Japan and US are 1% and
5% respectively. A 4% differential.
The US interest rate is 8%, Japan 4%. The spot rate S1
is 104￥/$. The one-year forward is S1 100￥/$. The
Spot rate one year from now is S2

a) Purchasing Power Parity (PPP)
S2 /S1= (1+∏￥)/(1+∏$)
S2=104*1,01/1,05=100￥/$
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
b) the Fisher Effect
The nominal interest rate differential =difference in
expected rate of inflation
8%-4%=-(1%-5%)
c) International Fisher Effect
The forcasted change in spot rate =the differential
between nominal interest rates
(S1-S2 ) /S2 =i$ -i￥
d) Interest Rate Parity
(S1-F ) /F=i$ -i￥
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
e) Forward rate as an unbiased predictor .
This is also called expectations theory.
Combining d) and c), we have F=S2 where S2
is expected spot rate in the future.
See exhibit 7.11 for the 5 parity conditions in
the exchange market.
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


Which do you believe is most important for sustaining the
sale of the new Carrera model, maintaining a profit margin or
maintaining the U.S. dollar price?
Given the change in exchange rates and the strategy
employed by Porsche, would you say that the purchasing
power of the U.S. dollar customer has grown stronger or
weaker?
In the long run, what do most automobile manufacturers do
to avoid these large exchange rate squeezes?
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Exhibit 1 Pass-Through Analysis for
the 911 Carrera 4S Cabriolet, 2003
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