Triangular and Locational Arbitrage

Bill Reese

International Finance

1

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

2

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

6

$ 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

15

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/$