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 be their names respectively. The relationship that should hold in an efficient market is the one that
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 be their names respectively. The relationship that should hold in an efficient market is the one that
References: · Understanding the foreign exchange market – Mao, James C.T. – CMA; May 1989; 63, 4; ABI/INFORM Global pg. 34 · Profit Possibilities in Currency Markets: Arbitrage, Hedging and Speculation – Dilip K.Ghosh, The Financial Review 38 (2003) 473-496; Eastern Finance Association · How efficient are FX markets? Empirical evidence of arbitrage opportunities using high-frequency data – Christos Kollias and Konstantinos Metaxas - Applied Financial Economics ISSN 0960-3107- www.tandf.co.uk/journals · Triangular arbitrage in the spot and forward foreign exchange markets – Imad Moosa – Quantitative Finance – Routledge · A neglected aspect of forward exchange theory and policy – Herbert G. Grubel – The journal of finance, Vol. 18; No.3. (Sep., 1963), pp. 537 - 548 · Central Bank of the Republic of Turkey - http://tcmbf40.tcmb.gov.tr/cbt.html · Bank of England - http://213.225.136.206/mfsd/iadb/Index.asp?first=yes&SectionRequired=I&HideNums=-1&ExtraInfo=true&Travel=NIx · Federal Reserve Bank of New York - http://www.newyorkfed.org/markets/fxrates/historical/home.cfm