INTERNATIONAL
FINANCIAL
MANAGEMENT
Fourth Edition
EUN / RESNICK
6-0
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
International Parity
Relationships & Forecasting
Chapter Six
Foreign Exchange Rates
INTERNATIONAL
FINANCIAL
Chapter Objective:
MANAGEMENT
6
This chapter examines several key international
parity relationships, such as interest rate parity and
Fourth Edition
purchasing power parity.
EUN / RESNICK
6-1
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
Interest Rate Parity
 Covered Interest

PowerArbitrage
Parity
 Purchasing

and
Exchange
Determination
 IRP
PPP
Deviations
andRate
the Real
Exchange Rate

Fisher
Effects
 The

for
Deviations
from
IRP
 Reasons
Evidence
on
Purchasing
Power
Parity

 Forecasting Exchange Rates

Power
Parity
 Purchasing
The
Fisher
Effects
 Efficient Market Approach

Fisher Effects
 The
Forecasting
Exchange
 Fundamental
ApproachRates
 Forecasting
Exchange Rates
 Technical Approach



6-2
Performance of the Forecasters
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Interest Rate Parity




Interest Rate Parity Defined
Covered Interest Arbitrage
Interest Rate Parity & Exchange Rate
Determination
Reasons for Deviations from Interest Rate Parity
6-3
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Interest Rate Parity Defined



IRP is an arbitrage condition.
If IRP did not hold, then it would be possible for
an astute trader to make unlimited amounts of
money exploiting the arbitrage opportunity.
Since we don’t typically observe persistent
arbitrage conditions, we can safely assume that
IRP holds.
6-4
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Interest Rate Parity Carefully Defined
Consider alternative one year investments for $100,000:
1.
Invest in the U.S. at i$. Future value = $100,000 × (1 + i$)
Trade your $ for £ at the spot rate, invest $100,000/S$/£ in
Britain at i£ while eliminating any exchange rate risk by
selling the future value of the British investment forward.
2.
F$/£
Future value = $100,000(1 + i£)×
S$/£
Since these investments have the same risk, they must have
the same future value (otherwise an arbitrage would exist)
F$/£
(1 + i£) ×
= (1 + i$)
S$/£
6-5
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Alternative 2:
Send your $ on a
round trip to
Britain
$1,000
S$/£
Step 2:
Invest those
pounds at i£
Future Value =
$1,000
Step 3: repatriate
future value to the
U.S.A.
Alternative 1:
invest $1,000 at i$
IRP
$1,000
 (1+ i£)
S$/£
IRP
$1,000
 (1+ i£) × F$/£
$1,000×(1 + i$) =
S$/£
Since both of these investments have the same risk, they must
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Companies,
Inc. All rights
reserved.
have6-6the same future value—otherwise
an arbitrage
would
exist
Interest Rate Parity Defined

The scale of the project is unimportant
$1,000
 (1+ i£) × F$/£
$1,000×(1 + i$) =
S$/£
F$/£
× (1+ i£)
(1 + i$) =
S$/£
6-7
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Interest Rate Parity Defined
Formally,
1 + i$
F$/¥
=
1 + i¥
S$/¥
IRP is sometimes approximated as
i$ – i ¥ ≈ F – S
S
6-8
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Forward Premium



It’s just the interest rate differential implied by
forward premium or discount.
For example, suppose the € is appreciating from
S($/€) = 1.25 to F180($/€) = 1.30
The forward premium is given by:
f180,€v$
6-9
F180($/€) – S($/€) 360 $1.30 – $1.25
=
× 180 =
× 2 = 0.08
S($/€)
$1.25
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Interest Rate Parity Carefully Defined

