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.)
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PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
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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
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PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
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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.)
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PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
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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
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11-6
Two-point arbitrage with bid-offer spreads
• With bid-offer spreads the no-arbitrage condition
becomes:
Sb , A  x / y   S a , B  x / y 
S a , 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
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PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
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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
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PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
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11-11
Commodity arbitrage
• The no-arbitrage condition in the case of commodity
arbitrage is the law of one price (LOP):
*
i
Pi  SP
(cont.)
Copyright  2010 McGraw-Hill Australia Pty Ltd
PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
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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
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11-14
Return on Investments
Investor
(K)
Foreign
investment
Domestic
investment
Converting at
spot rate
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
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11-16
Covered interest arbitrage
Foreign  domestic
Domestic  foreign
Borrowing
domestic currency
Converting at
spot rate
Investing at
foreign rate
Borrowing
foreign currency
1 unit
11unit
unit
Converting at
spot rate
1
S
SS
Loan
repayment
Loan
repayment
1
(1  i  )
S
Reconverting at
forward rate
Investing at
domestic rate
S (1  i )
Reconverting
at forward rate
F
(1  i )
S
1 i
1  i
S
(1  i )
F
Covered margin
Covered margin
F
(1  i )  (1  i )
S
S
(1  i )  (1  i )
F
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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)
F
π  (1  i )  (1  i )
S
π  i  i  f
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PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
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11-18
The interest parity forward rate
1 i 

F  S

1

i


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PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
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11-19
Covered arbitrage with bid-offer spreads
(domestic→foreign)
Fb

π  (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)
Sb
π  (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
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11-21
Arbitrage with bid-offer spreads
Foreign  domestic
Domestic  foreign
Borrowing
domestic currency
Converting at
spot offer rate
Investing at
foreign bid rate
Borrowing
foreign currency
1 unit
11unit
unit
Converting at
spot bid rate
1
Sa
SSb
Loan
repayment
Loan
repayment
1
(1  ib )
Sa
Reconverting at
forward bid rate
Fb
(1  ib )
Sa
Investing at
domestic bid rate
Sb (1  ib )
Reconverting at
forward offer rate
1  ia
Covered margin
Fb
(1  ib )  (1  ia )
Sa
1  ia
Sb
(1  ib )
Fa
Covered margin
Sb
(1  ib )  (1  ia )
Fa
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
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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
The UIP condition
Se
1  i  (1  i )
S

e

i i  S
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
11-26
Uncovered interest arbitrage
Foreign  domestic
Domestic  foreign
Borrowing
domestic currency
Converting at
spot rate
Investing at
foreign rate
Borrowing
foreign currency
1 unit
11unit
unit
Converting at
spot rate
1
S0
SS0
Loan
repayment
Loan
repayment
1
(1  i  )
S0
Reconverting at
spot rate
S1
(1  i  )
S0
Investing at
domestic rate
S0 (1  i )
Reconverting
at spot rate
1 i
1  i
S0
(1  i )
S1
Covered margin
Covered margin
S1
(1  i  )  (1  i )
S0
S0
(1  i )  (1  i  )
S1
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PPTs t/a International Finance: An Analytical Approach 3e by Imad A. Moosa
Slides prepared by Afaf Moosa
11-27
Uncovered arbitrage with bid-offer spreads
Foreign  domestic
Domestic  foreign
Borrowing
domestic currency
Converting at
spot offer rate
Investing at
foreign bid rate
Borrowing
foreign currency
1 unit
11unit
unit
Converting at
spot bid rate
1
Sa 0
SSb 0
Loan
repayment
Loan
repayment
1
(1  ib )
Sa 0
Reconverting at
spot bid rate
Sb1
(1  ib )
Sa 0
Investing at
domestic bid rate
Sb 0 (1  ib )
Reconverting at
spot offer rate
1  ia
Covered margin
Sb1
(1  ib )  (1  ia )
Sa 0
1  ia
Sb 0
(1  ib )
S a1
Covered margin
Sb 0
(1  ib )  (1  ia )
S a1
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
11-28