Int Parity Relationship

8/8/2019 Int Parity Relationship

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Copyright 2007 by The McGraw-Hill Companies, Inc. All rights re6-1

INTERNATIONAL

FINANCIAL

MANAGEMENT

EUN / RESNICK

Fourth Edition


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INTERNATIONAL

FINANCIAL

MANAGEMENT

EUN / RESNICK

Fourth Edition

Chapter Objective:

This chapter examines several key international

parity relationships, such as interest rate parity and

purchasing power parity.

6Chapter SixInternational Parity

Relationships & ForecastingForeign Exchange Rates


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Chapter Outline

Interest Rate Parity

Purchasing Power Parity

The Fisher Effects Forecasting Exchange Rates

Interest Rate Parity Covered Interest Arbitrage

IRP and Exchange Rate Determination

Reasons for Deviations from IRP


The Fisher Effects

Forecasting Exchange Rates



PPP Deviations and the Real Exchange Rate Evidence on Purchasing Power Parity

The Fisher Effects








Efficient Market Approach

Fundamental Approach Technical Approach

Performance of the Forecasters





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Interest Rate Parity Defined

Covered Interest Arbitrage

Interest Rate Parity & Exchange RateDetermination

Reasons for Deviations from Interest Rate Parity


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IRP is an arbitrage condition.

If IRP did not hold, then it would be possible for

an astute trader to make unlimited amounts ofmoney exploiting the arbitrage opportunity.

Since we dont typically observe persistent

arbitrage conditions, we can safely assume that

IRP holds.



Interest Rate Parity Carefully Defined

Consider alternative one year investments for $100,000:

1. Invest in the U.S. at i$. Future value = $100,000 (1 + i$)

2. 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 ofthe British investment forward.

S$/

F$/ Future value = $100,000(1 + i)

S$/

F$/ (1 + i) = (1 + i$)

Since these investments have the same risk, they must havethe same future value (otherwise an arbitrage would exist)



IRP

Invest those pounds ati

$1,000

S$/

$1,000

Future Value =

Step 3: repatriate

future value to the

U.S.A.

Since both of these investments have the same risk, they must

have the same future value otherwise an arbitrage would exist

Alternative 1:

invest $1,000 at i$

$1,000(1 + i$)

Alternative 2:

Send your $ on a

round trip to

BritainStep 2:

$1,000

S$/ (1+ i) F$/

$1,000

S$/

(1+ i)

=

IRP




The scale of the project is unimportant

(1 + i$

)F$/

S$/ (1+ i)=

$1,000(1 + i$

)$1,000

S$/ (1+ i) F$/ =




Formally,

IRP is sometimes approximatedas

i$i S

F S

1 + i$1 + i S$/

F$/=


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Forward Premium

Its just the interest rate differential implied by

forward premium or discount.

For example, suppose the is appreciating from

S($/) = 1.25 toF180

($/) = 1.30

The forward premium is given by:

F180 ($/) S($/)

S($/)

360

180f180, v$ = =

$1.30 $1.25

$1.25 2 = 0.08



Interest Rate Parity Carefully Defined

Depending upon how you quote the exchange rate

($ per or per $) we have:

1 + i$

1 + iS/$

F/$ =

1 + i$1 + i S$/

F$/=or

so be a bit careful about that



IRP and Covered Interest Arbitrage

If IRP failed to hold, an arbitrage would exist. Its

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 S($/) = $1.25/

360-day forward rate F360

($/) = $1.20/

U.S. discount rate i$ = 7.10%

British discount rate i = 11.56%



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 rateF

360($/) = $1,20/, the 892,48 will be exactly $1,071.



Arbitrage I

Invest 800 ati = 11.56%

$1,000

800

800 = $1,000

$1.25

1

In one year 800

will be worth

892.48 =800 (1+ i)

$1,071=

892.48 1

F(360)

Step 3: repatriate

to the U.S.A. atF360 ($/) =

$1.20/Alternative 1:invest $1,000

at 7.1%FV = $1,071

Alternative 2:buy pounds

Step 2:

892.48

$1,071




& 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?

IfF360($/) $1.20/, an astute trader could makemoney with one of the following strategies:



Arbitrage Strategy I

IfF360 ($/) > $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.

A biSt 2



Arbitrage I

Invest 800 ati = 11.56%

$1,000

800

800 = $1,000

$1.25

1

In one year 800

will be worth

892.48 =800 (1+ i)

$1,071 $1.20/ , 892.48 will be more than enough to repay

your dollar obligation of $1 071 The excess is your profit

Step 1:

borrow $1,000

Step 2:

buy pounds

Step 3:

Step 5: Repayyour dollar loan

with $1,071.

892.48

More

than $1,071


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Copyright 2007 by The McGraw-Hill Companies, Inc. All rights re6-

Arbitrage Strategy II

IfF360 ($/) < $1.20/

i. Borrow 800 at t= 0 at i= 11.56% .

ii. Exchange 800 for $1,000 at the prevailing spotrate, invest $1,000 at 7.1% for one year to achieve

$1,071.

iii. Translate $1,071 back into pounds, ifF360 ($/) < $1.20/, then $1,071 will be more than

enough to repay your debt of 892.48.