Depending upon how you quote the exchange rate
($ per ¥ or ¥ per $) we have:
1 + i¥
F¥/$
=
1 + i$
S¥/$
or
1 + i$
F$/¥
=
1 + i¥
S$/¥
…so be a bit careful about that
6-10
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
IRP and Covered Interest Arbitrage
If IRP failed to hold, an arbitrage would exist. It’s
easiest to see this in the form of an example.
Consider the following set of foreign and domestic
interest rates and spot and forward exchange rates.
Spot exchange rate
360-day forward rate
6-11
S($/£) = $1.25/£
F360($/£) = $1.20/£
U.S. discount rate
i$ = 7.10%
British discount rate
i£ =
11.56%
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IRP and Covered Interest Arbitrage
A trader with $1,000 could invest in the U.S. at 7.1%, in one
year his investment will be worth
$1,071 = $1,000  (1+ i$) = $1,000  (1,071)
Alternatively, this trader could
1.
Exchange $1,000 for £800 at the prevailing spot rate,
2.
Invest £800 for one year at i£ = 11,56%; earn £892,48.
3.
Translate £892,48 back into dollars at the forward rate
F360($/£) = $1,20/£, the £892,48 will be exactly $1,071.
6-12
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Alternative 2:
Arbitrage I
buy pounds
£800
£1
£800 = $1,000×
$1.25
$1,000
Alternative 1:
invest $1,000
at 7.1%
FV = $1,071
6-13
Step 2:
Invest £800 at
i£ = 11.56%
£892.48 In one year £800
will be worth
Step 3: repatriate
£892.48 =
to the U.S.A. at
£800 (1+ i£)
F360($/£) =
$1.20/£
$1,071
F£(360)
$1,071 = £892.48 ×
£1
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Interest Rate Parity
& Exchange Rate Determination
According to IRP only one 360-day forward rate,
F360($/£), can exist. It must be the case that
F360($/£) = $1.20/£
Why?
If F360($/£)  $1.20/£, an astute trader could make
money with one of the following strategies:
6-14
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Arbitrage Strategy I
If F360($/£) > $1.20/£
i. Borrow $1,000 at t = 0 at i$ = 7.1%.
ii. Exchange $1,000 for £800 at the prevailing spot
rate, (note that £800 = $1,000÷$1.25/£) invest
£800 at 11.56% (i£) for one year to achieve
£892.48
iii. Translate £892.48 back into dollars, if
F360($/£) > $1.20/£, then £892.48 will be more
than enough to repay your debt of $1,071.
6-15
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Step 2:
buy pounds
Arbitrage I
£800
£1
£800 = $1,000×
$1.25
$1,000
Step 1:
borrow $1,000
Step 5: Repay
your dollar loan
with $1,071.
Step 3:
Invest £800 at
i£ = 11.56%
£892.48 In one year £800
will be worth
£892.48 =
£800 (1+ i£)
Step 4: repatriate
to the U.S.A.
More
than $1,071
F£(360)
$1,071 < £892.48 ×
£1
If F£(360) > $1.20/£ , £892.48 will be more than enough to repay
your dollar obligationCopyright
of $1,071.
excess isCompanies,
your profit.
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Inc. All rights reserved.
6-16
Arbitrage Strategy II
If F360($/£) < $1.20/£
i. Borrow £800 at t = 0 at i£= 11.56% .
ii. Exchange £800 for $1,000 at the prevailing spot
rate, invest $1,000 at 7.1% for one year to
achieve $1,071.
iii. Translate $1,071 back into pounds, if
F360($/£) < $1.20/£, then $1,071 will be more
than enough to repay your debt of £892.48.
6-17
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Step 2:
buy dollars
$1.25
$1,000 = £800×
£1
Arbitrage II
£800
Step 1:
borrow £800
$1,000
Step 5: Repay
More
Step 3:
your pound loan
than
Invest $1,000
with £892.48 .
£892.48
at i$
Step 4:
repatriate to
the U.K.
In one year $1,000
F£(360)
will be worth
$1,071 > £892.48 ×
$1,071
£1
If F£(360) < $1.20/£ , $1,071 will be more than enough to repay
your dollar obligationCopyright
of £892.48.
Keep
the rest
as profit.
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Inc. All rights reserved.
6-18
IRP and Hedging Currency Risk
You are a U.S. importer of British woolens and have just ordered next
year’s inventory. Payment of £100M is due in one year.
Spot exchange rate
360-day forward rate
S($/£) = $1.25/£
F360($/£) = $1.20/£
U.S. discount rate
i$ = 7.10%
British discount rate
i£ =
11.56%
IRP implies that there are two ways that you fix the cash outflow to a
certain U.S. dollar amount:
a) Put yourself in a position that delivers £100M in one year—a long
forward contract on the pound.
You will pay (£100M)(1.2/£) = $120M in one year.
b) Form a forward market hedge as shown below.
6-19
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IRP and a Forward Market Hedge
To form a forward market hedge:
Borrow $112.05 million in the U.S. (in one year you
will owe $120 million).
Translate $112.05 million into pounds at the spot
rate S($/£) = $1.25/£ to receive £89.64 million.
Invest £89.64 million in the UK at i£ = 11.56% for
one year.
In one year your investment will be worth £100
million—exactly enough to pay your supplier.
6-20
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Forward Market Hedge
Where do the numbers come from? We owe our supplier
£100 million in one year—so we know that we need to
have an investment with a future value of £100 million.
Since i£ = 11.56% we need to invest £89.64 million at the
start of the year.
£100
£89.64 =
1.1156
How many dollars will it take to acquire £89.64 million at
the start of the year if S($/£) = $1.25/£?
$1.00
$112.05 = £89.64 ×
£1.25
6-21
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Reasons for Deviations from IRP

