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

Chapter 11

International
Arbitrage


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

(cont.)
Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-2


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

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-3


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

(cont.)
Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-4


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

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-5


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

S A ( x / y)

SB ( x / y)

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-6


Two-point arbitrage with bid-offer
spreads
• With bid-offer spreads the no-arbitrage condition
becomes:

Sb , A x / y

Sa, B x / y

Sa, A x / y

Sb , B x / y

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-7


Three-point (triangular) arbitrage
• It is triggered when cross exchange rates are
inconsistent, that is, when the following condition is
violated:

S ( x / z)
S ( x / y)
S ( y / z)

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-8


Profitable/unprofitable sequences
(b) Profitable sequence

(a) Unprofitable sequence

x

x
S ( x / y)

z

S ( x / z)
S ( y / z)

y z
Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

y
11-9


Multipoint arbitrage
• The condition precluding multipoint arbitrage is:

S ( x1 / x2 ) S ( x2 / x3 ) S ( xn / x1 ) 1

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-10

Five-point arbitrage
AUD

EUR

USD

 

GBP
JPY

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-11


Commodity arbitrage
• The no-arbitrage condition in the case of commodity
arbitrage is the law of one price (LOP):

Pi

*

SPi

(cont.)

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-12


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

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-13


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

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-14


Return on Investments
Investor
(K)
Foreign
investment

Converting at 
spot rate

Domestic
investment

K
S

  

Investing in 
foreign assets
K
   (1 i )
S

Reconverting at 
forward rate
KF

(1 i )
S

K (1 i )

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-15


The CIP equilibrium condition

F
(1 i )
(1 i )
S
i i
f

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-16


Covered interest arbitrage
Foreign   domestic

Domestic   foreign
Borrowing 
domestic currency
Converting at 
spot rate
Investing at 
foreign rate

1 unit  

1 unit  
1 unit  

Converting at 
spot rate

1
  
S

S  
  S

Loan 
repayment

Loan 
repayment

1
(1 i )
S

Reconverting at 
forward rate

Borrowing 
foreign currency

F
(1 i )
S

Investing at 
domestic rate
S   (1 i )

  

1 i

1 i

S
(  1 i )
F

Covered margin

Covered margin

F
(1 i )
S

S
(1 i )
F

(1 i )

Reconverting 
at forward rate

(1 i )

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-17


Profit from covered arbitrage
(domestic→foreign)

π

F

(1 i ) (1 i )
S

π i

i

f

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-18


The interest parity forward rate

F

1 i
S
1 i

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-19

Covered arbitrage with bid-offer
spreads (domestic→foreign)

π

Fb
(1 ib ) (1 ia )
Sa

π ib

ia

f

m

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-20


Covered arbitrage with bid-offer
spreads (foreign→domestic)

π

Sb
(1 ib ) (1 ia )
Fa

π ib ia

f

m

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-21


Arbitrage with bid-offer spreads
Foreign   domestic

Domestic   foreign
Borrowing 
domestic currency
Converting at 
spot offer rate
Investing at 
foreign bid rate

Reconverting at 
forward bid rate

1 unit  

1 unit  
1 unit  

Borrowing 
foreign currency
Converting at 
spot bid rate

1
  
Sa

Sb
  S

Loan 
repayment

Loan 
repayment

1
(1 ib )
Sa
Fb
(1 ib )
Sa

Sb   (1 ib )

   1 ia

Covered margin

Fb
(1 ib )
Sa

Investing at 
domestic bid rate

(1 ia )

1 ia

Sb
  (1 ib )
Fa

Reconverting at 
forward offer rate

Covered margin

Sb
(1 ib )
Fa

(1 ia )

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-22


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

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-23


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 highinterest currency

Copyright 2010 McGraw-Hill Australia Pty Ltd

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

11-24


Return on domestic investment
and foreign investment (with
uncovered position)
Investor
(K)
Foreign
Investment

Converting at 
spot rate

Domestic
Investment

K
S

  

Investing in 
foreign assets
K
(1 i )
S

Reconverting at    
expected spot rate
KS e
(1 i )
S

K (1 i )

Copyright 2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa

11-25