Step 2:


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Arbitrage II

$1,000

800

$1,000 = 800

1

$1.25

In one year $1,000

will be worth $1,071 > 892.48 1

F(360)

Step 4:

repatriate to

the U.K.

IfF(360) < $1.20/ , $1,071 will be more than enough to repay

your dollar obligation of 892 48 Keep the rest as profit

Step 1:

borrow 800

Step 2:

buy dollars

Invest $1,000

at i$

Step 3:Step 5: Repay

your pound loan

with 892.48 .

$1,071

More

than

892.48


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IRP and Hedging Currency Risk

You are a U.S. importer of British woolens and have just ordered nextyears inventory. Payment of 100M is due in one year.

IRP implies that there are two ways that you fix the cash outflow to acertain U.S. dollar amount:

a) Put yourself in a position that delivers 100M in one yeara longforward contract on the pound.

You will pay (100M)(1.2/) = $120M in one year.

b) Form a forward market hedge as shown below.

Spot exchange rate S($/) = $1.25/

360-day forward rate F360 ($/) = $1.20/

U.S. discount rate i$ = 7.10%

British discount rate i = 11.56%


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Copyright 2007 by The McGraw-Hill Companies Inc All rights re6-

Forward Market Hedge

Where do the numbers come from? We owe our supplier100 million in one yearso we know that we need tohave 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.

How many dollars will it take to acquire 89.64 million at

the start of the year ifS($/) = $1.25/?

89.64 =100

1.1156

$112.05 = 89.64 $1.00

1.25


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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


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Transactions Costs Example

Will an arbitrageur facing the following prices be

able to make money?

Borrowing Lending

$ 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

1 + i$1 + i

S$/

F$/ =


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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 $1.034.11Owe $1,050 on your dollar-based borrowing

Suffer loss of $15.89

Transactions Costs Example

Now

t ryt

hisbackw

ar

ds


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Purchasing Power Parity and Exchange Rate

Determination

PPP Deviations and the Real Exchange Rate

Evidence on PPP

P h i P P i d


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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:

S($/) = P

P$

S($/) =P

P$150

$300= = $2/

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 h i P P i d


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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)1.00(1.05)

$1.231.00

=

P h i P P it d


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Copyright 2007 by The McGraw-Hill Companies, Inc. All rights re6


Exchange Rate Determination The euro will trade at a 1.90% discount in the forward

market:

$1.25

1.00

=F($/)S($/)

$1.25(1.03)

1.00(1.05) 1.031.05 1 + $

1 + = =

Relative PPP states that the rate of change in the

exchange rate is equal to differences in the rates of

inflationroughly 2%

P h i P P it


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and Interest Rate ParityNotice that our two big equations today equal

each other:

==F($/)

S($/)

1 + $1 +

PPP

1 + i

1 + i$ =F($/)

S($/)

IRP

E t d R t f Ch i E h


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Expected Rate of Change in Exchange

Rate as Inflation DifferentialWe could also reformulate

our equations as inflation or

interest rate differentials:

=F($/) S($/)

S($/)

1 + $1 +

1 =1 + $1 +

1 + 1 +

=F($/)

S($/)

1 + $1 +

=F($/) S($/)

S($/)

$

1 + E(e) = $

E t d R t f Ch i E h


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Expected Rate of Change in Exchange

Rate as Interest Rate Differential

=F($/) S($/)

S($/)

i$ i

1 + iE(e) = i$i


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Quick and Dirty Short Cut

Given the difficulty in measuring expected

inflation, managers often use

i$

i $


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Evidence on PPP

PPP probably doesnt hold precisely in the realworld 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.

Approximate Equilibrium Exchange


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Approximate Equilibrium Exchange

Rate Relationships

E( $ )

IRP

PPP

FE FRPPP

IFE FEP

S

FS

E(e)

(i$ i)


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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 rateE(

$) is the expected rate of U.S. inflation

i$is the equilibrium expected nominal U.S. interest rate


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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

International Fisher Effect:E(1 + )

E(1 + $)1 + i$

1 + i =


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International Fisher Effect

If the International Fisher Effect holds,

then forward rate PPP holds:

E(1 + )

E(1 + $)1 + i$

1 + i =

and if IRP also holds

1 + i$

1 + i

S/$

F/$

=E(1 + )

E(1 + $)=

S/$

F/$

Exact Equilibrium Exchange Rate


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PPP

FRPPPFE

FEPIFE

Exact Equilibrium Exchange Rate

Relationships

$/

$/ )(

S

SE

$/

$/

S

FIRP

E(1 + )

E(1 + $)

1 + i$

1 + i


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Efficient Markets Approach

Fundamental Approach

Technical Approach



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Efficient Markets Approach

Financial Markets are efficientif prices reflect allavailable and relevant information.

If this is so, exchange rates will only change when

new information arrives, thus:S

t=E[S

t+1]

and

Ft =E[St+1|It] Predicting exchange rates using the efficient

markets approach is affordable and is hard to beat.


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Fundamental Approach

Involves econometrics to develop models that usea variety of explanatory variables. This involvesthree 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 orthe random walk model.


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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


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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 forwardrate.

The founder ofForbes Magazine once said:

You can make more money selling financialadvice than following it.

d Ch Si


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End Chapter Six

Int Parity Relationship

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