Chapter 7
International Parity
Conditions
The Goals of Chapter 7
• Describes the core financial theories surrounding the
determination of exchange rates (Chapter 10 will
further introduce two other models regarding the
currency valuation)
• More specifically, four international parity conditions
will be introduced among the exchanges rates, price
levels, and interest rates
–
–
–
–
Purchasing power parity
Fisher effect
International Fisher effect
Interest rate parity
• Introduce the relationship between the (future) spot
exchange rate and the forward exchange rate
7-2
International Parity Conditions
• Some fundamental questions that 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 financial theories that link exchange rates, price
levels, and interest rates together are called
international parity conditions
• These theories do not always work out to be “true”
when compared to what you observe in the real world,
but they are still fundamental to understand exchange
rates and thus the risk of international investments
– The mistake is sometimes not with the theory itself, but in
the way it is interpreted or applied in practice
7-3
Price Levels and Exchange
Rates
7-4
Price Levels and Exchange Rates
• If the identical product or service can be:
– Sold in two different markets (perfect substitutability of
goods and services)
– No restrictions exist on the sale (free trade)
– No transportation costs of moving the product between
markets (costless transportation)
※Then the product or service prices should be the
same in both markets
• In a word, perfectly tradable goods or services are
subject to the law of one price
• A primary principle of competitively efficient
markets is that prices of identical products or services
will equalize across them if frictions or transportation
costs do not exist
7-5
Price Levels and Exchange Rates
• If the two markets are in two different countries, the
product’s price may be stated in different currency
terms
– Price comparison in different markets (countries) would
require a conversion from one currency to the other, e.g.,
P$
?
× S = P¥
where the product price in US dollars is P$, the spot exchange
rate is S (yen per US$), and the price in Japanese yen is P¥
• If these two markets are competitively efficient, i.e.,
the law of one price holds, the purchasing power
parity (PPP) exchange rate could be deduced from
the relative local product prices: S = P¥ / P$
– If the price level in the U.S. P$ ↑, then S ↓, which means that
the US$ depreciates
7-6
Price Levels and Exchange Rates
• The absolute version of the PPP theory
– By comparing the prices of identical products denominated in
different competitively efficient currencies, we could
determine the PPP exchange rate
• The hamburger standard or said the Big Mac index is
calculated regularly by The Economist since 1986
Country
U.S.
Euro area
Big Mac price in
US$
Implied PPP
exchange rate
Under (-) / over(+) valuation
(FC vs. US$) relative to the
Big Mac index
$3.57
–
–
$5.34
= €3.37×$1.5846/€
$1.0593/€
=$3.57/€3.37
+49.58%
=($1.5846/€ - $1.0593/€) /
$1.0593/€
※ A Big Mac in the Euro area cost €2.92, and the actual exchange rate is $1.5846/€
※ An alternative to the hamburger standard is the “Starbucks tall-latte index”
introduced by The Economist in 2004
7-7
Price Levels and Exchange Rates
• Why is the Big Mac a good candidate for the
application of the law of one price?
– The product is nearly identical in each market
– The product is a result of predominantly local materials and
input costs, i.e., its price in each country represents domestic
costs and prices rather than imported ones
• Only a price of single product is not objective enough
to decide the exchange rate
– Replacing the price of a single product with a price index of
a basket of goods, the absolute PPP exchange rate between
two countries can be stated as
S = PI¥ / PI$
7-8
Price Levels and Exchange Rates
• Based on the absolute version of the PPP theory, we
can derive relative purchasing power parity (RPPP)
• RPPP is not particularly helpful in determining what
the spot exchange rate 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
• More specifically, the spot exchange rate should change
in an equal amount but in the opposite direction to the
difference in inflation rates between two countries
– Thus, the currency with higher (lower) inflation rate will
depreciate (appreciate)
7-9
Price Levels and Exchange Rates
• Given the exchange rate St = Pt¥ / Pt$ (yen per US$) at
time t,
Pt¥(1   ¥)
(1   ¥)
 St+1  $
 St
$
Pt (1   )
(1   $ )
• For the indirection quotation of Japanese ¥ for the U.S., the
change of the exchange rate is as follows (see Slide 6-37)
St  St+1
St+1

(1   ¥)
St  St
(1   $ ) (1   $ )  (1   ¥)


