Triangular Arbitrage

Table of Contents

Table of Contents 0

1 Introduction 1

2 Market Efficiency and Arbitrage Opportunities 1

2.1 Triangular Arbitrage without Transaction Costs 2

2.2 Triangular Arbitrage with Transaction Costs 2

2.3 Examples 5

3 Triangular Arbitrage Opportunities between Turkish, British and Euro Currencies 7

4 Can Triangular Arbitrage Opportunities Exploited in Real Life? 8

4.1 Artefacts 8

4.2 Slippage in Price Quotes 9

4.3 Stale Quote 9

4.4 Weekend effects and non-trading hours 9

5 Appendix 10

5.1 Spot Rates between 1/10/2007 and 11/01/2006 10

5.2 Triangular Arbitrage Calculations 12

6 References 13

1 Introduction

Triangular arbitrage is a financial activity that keeps cross exchange rates consistent. ‘Consistency’ means that the cross exchange rate between two currencies calculated from their exchange rates against a third currency must be identical to the cross rate that is actually quoted. If this is not the case then the equilibrium condition precluding triangular arbitrage is violated. Consequently, arbitragers will buy and sell currencies in a sequence dictated by the nature of the violation of the equilibrium condition is restored as a result of arbitrage itself. At this point the cross exchange rates are consistent and profit from arbitrage is zero.

2 Market Efficiency and Arbitrage Opportunities

According to the market efficiency theory, the minimum requirement that a market must satisfy is that no arbitrage opportunities exist. Consistent deviations from that rule, after accounting for market imperfections such as trading costs can be interpreted as evidence of market inefficiency in allowing such profit opportunities to go unexploited. Triangular arbitrage is in theory a type of risk less arbitrage that takes advantage of cross rate mispricing. Triangular arbitrage involves positions in three currencies. Let c1, c2, c3