Unit 4

International Parity Relation

1 SOMTU
 Contents

● Law of one price,

● purchasing power parity in absolute and
relative form,
● interest rate parity in covered and uncovered
basis,
● international fisher effect,

2
International Parity Conditions

● Some fundamental questions managers of MNEs, international

portfolio investors, importers, exporters and government
officials must deal with every day are:
– What are the determinants of exchange rates?
– Are changes in exchange rates predictable?
● 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 that is unique to international finance.
International Parity Conditions

● These theories do not always work out to be

“true” when compared to what students and
practitioners observe in the real world, but
they are central to any understanding of how
multinational business is conducted and
funded in the world today.
● The mistake is often not with the theory itself,
but with the interpretation and application of
said theories.
Prices and Exchange Rates

● 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 are equal, then
– the product’s price should be the same in both
markets.
● This is called the law of one price.
Prices and Exchange Rates

● A primary principle of competitive markets is

that prices will equalize across markets if
frictions (transportation costs) do not exist.
● Comparing prices then, would require only a
conversion from one currency to the other:
P$ x S(¥/$) = P¥
Where the product price in U.S. dollars is
(P$), the spot exchange rate is (S) and the
price in Yen is (P¥).
 Prices and Exchange Rates
● If the law of one price were true for all goods and
services, the purchasing power parity (PPP) exchange
rate could be found from any individual set of prices.
● By comparing the prices of identical products
denominated in different currencies, we could determine
the “real” or PPP exchange rate that should exist if
markets were efficient.
● This is the absolute version of the PPP theory.
Selected Rates from the Big Mac Index
 Prices and Exchange Rates
● If the assumptions of the absolute version of the PPP
theory are relaxed a bit more, we observe what is
termed relative purchasing power parity (RPPP).
● RPPP holds that PPP is not particularly helpful in
determining what the spot rate is today, but that the
relative change in prices between two countries over
a period of time determines the change in the
exchange rate over that period.
Prices and Exchange Rates

● 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.”
 The Relative (or Dynamic)
Form of PPP

● S*($/£) is the percentage change in the spot exchange

rate over a year, and
● p*US and p*UK are respectively the percentage annual
rates of change in the price levels in the United States
and Britain. That is, US and British annual rates of
inflation.
● If the PPP condition in its absolute form holds at some
moment in time, that is,
pUS = S($/£) pUK
● Then at the end of 1 year, for PPP to continue to hold
11
 pUS (1+p*US ) = S($/£) [1 +S*($/£)] pUK (1+p*UK )
● Taking the ratio of above two equations
(1+p*US ) = [1 +S*($/£)] (1+p*UK )
[1 +S*($/£)]= (1+p*US ) / (1+p*UK )
F($/£) / ($/£) = (1+p*US ) / (1+p*UK )
● The above two equations are the PPP condition in its
relative (or dynamic) form.
● If the United States experiences inflation of 5 percent
and Britain 10 percent then the dollar price of pounds
should fall, that is, the pound should depreciate at a
12 rate of 4.5%
 ● approximation of relative PPP
S*($/£) ≈ p*UK – p*US
● Approximation is good if inflation is low but produce a
worse result if inflation is high
● The relative or dynamic form of PPP in is not
necessarily violated by sales taxes or shipping costs
that make prices higher than static-form PPP levels.
● because of higher shipping costs of principal commodity
imports to Britain than to the United States, US prices
are consistently lower by the proportion τ than British
13 prices as given by equation
 pUS = S($/£) pUK (1 + τ)
● If the same connection exists 1 year later.
pUS (1+p*US ) = S($/£) [1 +S*($/£)] pUK (1+p*UK ) (1 + τ)
● Taking the ratio of above two equations
(1+p*US ) = [1 +S*($/£)] (1+p*UK )
● Which is exactly the same as equation in relative PPP.
● The relative (or dynamic) form of PPP can hold even if
the absolute (or static) form of PPP is (consistently)
violated.

