Lecture International finance: An analytical approach (3/e): Chapter 11 - Imad A. Moosa

Chapter 11 - International arbitrage. In this chapter, the learning objectives are: To define arbitrage and the no-arbitrage condition; to describe two-point, three-point and multi-point arbitrage in the foreign exchange market; to describe commodity arbitrage;…

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Chapter 11

International Arbitrage

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PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa

Slides prepared by Afaf Moosa

Objectives

• To define arbitrage and the no-arbitrage condition

• To describe two-point, three-point and multi-point

arbitrage in the foreign exchange market

• To describe commodity arbitrage

11-2

(cont.)

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Objectives (cont.)

• To describe covered interest arbitrage and show how the no-arbitrage condition can be used to determine the forward exchange rate

• To describe uncovered arbitrage and introduce the concept of carry trade

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Definition of arbitrage

• Arbitrage is generally defined as capitalising on a

discrepancy in quoted prices as a result of the

violation of an equilibrium (no-arbitrage) condition

• The arbitrage process restores equilibrium via

changes in the supply of and demand for the

underlying commodity, asset or currency

11-4

(cont.)

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Definition of arbitrage (cont.)

• The importance of arbitrage is that no-arbitrage

conditions are used for asset pricing, such that the equilibrium price of a financial asset is the price that

is consistent with the underlying no-arbitrage

condition

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Two-point arbitrage

• Also known as spatial or locational arbitrage, it arises when the following condition is violated:

) / ( )

/

11-6

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Two-point arbitrage with bid-offer spreads

• With bid-offer spreads the no-arbitrage condition

becomes:

y x

S y

x

S b , A / a , B /

y x

S y

x

S a , A / b , B /

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Three-point (triangular) arbitrage

• It is triggered when cross exchange rates are

inconsistent, that is, when the following condition is violated:

) / (

) /

( )

/

(

z y S

z x

S y

x S

11-8

Trang 9

) / ( )

/ (

z y S

z x S y

x S

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Multipoint arbitrage

• The condition precluding multipoint arbitrage is:

1 )

/ (

) /

( )

/

11-10

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Five-point arbitrage

AUD

USD EUR

GBP

JPY

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Commodity arbitrage

• The no-arbitrage condition in the case of commodity

arbitrage is the law of one price (LOP):

P i SP i *

11-12

(cont.)

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Commodity arbitrage (cont.)

• Commodity arbitrage is conducted by buying a

commodity in a market where it is cheap and selling

it in a market where it is more expensive

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Covered interest arbitrage

• Covered interest arbitrage is triggered by the

violation of the covered interest parity (CIP)

condition, which describes the equilibrium relation

between the spot exchange rate, the forward

exchange rate, domestic interest rates and foreign

interest rates

11-14

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Foreign investment

S K

) 1

S K

Investor

(K)

KF

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The CIP equilibrium condition

f i

i

i S

F

1 (

11-16

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Covered interest arbitrage

Covered margin

Investing at domestic rate

Domestic foreign Borrowing

Converting at spot rate

Loan repayment

S

) 1

S

F S

) 1 ( i S

S

i

) 1 ( ) 1

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Profit from covered arbitrage

(domestic→foreign)

f i

i

i S

F

π

) 1

( )

1 ( π

11-18

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The interest parity forward rate

i

i S

F

1 1

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Covered arbitrage with bid-offer

spreads (domestic→foreign)

m f

i i

i

i S

F

a b

a

b a

b

π

) 1

( )

1 ( π

11-20

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Covered arbitrage with bid-offer

spreads (foreign→domestic)

m f

i i

i

i F

S

a b

a

b a

b

π

) 1

( )

1 ( π

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Arbitrage with bid-offer spreads

Covered margin

Investing at domestic bid rate

Converting at spot bid rate

Loan repayment

Covered margin

Reconverting at forward offer rate

a

S

1

) 1 (

1

b a

a

F S

11-22

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Uncovered interest arbitrage

• Uncovered arbitrage is triggered by the violation of

the uncovered interest parity (UIP) condition It is

described as ‘uncovered’ because, unlike covered

arbitrage, the long currency position is not covered in the forward market but rather left uncovered or open

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Carry trade

• Carry trade is a kind of uncovered interest arbitrage

in which a short position is taken on a low-interest

currency and a long position is taken on a

high-interest currency

11-24

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Return on domestic investment

and foreign investment (with

uncovered position)

Investing in foreign assets

Foreign Investment

S K

) 1

S K

KSe

Investor

(K)

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The UIP condition

e

S i

i

i S

S i



) 1

( 1

11-26

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Uncovered interest arbitrage

Covered margin

Investing at domestic rate

Domestic foreign

Borrowing domestic currency

Converting at

spot rate

Investing at foreign rate

Foreign domestic

Borrowing foreign currency

Loan repayment

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Uncovered arbitrage with bid-offer spreads

Covered margin

Investing at domestic bid rate

domestic currency

Converting at spot offer rate

Investing at foreign bid rate

Foreign domestic

Borrowing foreign currency

Converting at spot bid rate

Loan repayment

Covered margin

Reconverting at spot offer rate

(

0

1

b a

0

1

a b

a

S S

11-28

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