Chapter 7

International Parity Conditions
ESM chapter 7 PhD in Finance
Introduction to Parity Conditions
Absolute & Relative Purchasing Power Parity
Real Exchange Rate
Fisher Effect (FE)
International Fisher Effect (IFE)
Unbiased Forward Rate (UFR)
Interest Rate Parity (IRP)
Covered Interest Arbitrage PhD in Finance
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? PhD in Finance
International Parity Conditions
 The economic theories that link exchange
rates, price levels, and interest rates together
are called international parity
 These international parity conditions form
the core of the exchange rate theory. PhD in Finance
International Parity Conditions
 The derivation of these conditions requires the
assumption of Perfect Capital Markets (PCM).
 no transaction costs
 no taxes
 complete certainty in interest rate
 NOTE – Parity Conditions are expected to hold in
the long-run, but not always in the short term.
Interest rate parity generally holds where forward
differential equals to the interest rate differential of
two currencies.
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, or trivial, 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.
That is:
P$ x S = P¥ or S= P¥ / P$
Where the product price in US dollars is (P$), the spot
exchange rate is (S) and the price in Yen is (P¥). PhD in Finance
Exhibit 7.1 Selected Rates from the
Big Mac Index
Absolute PPP theory
 Law of one price should hold for a basket of
identical goods and services in different currencies.
 By comparing the prices of identical products
denominated in different currencies, we could
determine the PPP exchange rate that should exist if
markets were efficient.
S ¥/$= ∑P¥/ ∑P$
 Note that Big Mac index is potentially misleading but fun to know. PhD in Finance
Relative purchasing power parity
 If the exchange rate between two currencies starts
in equilibrium, then, we have what is termed
Relative purchasing power parity (RPPP).
S t  S t 1
Definition of RPPP:
S t 1
D F
 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.
 Note: πD is demestic price change (inflation), πF is foreign price change. We
use sometimes P for price level changes!
 St is future spot rate. St-1 is the spot rate. PhD in Finance
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.” PhD in Finance
Exhibit 7.2 Relative Purchasing Power
Parity (RPPP)
%∆P PhD in Finance
Relative PPP Example
 Given yearly inflation rates of 5% and 10% in Australia
and the UK respectively, what is the prediction of PPP
with regards to $A/£ exchange rate?
S t  S t 1
S t 1
D F
Relative PPP
= (0.05 – 0.10)/(1 + 0.10) = - 0.045 = - 4.5%
We expect £ to trade at a discount of 4,5% at the end of 1 year.
The general implication of relative PPP is that countries with
high rates of inflation will see their currencies depreciate against
those with low rates of inflation.
Relative PPP
 Relative PPP implies that the change in the exchange rate
will offset the difference between the relative inflation of
two countries.
 The previous formula can be approximated as:
s %   D   F
where, πD and πF refers to the percentage change in domestic
and foreign price levels respectively and s % to the
percentage change in the exchange rate.
If domestic inflation > foreign inflation, PPP predicts the
domestic currency should depreciate. Ceteris paribus.
Relative Purchasing Power Parity
Applications of Relative PPP:
1. Forecasting future spot exchange rates.
2. Calculating appreciation in “real” exchange
rates. This will provide a measure of how
expensive a country’s goods have become
(relative to another country’s).
Prices and Exchange Rates
 RPPP is not accurate in predicting future exchange
 Two general conclusions can be made from empirical
 RPPP holds well over the very long run but poorly for
shorter time periods;
 the theory holds better for countries with relatively high
rates of inflation and underdeveloped capital markets. PhD in Finance
Relative Purchasing Power Parity
 Relative PPP claims that exchange rate movements
should exactly offset any inflation differential
between two countries:
S t 1
Relative PPP:
S t 1  S t
1  D
change in
domestic prices
1  F
D F
1  F
 We can also write: S
t 1
1  D
1  F
Forecasting Future Spot Rates
 Suppose the spot exchange rate and expected
inflation rates are:
S ¥/$, t0  90 ¥ / $;  U . S .  5%;  Japan  2%
What is the expected ¥/$ exchange rate if relative PPP
¥ / $, t 1
 S ¥ / S ,t 0
1  ¥
1 
 1 . 02 
 90 ¥ / $   
  87 . 43 ¥ / $
 1 . 05 
Relative Purchasing Power
 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. PhD in Finance
Exhibit 7.3 IMF’s Real Effective Exchange Rate Indexes for the
United States, Japan, and the Euro Area
Prices and Exchange Rates
 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. PhD in Finance
Prices and Exchange Rates
 Price elasticity of demand is an important
factor when determining pass-through
 The price elasticity of demand for a good is
the percentage change in quantity of the
good demanded as a result of the percentage
change in the goods price.
P PhD in Finance
Exhibit 7.4 Exchange Rate PassThrough
The Fisher Effect
 The international Fisher relation is inspired by the
domestic relation postulated by Irving Fisher (1930).
 The Fisher effect states:
1  i   1  r 1   
i  r    r
 It can be reduced to:
i  r 
the nominal interest rate is equal to a real interest rate
plus expected inflation:
The Fisher Effect
 Applied to two different countries, USA and Japan,
The Fisher Effect would be stated as:
i  r 
i¥  r¥ 
 Note that the inflation term π is expected rate of
inflation, not what inflation has been in the past.