Transactions Costs




The interest rate available to an arbitrageur for
borrowing, ib,may exceed the rate he can lend at, il.
There may be bid-ask spreads to overcome, Fb/Sa < F/S
Thus
(Fb/Sa)(1 + i¥l)  (1 + i¥ b)  0
Capital Controls

6-22
Governments sometimes restrict import and export of
money through taxes or outright bans.
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Transactions Costs Example

Will an arbitrageur facing the following prices be
able to make money?
1 + i$
F$/ €
Borrowing
Lending
=
1 + i€
S$/ €
$
5%
4.50%
€
6%
5.50%
Bid
Ask
Spot
$1.00=€1.00 $1,01=€1,00
Forward $0.99=€1.00 $1.00=€1.00
6-23
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






Try borrowing $1.000 at 5%:
Trade for € at the ask spot rate $1.01 = €1.00
Invest €990.10 at 5.5%
Hedge this with a forward contract on
€1,044.55 at $0.99 = €1.00
Receive $1.034.11
Owe $1,050 on your dollar-based borrowing
Suffer loss of $15.89
6-24
Now try this backwards
Transactions Costs Example
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Purchasing Power Parity



Purchasing Power Parity and Exchange Rate
Determination
PPP Deviations and the Real Exchange Rate
Evidence on PPP
6-25
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Purchasing Power Parity and
Exchange Rate Determination
The exchange rate between two currencies should
equal the ratio of the countries’ price levels:
P$
S($/£) =
P£

For example, if an ounce of gold costs $300 in
the U.S. and £150 in the U.K., then the price of
one pound in terms of dollars should be:
P$ $300
S($/£) =
=
= $2/£
P£ £150

6-26
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Purchasing Power Parity and
Exchange Rate Determination



Suppose the spot exchange rate is $1.25 = €1.00
If the inflation rate in the U.S. is expected to be
3% in the next year and 5% in the euro zone,
Then the expected exchange rate in one year
should be $1.25×(1.03) = €1.00×(1.05)
F($/€) = $1.25×(1.03) = $1.23
€1.00×(1.05)
€1.00
6-27
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Purchasing Power Parity and
Exchange Rate Determination

The euro will trade at a 1.90% discount in the forward
market:
F($/€)
=
S($/€)
$1.25×(1.03)
€1.00×(1.05)
$1.25
€1.00
1.03
1 + $
=
=
1.05
1 + €
Relative PPP states that the rate of change in the
exchange rate is equal to differences in the rates of
inflation—roughly 2%
6-28
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Purchasing Power Parity
and Interest Rate Parity

Notice that our two big equations today equal each
other:
PPP
IRP
F($/€)
1 + $
=
S($/€)
1 + €
1 + i$
F($/€)
=
1 + i€
S($/€)
6-29
=
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Expected Rate of Change in Exchange
Rate as Inflation Differential

