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8/10/2019 Rose Chapter 7

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International Arbitrage AndInterest Rate Parity

7

Chapter

South-Western/Thomson Learning 2006


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Chapter Objectives

To explain the conditions that will

result in various forms of international

arbitrage, along with the realignments thatwill occur in response; and

To explain the concept of interest rate

parity, and how it prevents arbitrage

opportunities.


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International Arbitrage

Arbitragecan be loosely defined as

capitalizing on a discrepancy in quoted

prices to make a riskless profit. The effect of arbitrage on demand and

supply is to cause prices to realign, such

that no further risk-free profits can be

made.


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As applied to foreign exchange and

international money markets, arbitrage

takes three common forms: locational arbitrage

triangular arbitrage

covered interest arbitrage

International Arbitrage


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Locational arbitrageis possible when a

banks buying price (bid price) is higher

than another banks selling price (ask

price) for the same currency.

Example

Bank C Bid Ask Bank D Bid Ask

NZ$ $.635 $.640 NZ$ $.645 $.650

Buy NZ$ from Bank C @ $.640, and sell it to

Bank D @ $.645. Profit = $.005/NZ$.

Locational Arbitrage


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Triangular arbitrageis possible when across exchange rate quote differs from therate calculated from spot rate quotes.

Example Bid AskBritish pound () $1.60 $1.61

Malaysian ringgit (MYR) $.200 $.202British pound () MYR8.10 MYR8.20

MYR8.10/ $.200/MYR = $1.62/Buy @ $1.61, convert @ MYR8.10/, thensell MYR @ $.200. Profit = $.01/.

Triangular Arbitrage


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Covered interest arbitrageis the process

of capitalizing on the interest rate

differential between two countries whilecovering for exchange rate risk.

Covered interest arbitragetends to force a

relationship between forward rate

premiums and interest rate differentials.

Covered Interest Arbitrage


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Example

spot rate = 90-day forward rate = $1.60

U.S. 90-day interest rate = 2%

U.K. 90-day interest rate = 4%

Borrow $ at 3%, or use existing funds which

are earning interest at 2%. Convert $ to at

$1.60/ and engage in a 90-day forwardcontract to sell at $1.60/. Lend at 4%.

Note: Profits are not achieved instantaneously.

Covered Interest Arbitrage


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Comparing Arbitrage Strategies

Any discrepancy will trigger arbitrage,

which will then eliminate the discrepancy,

thus making the foreign exchange marketmore orderly.


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Interest Rate Parity (IRP)

As a result of market forces, the forward

rate differs from the spot rate by an

amount that sufficiently offsets the

interest rate differential between twocurrencies.

Then, covered interest arbitrage is no

longer feasible, and the equilibrium stateachieved is referred to as interest rate

parity(IRP).


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Derivation of IRP

When IRP exists, the rate of return

achieved from covered interest arbitrage

should equal the rate of return available in

the home country.

End-value of a $1 investment in covered

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

= (1/S) (1+iF) [S (1+p)]= (1+iF) (1+p)

where pis the forward premium.


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End-value of a $1 investment in the home

country = 1 + iH

Equating the two and rearranging terms:

p=(1+iH)1(1+iF)

i.e.

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

Derivation of IRP


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Determining the Forward Premium

Example

Suppose 6-month ipeso= 6%, i$= 5%.

From the U.S. investors perspective,forward premium = 1.05/1.061 -.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

The IRP relationship can be rewritten as

follows:

FS =S(1+p)S = p=(1+iH)1 = (

iH

iF)

S S (1+iF) (1+iF)

The approximated form, p iHiF,

provides a reasonable estimate when theinterest rate differential is small.


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Graphic Analysis of Interest Rate Parity

Interest Rate Differential (%)home interest rateforeign 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 actual

interest rate differentials and forward

premiums for various currencies, and plotthem on a graph.

IRP holds when covered interest arbitrage

is not possible or worthwhile.


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Interpretation of IRP

When IRP exists, it does not mean that

both local and foreign investors will earn

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

covered interest arbitrage to achieve

higher returns than those achievable in

their respective home countries.


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Does IRP Hold?

Forward Rate

Premiums andInterest Rate

Differentials forSeven Currencies


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Does IRP Hold?

Various empirical studies indicate that IRP

generally holds.

While there are deviations from IRP, they

are often not large enough to make

covered interest arbitrage worthwhile.

This is due to the characteristics of

foreign investments, such as transactioncosts, political risk, and differential tax

laws.


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Considerations When Assessing IRP

Transaction Costs

iHiF

p


arbitrage byforeign investors Zone of

potentialcovered

interestarbitrageby local

investors

IRP line

Zone where

covered interestarbitrage is notfeasible due to

transaction costs

8%e


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0%

2%

4%

6%

8%

Q1 Q3 Q1 Q3 Q1 Q3 Q1 Q3 Q1

U.S. interest rate0%

2%

4%

6%

8%

Q3 Q1 Q3 Q1 Q3 Q1 Q3

Annualize

dinterestrate

2000 2001 2002 2003

i$

iEuros interest rate

-2%

0%

2%

Q3 Q1 Q3 Q1 Q3 Q1 Q3

2000 2001 2002 2003

i$< ii$

i

i$= i

i$> i

-2%

0%

2%

Q3 Q1 Q3 Q1 Q3 Q1 Q3F

orwardpremium

of

2000 2001 2002 2003

premium

discount

Changes in Forward Premiums

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