Chap 7 International Parity Conditions
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Q: 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.
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
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 products price should be the same in both
markets.

This is called the law of one price.
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

A primary principle of competitive markets is
that prices will equalize across markets if
frictions (transportation costs) do not exist.
Comparing prices would require only a
conversion from one currency to the other:
P$ x S = 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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Under or
over
value? It
changes
all the
time!
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
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.
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
If the assumptions of the absolute version of
the PPP theory are relaxed, we observe what
is termed relative purchasing power parity
(RPPP).

the relative change in prices between two
countries over a period of time determines
the change in the exchange rate over that
period. This is RPPP.
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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.”
Q2: Why?
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%∆S
%∆P
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
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.
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
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.
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


Incomplete exchange rate pass-through is one
reason that a country’s real effective exchange
rate index can deviate from the exchange rate
The degree to which the prices of imported and
exported goods change as a result of exchange
rate changes is termed pass-through.
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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


Pass-through can also be partial as there are
many mechanisms by which companies can
absorb the impact of exchange rate changes.
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 (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).
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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 is known as the international Fisher
effect.

“Fisher-open” 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.
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
formally: 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 be rewarded or penalized to offset the
expected change in exchange rates.
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
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.
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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 is the
percentage difference between forward
exchange rate and spot rate, stated in annual
percentage terms.
f SF = Spot – Forward
Forward

x
360
days
x
100
Note that here SF/$ is used. If use $/SF, then
it is (F-S)/S instead. Use common sense.
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The theory of Interest Rate Parity (IRP) provides
the linkage between the foreign exchange markets
and the international money markets.

The theory states: The difference in the national
interest rates for securities of similar risk and
maturity (i$ -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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