(1   ¥)
1  ¥
St
(1   $ )
St  St+1
 (1   $ )  (1   ¥)   $   ¥
St+1
+: FC appreciates against DC
–: FC depreciates against DC
※ If π¥ is smaller than π$ (the U.S. is with a higher inflation rate), St+1 is smaller than
St, which indicates the appreciation of Japanese ¥ (depreciation of US$)
※ Furthermore, the percentage change of the PPP exchange rate is proportional to
7-10
the difference of the inflation rate (see Exhibit 7.2 on the next slide)
Exhibit 7.2 Relative Purchasing
Power Parity (RPPP)
※ For instance, point P represents an equilibrium point where the inflation rate in
the foreign country, Japan, is 4% lower than that in the home country, the U.S.
※ Therefore, RPPP would predict that the Japanese yen would appreciate by 4% per
annum with respect to the U.S. dollars
※ If the domestic country is with a higher inflation rate  prices of domestic
products become relatively expensive  export ↓, import ↑  deficit on current
account (and on BOP)  supply of domestic currency > demand of domestic
currency  domestic currency depreciates
1-11
Price Levels 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
• Possible reasons for the poor performance of PPP
– Transportation costs of goods and services are not zero
– Many services are not tradable, e.g., legal services
– Many goods and services are not of the same quality across
countries, reflecting different tastes of consumers in
different countries
– Different tax rules in different countries
7-12
Price Levels and Exchange Rates
• Two general conclusions from these studies:
– PPP or RPPP hold 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
• A higher inflation rate generates a strong enough pressure to
affect the currency to depreciate
• For countries with underdeveloped capital markets, the effect
of the current account dominates BOP (comparing to the
financial and capital accounts), so there is a closer relationship
between price levels and exchange rates
7-13
Nominal and Real Exchange Rates
• According to the RPPP, the change of the (nominal)
exchange rate is to offset the change in the
differential growths of price levels between two
countries
– For the country with a higher inflation rate, the prices of
products increase inside the country, but due to the
depreciation of the currency of that country, the prices of
products in foreign currency remain the same
• So, the change of the nominal exchange rate will not
affect the relatively competitive power for different
countries
• Only the change of the real exchange rate, which
measures the purchasing power of a currency, will
affect the price competitiveness of a country
7-14
Nominal and Real Exchange Rates
• The real exchange rate is defined as follows
SR,t = SN,t 
Pf,t
Pd,t
– SR,t: real exchange rate at time t
– SN,t: nominal exchange rate at time t (1 foreign dollar = SN,t
domestic dollars)
– Pf,t: foreign price level at time t relative to the base period at
time 0 (Pf,0=100)
– Pd,t: domestic price level at time t relative to the base period
at time 0 (Pd,0=100)
※ If RPPP holds, the magnitude of the increase of the foreign
price level (Pf,t ↑) and the magnitude of the depreciation of
the foreign currency (SN,t ↓) will be the same and offset for
each other, so the real exchange rate will not change
7-15
Nominal and Real Effective
Exchange Rate Indices
• Individual national currencies often need to be
evaluated against all 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 and the real
effective exchange rate index
7-16
Nominal and Real Effective
Exchange Rate Indices
• Nominal effective exchange rate index (NEERI) uses
nominal exchange rates to create an index, on a
weighted average basis, of the value of the main
trading currencies over a period of time, which is
defined as follows
n
(1/SN,i,t )
i=1
(1/SN,i,0 )
NEERI t = Wi  (
100)
– n: number of major trading currencies for the domestic
country
– Wi: weight of a foreign currency, depending on the trading
volume between the domestic country and that foreign
country
– SN,i,t: nominal exchange rates for the i-th foreign currency at
time t (1/SN,i,t measures the domestic currency value in terms
of foreign currencies)
7-17
Nominal and Real Effective
Exchange Rate Indices
• Example to calculate NEERI for NT$ against the US$
and Japanese yen (Year 2000 is the base period)
SN,i,2000
SN,i,2008
Trading volume
U.S. (i=1)
1US$=30NT$
1US$=32NT$
NT$ 600 billion
Japan (i=2)
1¥=0.25NT$
1¥=0.2NT$
NT$ 400 billion
NEERI2000 =W1  (
(1/SN,1,2000 )
(1/SN,1,2000 )
100)  W2  (
(1/SN,2,2000 )
(1/SN,2,2000 )
100)
(1/30)
(1/0.25)
100)  0.4  (
100)  100
(1/30)
(1/0.25)
(1/SN,1,2008 )
(1/SN,2,2008 )
NEERI2008 =W1  (
100)  W2  (
100)
(1/SN,1,2000 )
(1/SN,2,2000 )
 0.6  (
 0.6  (
(1/32)
(1/0.2)
100)  0.4  (
100)  106.25
(1/30)
(1/0.25)
※ From 2000 to 2008, NT$ depreciates against US$ (by 6.3%) and appreciates
against Japanese ¥ (by 25%)
※ From the analysis of NEERI, overall speaking, the nominal exchange rate of
NT$ appreciates by 6.25% against the US$ and Japanese ¥
7-18
Nominal and Real Effective
Exchange Rate Indices
• Real effective exchange rate index (REERI) indicates
how the weighted average purchasing power of the
domestic currency has changed relative to some
arbitrarily selected base period, which is defined as
follows
n
(1/SR,i,t )
i=1
(1/SR,i,0 )
REERI t = Wi  (
100)
– SR,i,t: real exchange rates for the i-th foreign currency at time t
7-19
Nominal and Real Effective
Exchange Rate Indices
• Example to calculate REERI for NT$ against the US$
and Japanese yen (Year 2000 is the base period)
U.S. (i=1)
SN,i,2000
SN,i,2008
Price level
in 2000
Price level
in 2008
Trading volume
1US$=30NT$
1US$=32NT$
100
125
NT$ 600 billion
1¥=0.2NT$
100
95
NT$ 400 billion
100
110
Japan (i=2) 1¥=0.25NT$
Taiwan
SR,1,2000 = SN,1,2000 
SR,2,2000 =SN,2,2000 
Pd,2000
Pf,2,2000
Pd,2000
SR,1,2008 = SN,1,2008 
SR,2,2008 =SN,2,2008 
Pf,1,2000
Pf,1,2008
Pd,2008
Pf,2,2008
Pd,2008
=30 
100
 30
100
=0.25 
=32 
100
 0.25
100
125
 36.3636
110
=0.20 
95
 0.1727
110
Pf,t