We could also reformulate
our equations as inflation or
interest rate differentials:
F($/€)
1 + $
=
S($/€)
1 + €
F($/€) – S($/€)
1 + $
1 + $ 1 + €
=
–1=
–
S($/€)
1 + €
1 + € 1 + €
F($/€) – S($/€)
$ – €
E(e) =
≈ $ – €
=
S($/€)
1 + €
6-30
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Expected Rate of Change in Exchange
Rate as Interest Rate Differential
E(e) =
6-31
F($/€) – S($/€)
=
S($/€)
i$ – i€
1 + i€
≈ i$ – i€
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Quick and Dirty Short Cut

Given the difficulty in measuring expected
inflation, managers often use
$ – € ≈ i$ – i€
6-32
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Evidence on PPP

PPP probably doesn’t hold precisely in the real
world for a variety of reasons.




Haircuts cost 10 times as much in the developed world
as in the developing world.
Film, on the other hand, is a highly standardized
commodity that is actively traded across borders.
Shipping costs, as well as tariffs and quotas can lead to
deviations from PPP.
PPP-determined exchange rates still provide a
valuable benchmark.
6-33
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Approximate Equilibrium Exchange
Rate Relationships
E(e)
≈ IFE
(i$ – i¥)
≈ FEP
≈ PPP
F–S
≈ IRP
S
≈ FE
≈ FRPPP
E($ – £)
6-34
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The Exact Fisher Effects
An increase (decrease) in the expected rate of inflation
will cause a proportionate increase (decrease) in the
interest rate in the country.
 For the U.S., the Fisher effect is written as:
1 + i$ = (1 + $ ) × E(1 + $)
Where
$ is the equilibrium expected “real” U.S. interest rate
E($) is the expected rate of U.S. inflation
i$ is the equilibrium expected nominal U.S. interest rate

6-35
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International Fisher Effect
If the Fisher effect holds in the U.S.
1 + i$ = (1 + $ ) × E(1 + $)
and the Fisher effect holds in Japan,
1 + i¥ = (1 + ¥ ) × E(1 + ¥)
and if the real rates are the same in each country
$ = ¥
then we get the
E(1 + ¥)
1 + i¥
International Fisher Effect: 1 + i = E(1 +  )
6-36
$
$
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International Fisher Effect
If the International Fisher Effect holds,
E(1 + ¥)
1 + i¥
=
1 + i$
E(1 + $)
and if IRP also holds
1 + i¥
F¥/$
=
1 + i$
S¥/$
F¥/$
E(1 + ¥)
then forward rate PPP holds:
=
S¥/$
E(1 + $)
6-37
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Exact Equilibrium Exchange Rate
Relationships
E (S ¥ / $ )
S¥ /$
IFE
1 + i¥
1 + i$
FEP
PPP
F¥ / $
S¥ /$
IRP
FE
FRPPP
E(1 + ¥)
E(1 + $)
6-38
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Forecasting Exchange Rates




Efficient Markets Approach
Fundamental Approach
Technical Approach
Performance of the Forecasters
6-39
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Efficient Markets Approach



Financial Markets are efficient if prices reflect all
available and relevant information.
If this is so, exchange rates will only change when
new information arrives, thus:
St = E[St+1]
and
Ft = E[St+1| It]
Predicting exchange rates using the efficient
markets approach is affordable and is hard to beat.
6-40
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Fundamental Approach

Involves econometrics to develop models that use
a variety of explanatory variables. This involves
three steps:




step 1: Estimate the structural model.
step 2: Estimate future parameter values.
step 3: Use the model to develop forecasts.
The downside is that fundamental models do not
work any better than the forward rate model or
the random walk model.
6-41
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Technical Approach



Technical analysis looks for patterns in the past
behavior of exchange rates.
Clearly it is based upon the premise that history
repeats itself.
Thus it is at odds with the EMH
6-42
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Performance of the Forecasters



Forecasting is difficult, especially with regard to
the future.
As a whole, forecasters cannot do a better job of
forecasting future exchange rates than the forward
rate.
The founder of Forbes Magazine once said:
“You can make more money selling financial
advice than following it.”
6-43
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End Chapter Six
6-44
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