Chapter 6
International Parity
Conditions
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.
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6-2
Prices and Exchange Rates
• If the identical product or service can be
sold in two different markets, and no
restrictions exist on the sale or
transportation costs of moving the
product between markets, the products
price should be the same in both markets.
• This is called the law of one price.
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6-3
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 US dollars is (P$),
the spot exchange rate is (S) and the price in
Yen is (P¥).
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6-4
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.
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6-5
Exhibit 6.2 Purchasing Power Parity (PPP)
4
P
Percent change in the spot exchange
rate for foreign currency
3
2
1
-6
-5
-4
-3
-2
-1
1
-1
-2
2
3
4
5
6
Percent difference in
expected rates of inflation
(foreign relative to
home country)
-3
-4
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6-6
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.
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6-7
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.
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6-8
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
– The theory holds better for countries with relatively
high rates of inflation and underdeveloped capital
markets
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6-9
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.
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6-10
Exhibit 6.3 IMF’s Real Effective Exchange Rate
Indexes for the United States & Japan (1995 = 100)
180
160
United States
Japan
140
120
100
80
60
40
20
0
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
Source: International Financial Statistics, International Monetary Fund, monthly, 1995=100.
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6-11
Prices and Exchange Rates
• The degree to which the prices of imported and exported goods change
as a result of exchange rate changes is termed pass-through.
• Although PPP implies that all exchange rate changes are passed
through by equivalent changes in prices to trading partners, empirical
research in the 1980s questioned this long-held assumption.
• 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.
• Pass-through can also be partial as there are many mechanisms by
which companies can compartmentalize or absorb the impact of
exchange rate changes.
• Price elasticity of demand is an important factor when determining
pass-through levels.
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6-12
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+π
Where i = nominal interest rate, r = real interest rate
and π = expected inflation.
• Empirical tests (using ex-post) national inflation rates
have shown the Fisher effect usually exists for shortmaturity government securities (treasury bills and
notes).
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6-13
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.
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6-14
Interest Rates
and Exchange Rates
• More formally:
S1 – S2
x 100 = 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.
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6-15
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.
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6-16
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/US 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$).
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6-17
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)]
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6-18
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.
360
f SF = Spot – Forward
x 100
x
days
Forward
• This is the case when the foreign currency
price of the home currency is used (SF/$).
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6-19
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.
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6-20
Exhibit 6.5 Currency Yield Curves
& The Forward Premium
Interest
yield
Eurodollar
yield curve
10.0 %
9.0 %
8.0 %
7.0 %
Forward premium is the
percentage difference of 3.96%
6.0 %
5.0 %
Euro Swiss franc
yield curve
4.0 %
3.0 %
2.0 %
1.0 %
30
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60
90
120
Days Forward
150
180
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Exhibit 6.6 Interest Rate Parity (IRP)
i $ = 8.00 % per annum
(2.00 % per 90 days)
Start
End
$1,000,000
x 1.02
$1,020,000
$1,019,993*
Dollar money market
90 days
S = SF 1.4800/$
F90 = SF 1.4655/$
Swiss franc money market
SF 1,480,000
x 1.01
SF 1,494,800
i SF = 4.00 % per annum
(1.00 % per 90 days)
•Note that the Swiss franc investment yields $1,019,993, $7 less on a $1 million investment.
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6-22
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).
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6-23
Exhibit 6.7 Covered Interest Arbitrage (CIA)
Eurodollar rate = 8.00 % per annum
Start
End
$1,000,000
x 1.04
$1,040,000
$1,044,638
Arbitrage
Potential
Dollar money market
180 days
S =¥ 106.00/$
F180 = ¥ 103.50/$
Yen money market
¥ 106,000,000
x 1.02
¥ 108,120,000
Euroyen rate = 4.00 % per annum
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6-24
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
no 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.
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6-25
Exhibit 6.8 Uncovered Interest Arbitrage (UIA):
The Yen Carry Trade
Investors borrow yen at 0.40% per annum
Start
¥ 10,000,000
End
x 1.004
Japanese yen money market
S =¥ 120.00/$
360 days
¥ 10,040,000 Repay
¥ 10,500,000 Earn
¥
460,000 Profit
S360 = ¥ 120.00/$
US dollar money market
$ 83,333,333
x 1.05
$ 87,500,000
Invest dollars at 5.00% per annum
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.
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Interest Rates
and Exchange Rates
• The following exhibit 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.
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6-27
Exhibit 6.9 Interest Rate Parity (IRP) and Equilibrium
4
3
2
Percentage premium on
foreign currency (¥)
1
4.83
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
-1
-2
-3
Percent difference between foreign (¥) -4
and domestic ($) interest rates
X
U
Y
Z
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6-28
Exhibit 6.11 International Parity Conditions in
Equilibrium (Approximate Form)
Forward rate
as an unbiased
predictor
(E)
Forward premium
on foreign currency
+4%
(yen strengthens)
Interest
rate
parity
(D)
Forecast change in
spot exchange rate
+4%
(yen strengthens)
International
Fisher Effect
(C)
Difference in nominal
interest rates
-4%
Purchasing
power
parity
(A)
Forecast difference
in rates of inflation
-4%
(less in Japan)
Fisher
effect
(B)
(less in Japan)
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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.
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6-30
Exhibit 6.10 Forward Rate as an Unbiased
Predictor for Future Spot Rate
Exchange rate
t1
t2
t3
t4
F2
S2
S1
Error
Error
F1
F3
Error
S3
S4
t1
t2
t3
t4
Time
The forward rate available today (Ft,t+1), time t, for delivery at future time t+1, is used as a “predictor” of the
spot rate that will exist at that day in the future. Therefore, the forecast spot rate for time S t2 is F1; the actual spot
rate turns out to be S2. The vertical distance between the prediction and the actual spot rate is the forecast error.
When the forward rate is termed an “unbiased predictor of the future spot rate,” it means that the forward rate
over or underestimates the future spot rate with relatively equal frequency and amount. It therefore “misses the
mark” in a regular and orderly manner. The sum of the errors equals zero.
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6-31