 SR,t = SN,t 
Pd,t

 on Slide7-15






7-20
Nominal and Real Effective
Exchange Rate Indices
REERI2000 =W1  (
(1/SR,1,2000 )
(1/SR,1,2000 )
100)  W2  (
(1/SR,2,2000 )
(1/SR,2,2000 )
100)
(1/30)
(1/0.25)
100)  0.4  (
100)  100
(1/30)
(1/0.25)
(1/SR,1,2008 )
(1/SR,2,2008 )
REERI 2008 =W1  (
100)  W2  (
100)
(1/SR,1,2000 )
(1/SR,2,2000 )
 0.6  (
 0.6  (
(1/36.3636)
(1/0.1727)
100)  0.4  (
100)  107.40
(1/30)
(1/0.25)
※ Overall speaking, the real exchange rate of NT$ appreciates by 7.40% against
the US$ and Japanese ¥
※ In other words, the purchasing power of NT$ increases by 7.40% against the
US$ and Japanese ¥ from 2000 to 2008
7-21
Nominal and Real Effective
Exchange Rate Indices
• The meaning of real effective exchange rate index
(REERI):
– REERIt > REERI0: Real exchange rate of the domestic
currency against foreign currencies appreciates relative to
the base period, so the competitive power of domestic
products decreases relative to the base period
– REERIt < REERI0: Real exchange rate of the domestic
currency against foreign currencies depreciates relative to
the base period, so the competitive power of domestic
products increases relative to the base period
7-22
Exhibit 7.3 Real Effective Exchange Rate Indexes
for Some Selected Currencies (Y2000 = 100)
※ From 1981 to 1995, the real exchange rate of Japanese ¥ against foreign currencies
appreciates, so the competitive power of the Japanese products declines
※ From 1995 to 2008, the real exchange rate of Japanese ¥ against foreign currencies
depreciates generally, so the competitive power of the Japanese products increases
※ If the RPPP is true for the long term, i.e., the real exchange rate remains stable due
to the offset of the effects of the changes in nominal exchange rates and inflation
rates, the REERI should fluctuate around 100
7-23
Exchange Rate Pass-Through
• The degree to which the prices of imported and
exported goods change as a result of exchange rate
changes is termed exchange rate pass-through
• Although PPP implies that all exchange rate changes
are passed through by equivalent changes in prices to
trading partners, empirical researches 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 absorb the
impact of exchange rate changes
7-24
Exchange Rate Pass-Through
※The reason for absorption is trying not to affect the selling volume too much
※The absorption could result from reducing profit margins, cost reductions, or both
※Cost reductions arises from the lower imported price for components and raw
materials to Germany when the euro appreciates
7-25
Interest Rates and
Exchange Rates
7-26
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
• Because investors concern about the real returns (i.e.,
the growth of their purchasing power), we would
expect that as inflation increases, investors will
demand higher nominal rates of returns on their
investment
• The nominal interest rate is derived from (1+r) × (1+
π) – 1, and can be reduced to:
i = r + π + rπ  r + π
where i = nominal interest rate, r = real interest rate,
and π = expected inflation
7-27
Interest Rates and Exchange Rates
• Because of the arbitrage investment activities among
countries, the real interest rates were to be held
constant among countries, e.g., if the r$ is larger
than the r¥, the capital will flow from Japan to the U.S.
continuously until the r$ equals the r¥
• So, according to the Fisher effect, the nominal interest
rate and the inflation rate have to be adjusted on a
one-for-one basis
• Empirical tests using ex post national inflation rates
and the nominal rates of return of fixed-income