International Fisher effect
Definition: if real interest rates r across countries are the
same, then
the percentage change in the spot exchange rate over
time is equal to the interest rates differential of the two
 Also called “Fisher-open”.
it 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. PhD in Finance
Interest Rates Parity
 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
 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. PhD in Finance
Interest Rate Parity
 Interest rate parity (IRP) is an arbitrage condition
that provides the linkage between the foreign
exchange markets and the international money
Interest Rate Parity (IRP)
Ft , t  1
1  id
1  if
where, Ft and St are the forward and spot rates and id
and if are domestic and foreign interest rates
Interest Rate Parity
 The approximate form of IRP says that the %
forward premium equals the difference in interest
Approximation of IRP
Ft , t  1
 1  id  i f
Ft , t 1  S t
 id  i f
 In general, the currency trading at a forward premium
(discount) is the one from the country with the lower
(higher) interest rate.
Interest Rates Parity
 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$). PhD in Finance
Caculating Forward Rates
 Calculation of the 90 day forward rate:
1  (i
 90/360)
1  ( i  90 / 360 )
Note, to use the same time period on both sides PhD in Finance
Interest Rates and Exchange Rates
The theory of Interest Rate Parity (IRP) provides
the linkage between the foreign exchange markets
and the international money markets.
The theory states:
 The difference in the national interest rates for
securities of similar risk and maturity (i$ -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 PhD in Finance
Exhibit 7.5 Currency Yield Curves
and the Forward Premium
isf PhD in Finance
Interest Rate Parity – An Example
 Basic idea: Two alternative ways to invest funds
over same time period should earn the same return.
Ex: Suppose the 3-month money market rate is 8% p.a.
(2% for 3-months) in the U.S. and 4% p.a. (1% for 3months) in Switzerland, and the spot exchange rate
is SFr1.48/$.
Calculate the 3 month forward rate.
 The 3-month forward rate must be SFr1.4655/$ to
prevent arbitrage opportunities (i.e., interest rate
parity must hold).
Exhibit 7.6 Interest Rate Parity
Exchange market
Exchange market
Covered interest arbitrage (CIA)
 it involves 4 steps: if IRP does not hold (check
which way to arbitrage)
 Borrow the domestic currency;
 Exchange the domestic currency for the
foreign currency in the spot market;
 Invest the foreign currency in an interestbearing instrument; and then
 Sign a forward contract to “lock in” a future exchange
rate at which to convert the foreign currency proceeds
back to the domestic currency.
Covered Interest Arbitrage: Example
 The annual interest rate in the AUS and UK are 5% and 8%
respectively. The current spot rate is $1.50/£ and the 1 year
forward rate is $1.48/£. Can arbitrage profits be made?
1  id 
Ft , t  1
 (1  i f )
1 . 05 
1 . 48
 (1 . 08 )
1 . 50
Forward pound is overvalued
1.05 ≠ 1.0656
1. Borrow $1m (at 5%)
2. Purchase £666,667 using $1m
3. Invest £ at 8% (will receive £720,000 in one year’s time)
4. Simultaneously sell £720,000 forward ($1,065,600)
5. Repay loan + interest of $1,050,000
The Example Continued
1 Borrow
at $1.50/£
for 1 year
at i$ = 5%
Profit = $15,600
Invest for 1 year
at i£ = 8%
at $1.48/£
Exhibit 7.7 Covered Interest
Arbitrage (CIA)
Covered Interest Arbitrage
 Covered interest arbitrage should continue until
interest rate parity is re-established, because the
arbitrageurs are able to earn risk-free profits by
repeating the cycle.
 But their actions nudge the foreign exchange and
money markets back toward equilibrium:
Purchase of Pounds in the spot market and sale of £ in the
forward market narrow the premium on forward pounds.
The demand for pound-denominated securities causes
pound interest rates to fall, while the higher level of
borrowing in US causes dollar interest rates to rise.
Uncovered interest arbitrage
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. PhD in Finance
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 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.
Interest Rates
and Exchange Rates
 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. PhD in Finance
Exhibit 7.9 Interest Rate Parity
(IRP) and Equilibrium
Unbiased Forward Rate (UFR)
 This hypothesis states that for the major floating
currencies, foreign exchange markets are “efficient”
and forward exchange rates are unbiased predictors
of future exchange rates.
 The unbiased forward rate (UFR) concept states
that the forward exchange rate, quoted at time t for
delivery at time t+1, is equal to the expected value of
the spot exchange rate at time t+1.
Unbiased Forward Rate (UFR)
Ft t+1 = Et[St+1]
 An unbiased predictor, however, does not mean the
future spot rate will actually be equal to what the
forward rate predicts.
 Unbiased prediction means that the forward rate
will, on average, overestimate and underestimate
the actual future spot rate in equal frequency and
Exhibit 7.10 Forward Rate as an Unbiased Predictor for Future
Spot Rate
Empirical Tests of unbiased predictor of
future spot rate
 A consensus is developing that rejects the efficient
market hypothesis.
 It appears that the forward rate is not an unbiased
predictor of the future spot rate and that
 it does pay to use resources in an attempt to forecast
exchange rates.
Ex: International Parity Conditions
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¥/$.
The Spot rate one year from now is S2
 a) Purchasing Power Parity (PPP)
S2 /S1= (1+π¥)/(1+π$)
S2=104*1,01/1,05=100¥/$ PhD in Finance
International Parity Conditions
 b) the Fisher Effect
The nominal interest rate differential =difference in
expected rate of inflation
c) International Fisher Effect
The forcasted change in spot rate =the differential
between nominal interest rates
d) Interest Rate Parity PhD in Finance
International Parity Conditions
 e) Forward rate as an unbiased predictor . This is also
called expectations theory. PhD in Finance
Exhibit 7.11 International Parity Conditions in Equilibrium (Approximate
Mini-Case Questions: Currency
Pass-Through at Porsche
 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
 In the long run, what do most automobile manufacturers
do to avoid these large exchange rate squeezes? PhD in Finance
Exhibit 1 Pass-Through Analysis for
the 911 Carrera 4S Cabriolet, 2003

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