fin 444 - chapter 7 slides

8/13/2019 Fin 444 - Chapter 7 Slides

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International Arbitrage AndInterest Rate Parity

7

Chapter

South-Western/Thomson Learning 2003


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B7 - 2

Chapter Objectives

To explain the conditions that will result invarious forms of international arbitrage,

along with the realignments that will occurin response; and To explain the concept of interest rate

parity, and how it prevents arbitrageopportunities.


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B7 - 3

International Arbitrage

Arbi t rage can be loosely defined ascapitalizing on a discrepancy in quoted

prices. Often, the funds invested are nottied up and no risk is involved. In response to the imbalance in demand

and supply resulting from arbitrageactivity, prices will realign very quickly,such that no further risk-free profits canbe made.


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Lo cat ional arb i t rage is possible when abanks buying price (bid price) is higher

than another banks selling price (askprice) for the same currency.

Example:

Bank C Bid Ask Bank D Bid AskNZ$ $.635 $.640 NZ$ $.645 $.650Buy NZ$ from Bank C @ $.640, and sell it toBank D @ $.645. Profit = $.005/NZ$.



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Triang ular arb i t rage is possible when across exchange rate quote differs from the

rate calculated from spot rates. Example : Bid Ask

British pound () $1.60 $1.61

Malaysian ringgit (MYR) $.200 $.202 MYR8.1 MYR8.2Buy @ $1.61, convert @ MYR8.1/, thensell MYR @ $.200. Profit = $.01/. (8.1 .2=1.62)



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When the exchange rates of the currenciesare not in equilibrium, triangular arbitrage willforce them back into equilibrium.


$

MYR

Value of in $

Value ofMYR in $

Value of in MYR


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Cov ered interes t arb i t rage is the processof capitalizing on the interest rate

differential between two countries, whilecovering for exchange rate risk. Covered interest arbitrage tends to force a

relationship between forward ratepremiums and interest rate differentials.



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Locational arbitrage ensures that quotedexchange rates are similar across banks

in different locations. Triangular arbitrage ensures that cross

exchange rates are set properly.

Covered interest arbitrage ensures thatforward exchange rates are set properly.



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Any discrepancy will trigger arbitrage,which will then eliminate the discrepancy.

Arbitrage thus makes the foreignexchange market more orderly.



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Interest Rate Parity (IRP)

Market forces cause the forward rate todiffer from the spot rate by an amount that

is sufficient to offset the interest ratedifferential between the two currencies. Then, covered interest arbitrage is no

longer feasible, and the equilibrium stateachieved is referred to as in teres t ra tep arity (IRP) .


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Derivation of IRP

When IRP exists, the rate of returnachieved from covered interest arbitrage

should equal the rate of return available inthe home country. End-value of a $1 investment in covered

interest arbitrage = (1/S) (1+ i F) F

= (1/S) (1+ i F) [S (1+p)]= (1+ i F) (1+p)

where p is the forward premium.


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Derivation of IRP

End-value of a $1 investment in the homecountry = 1 + i H

Equating the two and rearranging terms:

p = (1+ i H) 1 (1+ i F)

i.e.

forward = (1 + home interest rate) 1 premium (1 + foreign interest rate)


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Determining the Forward Premium

Example : Suppose 6-month i peso = 6%, i $ = 5%. From the U.S. investors perspective,

forward premium = 1.05/1.06 1 - .0094 If S = $.10/peso, then

6-month forward rate = S (1 + p).10 (1 _ .0094)$.09906/peso


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Determining the Forward Premium

Note that the IRP relationship can berewritten as follows:

F S = S(1+p) S = p = (1+ i H) 1 = (i H i F)S S (1+ i F) (1+ i F)

The approximated form, p i H i F, provides

a reasonable estimate when the interestrate differential is small.


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Graphic Analysis of Interest Rate ParityInterest Rate Differential (%)

home interest rate foreign interest rate

ForwardPremium (%)

ForwardDiscount (%)

- 2

- 4

2

4

1 3- 1- 3

IRP line


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Graphic Analysis of Interest Rate ParityInterest Rate Differential (%)

home interest rate foreign interest rate

ForwardPremium (%)

ForwardDiscount (%)

- 2

- 4

2

4

1 3- 1- 3

IRP line

Zone of potentialcovered interest

arbitrage bylocal investors


arbitrage byforeign investors


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Test for the Existence of IRP

To test whether IRP exists, collect theactual interest rate differentials and

forward premiums for various currencies.Pair up data that occur at the same pointin time and that involve the samecurrencies, and plot the points on a graph.

IRP holds when covered interest arbitrageis not worthwhile.


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Interpretation of IRP

When IRP exists, it does not mean thatboth local and foreign investors will earn

the same returns. What it means is that investors cannot use

covered interest arbitrage to achievehigher returns than those achievable intheir respective home countries.


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Does IRP Hold?

Various empirical studies indicate that IRPgenerally holds.

While there are deviations from IRP, theyare often not large enough to makecovered interest arbitrage worthwhile.

This is due to the characteristics offoreign investments, including transactioncosts, political risk, and differential taxlaws.


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Considerations When Assessing IRP

Trans ac t ion Cos ts

i H i F

p


arbitrage byforeign investors Zone of

potential

coveredinterestarbitrageby local

investors

IRP line

Zone wherecovered interestarbitrage is notfeasible due to

transaction costs


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Poli t ical Risk A crisis in the foreign country could cause

its government to restrict any exchange ofthe local currency for other currencies. Investors may also perceive a higher

default risk on foreign investments.

Different ia l Tax Law s If tax laws vary, after-tax returns should be

considered instead of before-tax returns.

Considerations When Assessing IRP


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Because of IRP,a forward ratewill normallymove in tandemwith the spotrate.

This correlation

depends oninterest ratemovements,i.e. p i H i F

t0 t2t1 I n t e r e s

t R a t e s

i A i U.S.

time

t0 t2t1

S p o t a n

d

F o r w a r d

R a

t e s

SAFA

time

Explaining Changes in Forward Premiums


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Explaining Changes in Forward Premiums

During the 1997-98 Asian crisis, theforward rates offered to U.S. firms onsome Asian currencies were substantiallyreduced for two reasons.

The spot rates of these currenciesdeclined substantially during the crisis.

Their interest rates had increased as theirgovernments attempted to discourageinvestors from pulling out their funds.


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Impact of Arbitrage on an MNCs Value

n

t t

m

j t j t j

k 1=1 ,,

1

ERECFE

=Value

E (CF j ,t ) = expected cash flows in currency j to be receivedby the U.S. parent at the end of period t

E (ER j ,t ) = expected exchange rate at which currency j canbe converted to dollars at the end of period t

k = weighted average cost of capital of the parent

Forces of Arbitrage


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International Arbitrage Locational Arbitrage

Triangular Arbitrage Covered Interest Arbitrage Comparison of Arbitrage Effects

Chapter Review


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Chapter Review

Interest Rate Parity (IRP) Derivation of IRP

Determining the Forward Premium Graphic Analysis of IRP Test for the Existence of IRP Interpretation of IRP Does IRP Hold? Considerations When Assessing IRP


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Chapter Review

Explaining Changes in Forward Premiums Impact of Arbitrage on an MNCs Value

fin 444 - chapter 7 slides

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