securities have shown the Fisher effect usually exists
for short-maturity government securities (see the next
slide)
7-28
Interest Rates and Exchange Rates
※ According to the above figure, it is obvious that investors indeed require higher
nominal risk-free rates (T-bill rates) with the increase of higher inflation rates
※However, studies about longer-term government bonds and private sector bonds do
not support the Fisher effect
7-29
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 found 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
– The opposite direction means for a country with lower
(higher) interest rates, its currency will appreciate
(depreciate)
7-30
Interest Rates and Exchange Rates
• The equation of the international Fisher effect:
$) – (1+i¥)
St  St+1
i$ – i¥
(1+i
$ – i¥



i
St+1
1 + i¥
1 + i¥
where i$ and i¥ are the respective nominal interest
rates of the investing period, and St and St+1 are the
spot exchange rates using indirect quotes at the
beginning and the end of that period (¥/$) (if St+1 < St,
it means that the Japanese ¥ appreciates)
• According to the above equation, the currency with
lower interest rate will appreciate
– If i$ =6% and i¥ =4%, St+1 is expected to be smaller than St
by 2%, which means that the Japanese ¥ should appreciate
about 2% per year
7-31
Interest Rates and Exchange Rates
• The unrestricted capital flows will see the
opportunity around the world and make the
international Fisher effect to be true
• For example, if i$ =6% and i¥ =5%, and the
Japanese ¥ is expected to appreciate 2%, the
unrestricted capital will flow from the U.S. to Japan
to earn 7% (=5% + 2%) return. This activity will
increase the money supply in the Japanese
economy and thus reduce the i¥ until it becomes 4%
(thus the international Fisher effect holds again)
7-32
Interest Rates and Exchange Rates
• The international Fisher effect (on Slide 7-31) vs.
the Relative Purchase Power Parity (RPPP) (on
Slide 7-10)
St  St+1 $ ¥
 i  i  (r $   $ )  (r ¥   ¥ )
St+1
  $  ¥
By force of the international arbitrage,
real rates of return between markets
should be equal, i.e., r$=r¥
※ The international Fisher effect and the RPPP is consistent if the Fisher effect
is valid
※ The only difference is that in the international Fisher effect, the interest rate,
i, is applied to a future time period and thus the inflation rate, π, is the
expected inflation rate
※ In the RPPP, however, the inflation rate, π, is ex post, i.e., only at the end of
the period, the inflation rate for that period is known, and thus the exchange
rate should change in response to the realized inflation rate
7-33
Interest Rates and Exchange Rates
• A forward (exchange) rate is an exchange rate
quoted today for settlement at some future date
• A forward exchange agreement between currencies
states the exchange rate at which a foreign currency
will be bought forward or sold forward on a
specific date in the future
• As to the theoretical value for the forward
exchange rate of any specific maturity, it is
calculated by adjusting the current spot exchange
rate by the ratio of interest rates of the same
maturity for the two currencies (see the equation on
the next slide)
7-34
Interest Rates and Exchange Rates
• For example, the 90-day forward rate for the Swiss
franc/US dollar exchange rate (F90SF/$ ) is found by
multiplying the current spot rate ( SSF/$) by the ratio of
the 90-day Swiss franc deposit rate (iSF) over the 90day dollar deposit rate (i$)
• The formula for the forward exchange rate (Exhibit 7.6):
F90SF/$
90 