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Relative Purchasing Power Parity
(PPP)
Prices and Exchange Rates

● Empirical testing of PPP and the law of one

price has been done, but has not proved PPP
to be accurate in predicting future exchange
rates.
● Two general conclusions can be made from
these tests:
– PPP holds up well over the very long run but
poorly for shorter time periods; and,
– the theory holds better for countries with relatively
high rates of inflation and underdeveloped capital
markets.
Prices and Exchange Rates

● Individual national currencies often need to be evaluated

against other currency values to determine relative
purchasing power.
● The objective is to discover whether a nation’s exchange
rate is “overvalued” or “undervalued” in terms of PPP.
● This problem is often dealt with through the calculation of
exchange rate indices such as the nominal effective
exchange rate index.
● The real effective exchange rate index for the U.S. dollar
Interest Rates and Exchange
Rates

● 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 (in approximate form):
i=r+
Where i = nominal interest rate, r = real interest rate and
= expected inflation.
● Empirical tests (using ex-post) national inflation rates have
shown the Fisher effect usually exists for short-maturity
government securities (treasury bills and notes).
Interest Rates and Exchange
Rates

● 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 is known as the international Fisher
effect.
● “Fisher-open,” as it is termed, states that the
spot exchange rate should change in an
equal amount but in the opposite direction to
the difference in interest rates between two
countries.
Interest Rates and Exchange
Rates

● More formally:
S1 – S 2
= i $ - i¥
S2
● Where i$ and i¥ are the respective national
interest rates and S is the spot exchange rate
using indirect quotes (¥/$).
● Justification for the international Fisher effect is
that investors must be rewarded or penalized to
offset the expected change in exchange rates.
Interest Rates and Exchange
Rates

● A forward rate is an exchange rate quoted for

settlement at some future date.
● A forward exchange agreement between
currencies states the rate of exchange at
which a foreign currency will be bought
forward or sold forward at a specific date in
the future.
Interest Rates and Exchange
Rates

● 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/U.S. dollar exchange rate (FSF/$90) is found by
multiplying the current spot rate (SSF/$) by the ratio
of the 90-day euro-Swiss franc deposit rate (iSF) over
the 90-day eurodollar deposit rate (i$).
23
Interest Rates and Exchange
Rates

● Formulaic representation of the forward rate:

FSF/$90 = SSF/$ x [1 + (iSF x 90/360)]
[1 + (i$ x 90/360)]
Interest Rates and Exchange
Rates

● The forward premium or discount is the

percentage difference between the spot and
forward exchange rate, stated in annual
percentage terms.
f SF = Spot – Forward 360
x x 100
Forward days
● This is the case when the foreign currency
price of the home currency is used (SF/$).
Interest Rates and Exchange
Rates

● 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 should be equal to, but opposite in sign
to, the forward rate discount or premium for the
foreign currency, except for transaction costs.
Interest Rate Parity (IRP)
Interest Rates and Exchange Rates

● The spot and forward exchange rates are not, however,

constantly in the state of equilibrium described by interest
rate parity.
● When the market is not in equilibrium, the potential for
“risk-less” or arbitrage profit exists.
● The arbitrager will exploit the imbalance by investing in
whichever currency offers the higher return on a covered
basis.
● This is known as covered interest arbitrage (CIA).
Covered Interest Arbitrage (CIA)
Interest Rates and Exchange Rates

● A deviation from covered interest arbitrage is uncovered

interest arbitrage (UIA).
● In this case, investors borrow in countries and currencies
exhibiting relatively low interest rates and convert the
proceed into currencies that offer much 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 currency
risk of exchanging the higher yield currency into the
lower yielding currency at the end of the period.
 Uncovered Interest Arbitrage (UIA):
The Yen Carry Trade

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. 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.
Interest Rates and Exchange
Rates

● Exhibit 7.9 illustrates the conditions necessary for

equilibrium 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
is virtually risk-free.
Interest Rates and Exchange Rates

● Some forecasters believe that 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.
Forward Rate as an Unbiased Predictor for
Future Spot Rate
International Parity Conditions in
Equilibrium (Approximate Form)