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Triangular and Locational Arbitrage
Bill Reese
International Finance
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Learning Objectives
In this unit we will learn: How to execute triangular arbitrage
Why cross-rates generally prevent triangular arbitrage
How to execute locational arbitrage Why XR quotes generally prevent locational arbitrage
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Triangular Arbitrage
Single XR example:• 0.8155 €/$• 1.3235 CD/$• 0.635 €/CD
“Fair” crossrate0.8155 €/$ = 0.61617 €/CD
1.3235 CD/$
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Triangular Arbitrage
0.61617 €/CD = fair rate 0.635 €/CD = actual rate CD is expensive € is cheap Sell the expensive currency: Canadian
dollars Buy the cheap currency: Euros
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Triangular Arbitrage
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Triangular Arbitrage
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$ 1,030,561
Triangular Arbitrage
Start with $1 million Earn riskless profit of $30,561 Cannot remain for long in competitive
markets Price of CD drops from selling Price of euro rises from buying Actual cross-rate adjusts
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Triangular Arbitrage
Dual XR example:
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Bid (indirect) Ask (indirect)
1.25 SF/$ 1.28 SF/$
.812 €/$ .818 €/$
1.58 SF/€ 1.60 SF/€
Bid (direct) Ask (direct)
0.78125 $/SF 0.80 $/SF
1.2225 $/€ 1.2315 $/€
0.625 €/SF 0.6329 €/SF
Triangular Arbitrage
Fair crossrates• Bid: 1.25 SF/$ = 1.539 SF/€
.812 €/$• Ask: 1.28 SF/$ = 1.565 SF/€
.818 €/$
Actual crossrates > fair crossrates
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Triangular Arbitrage
Euro should equal (cost) 1.539 or 1.565 SF• Actually costs 1.58 or 1.60 SF• Euro is expensive• Swiss Franc is cheap• Buy cheap currency (SF)• Sell expensive currency (€)
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Triangular Arbitrage
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Triangular Arbitrage
Start with $1,000 Sell $ at .812 €/$ (indirect bid)
Or buy euros at 1.2315 $/€ (dir ask)Now own €812
Sell euros at 1.58 SF/€ (indir bid)Or buy SF at 0.6329 €/SF (dir ask)Now own SF 1,282.96
Sell SF at 0.78125 $/SF (dir bid)Or buy $ at 1.28 SF/$ (indir ask)Now own 1,002.3112
Triangular Arbitrage
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$1,002.31
Triangular Arbitrage
Will go away as investors Sell dollars and buy euros
Bid price drops from .812 €/$
Sell euros and buy SF Bid price drops from 1.58 SF/€
Sell SF and buy dollars Ask price goes up from 1.28 SF/$
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Triangular Arbitrage
SF/$ goes up €/$ goes down “Fair” crossrate SF/€ goes up Actual crossrate SF/€ goes down “Fair” crossrate equals actual in equilibrium
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Locational Aribrage
Example
Do you see the arbitrage opportunity?
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Dealer A Dealer B
Bid Ask Bid Ask
2680 Peso/$ 2683 Peso/$ 2685 Peso/$ 2688 Peso/$
Locational Aribrage
Note: ask price of A < bid price of B
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Dealer A Dealer B
Bid Ask Bid Ask
2680 Peso/$ 2683 Peso/$ 2685 Peso/$ 2688 Peso/$
Locational Aribrage
Buy dollars from A and sell them to B Start with 1 million pesos Purchase $372.72 from A Sell them to B for 1,000,745 pesos
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Dealer A Dealer B
Bid Ask Bid Ask
2680 Peso/$ 2683 Peso/$ 2685 Peso/$ 2688 Peso/$
Locational Aribrage
Investors buy dollars from A Ask price of A goes up
Investors sell dollars to B Bid price of B goes down
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Dealer A Dealer B
Bid Ask Bid Ask
2680 Peso/$ 2683 Peso/$ 2685 Peso/$ 2688 Peso/$