1   iSF 

360 

SF/$
S 
(indirect quotation for the U.S.)
 $ 90 
1  i 

360 



 $ 90 
1  i 



360


$/SF
$/SF
 F90  S 
(direct quotation for the U.S.) 
 SF 90 


1

i





360 



7-35
Exhibit 7.6 Interest Rate Parity (IRP)
Start
$1,000,000
i $ = 8.00 % per annum
(2.00 % for 90 days)
x 1.02
End
$1,020,000
Dollar money market
S = SF1.4800/$
90 days
F90 is derived to be SF1.4655/$
Swiss franc money market
SF 1,480,000
x 1.01
SF 1,494,800
i SF = 4.00 % per annum
(1.00 % for 90 days)
 
90 
  SF 90  1
SF/$
P  1   i$ 

P

S

1  i 

  SF/$

360 
360  F90
 
 
※ Later, I will show that if F90 deviates from SF1.4655/$, it is possible to design
an arbitrage strategy (covered interest arbitrage) to make profit for sure
7-36
Interest Rates and Exchange Rates
• The theory of Interest Rate Parity (IRP) provides
the link between the foreign exchange markets and
the international money markets
• The theory states that the difference in the national
interest rates should be equal to, but opposite in sign
to, the forward rate premium or discount for the
foreign currency, except for transaction costs
– In the example on the previous slide, the difference between
iSF and i$ is –4% per annum
– The forward premium for the Swiss Franc against the US$
is +3.96% (+4%) per annum (see the next slide)
※ The above opposite but the-same-magnitude numbers
demonstrate the theory of the interest rate parity
※For the currency with the lower interest rate (SF in the
above example), its forward exchange rate is at a premium,
which implies a pressure to appreciate for that currency
7-37
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
Spot  Forward 360

