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International Arbitrage AndInterest Rate Parity
7
Chapter
South-Western/Thomson Learning 2003
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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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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 = $.005/NZ$.
International Arbitrage
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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)
International Arbitrage
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When the exchange rates of the currenciesare not in equilibrium, triangular arbitrage willforce them back into equilibrium.
International Arbitrage
$
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.
International Arbitrage
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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.
International Arbitrage
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Any discrepancy will trigger arbitrage,which will then eliminate the discrepancy.
Arbitrage thus makes the foreignexchange market more orderly.
International Arbitrage
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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
Zone of potentialcovered interest
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
Zone of potentialcovered interest
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