100%
Forward
n days
SF1.4800 / $  SF1.4655/$ 360


100%  3.96% per annum
SF1.4655/$
90
f SF 
– This is the case when the indirect quotation of the Swiss
Franc for the U.S., SF/$, is used
– Please refer to Slide 6-36 for the calculation of forward
premium or discount for the direct or the indirect
quotations
7-38
Interest Rates and Exchange Rates
• The spot and forward exchange rates are determined
by the demand and the supply and are not constantly
in the state of equilibrium described by the interest
rate parity (IRP)
– 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 arbitrage strategy is known as covered interest
arbitrage (CIA) (see the example on Exhibit 7.7)
– So, the relation between the spot exchange rate and the
forward exchange cannot derivate from the IRP too much
7-39
Exhibit 7.7 Covered Interest
Arbitrage (CIA)
Steps at the beginning of the period:
1. Borrow $1,000,000
2. Convert it into ¥106,000,000 at the spot exchange rate and deposit the proceeds in
yen money market to earn 4% return per annum
3. Sell the forward of ¥108,120,000 for dollars at the 180-day forward exchange rate
of ¥103.50/$
1-40
Interest Rates and Exchange Rates
• Until the IRP holds again, the arbitrage strategy will
–
–
–
–
Increase the dollar interest rate
Japanese ¥ appreciates (lower S)
Lower the yen interest rate
Due to the continuous selling yen forward, and thus yen is
inclined to depreciate after 180 days (increase F180)
※It is obvious that the arbitrage opportunity becomes thinner
and thinner
• Arbitrage rule of thumb
– If the difference in interest rates is greater (less) than the
forward premium, borrow the lower (higher) interest rate
currency and invest in the higher (lower) interest rate currency
※For example, in the above case, the forward premium is
4.8309%, which is larger than the difference in interest rates
(4%), so borrow US$ and invest in Japanese ¥
7-41
Interest Rates and Exchange Rates
• A deviation from covered interest arbitrage is
uncovered interest arbitrage (UIA)
• In this case, investors borrow in currencies exhibiting
relatively low interest rates and convert the proceeds
into currencies that offer much higher interest rates
(to earn the interest rate spread)
• 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
– According to the international Fisher effect, however, the
higher yield currency is inclined to depreciate
7-42
Exhibit 7.8 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 US$ were to depreciate
versus the Japanese ¥ over that period, the UIA strategy may result in significant loss1-43
Spot Exchange Rates and
Forward Exchange Rates
5-44
Spot Exchange Rates and Forward
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
spot exchange rates in the future is centered on the
forward exchange rate
• Unbiased prediction simply means that the forward
exchange rate will, on average, overestimate and
underestimate the actual future spot exchange rate in
equal frequency and degree
• In fact, however, the forward rate usually does not
equal the future spot rate
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Exhibit 7.10 Forward Exchange Rate as an
Unbiased Predictor for Future Spot Exchange Rate
Exchange rate
t1
t2
t3
t4
F2,3
S2
S1
Error
Error
F1,2
F3,4
Error
S3
S4
t1
t2
t3
t4
Time
※The forward exchange rate (Ft,t+1), which is decided at time t for delivery at future time
t+1, is used as a “predictor” of the future spot exchange rate at the future time point t+1.
Therefore, the forecast spot exchange rate for time t2 is F1,2; the actual spot exchange
rate turns out to be S2. The vertical distance between the prediction and the actual spot
exchange rate is the forecast error
※When the forward exchange rate is termed an “unbiased predictor of the future spot
exchange rate,” it just means that the forward rate over- or under-estimates the future
spot exchange rate with relatively equal frequency and amount. It therefore “misses the
1-46
mark” in a regular and orderly manner, but the sum of the errors equals zero
Spot Exchange Rates and Forward
Exchange Rates
• Empirical studies, based on the long-term data,
analyze the foreign exchange markets and suggest
that the forward exchange rate is NOT an unbiased
predictor of the future spot exchange rate
• Furthermore, the existence and success of foreign
exchange forecasting services in the real world imply
that managers are willing to pay a price for forecast
information even though they can use the forward
exchange rate as a forecast at no cost
• The above fact further proves that it is difficult to
predict future spot exchange rate using only the
information of the forward exchange rate
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Summary
5-48
Exhibit 7.11 International Parity Conditions in
Equilibrium (Approximate Form)
※ The forecasted inflation rates for Japan and the U.S. are 1% and 5%, respectively
※ The nominal interest rates for Japan and the U.S. are 4% and 8%, respectively
※ The spot exchange rate, S1, is ¥104/$, one-year forward exchange rate is ¥100/$, and the
expected change of the spot exchange rate is 4% (yen strengthens)
Forward exchange
rateas 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 %
(less in Japan)
Relative
purchasing
power
parity
(A)
Forecast difference
in rates of inflation
–4 %
(less in Japan)
Fisher
effect
(B)
1-49
Interest Rates
and Exchange Rates
• Relation (A) (RPPP): the currency with lower inflation
rate will appreciate, and the magnitude of the difference
of inflation rates (–4%) and the change of the spot
exchange rate are the same (4%)
• Relation (B) (Fisher effect): the real interest rates were
to be held constant among countries, and the nominal
interest rate and the inflation rate have to be adjusted on
a one-for-one basis
– For both the U.S. and Japan, the real interest rates are 3%, and
the difference of nominal interest rates (8% –4%=4%) results
from the difference of inflation rates (5% –1%=4%)
• Relation (C) (International Fisher effect): spot exchange
rate should change (+4%) in an equal amount but in the
opposite direction to the difference in interest rates (–4%)
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Interest Rates
and Exchange Rates
• Relation (D) (IRP): for the currency with the lower
interest rate, its forward exchange rate is at a
premium, and the magnitude of the difference of
interest rates (–4%) and the forward premium on
foreign currency (4%) are the same
• Relation (E) (Forward rate as an unbiased predictor):
the one-year forward rate on the Japanese yen, ¥100/$,
which is an unbiased predictor of the future spot
exchange rate
– The market expects that the Japanese yen will strengthen by
4%, which is approximately from the current exchange rate
¥104/$ to the forward exchange rate ¥100/$
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