Triangular arbitrage: Difference between revisions

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'''Triangular arbitrage''' (also referred to as '''cross currency arbitrage''' or '''three-point arbitrage''') is the act of exploiting an [[arbitrage]] opportunity resulting from a pricing discrepancy among three different [[currency|currencies]] in the [[foreign exchange market]].<ref name="Carbaugh 2005">{{Cite book | title = International Economics, 10th Edition | author = Carbaugh, Robert J. | year = 2005 | publisher = Thomson South-Western | ___location = Mason, OH | isbn = 978-0-324-52724-7}}</ref><ref name="Pilbeam 2006">{{Cite book | title = International Finance, 3rd Edition | author = Pilbeam, Keith | year = 2006 | publisher = Palgrave Macmillan | ___location = New York, NY | isbn = 978-1-4039-4837-3}}</ref><ref name="Aiba et al. 2002">{{Cite journal | title = Triangular arbitrage as an interaction among foreign exchange rates | journal = Physica A: Statistical Mechanics and itsIts Applications | volume = 310 | issue = 4 | year = 2002 | pages = 467–479 | author = Aiba, Yukihiro | author2 = Hatano, Naomichi | author3 = Takayasu, Hideki | author4 = Marumo, Kouhei | author5 = Shimizu, Tokiko | url = http://www.sciencedirect.com/science/article/pii/S0378437102007999 | accessdate = 2011-07-07 | doi=10.1016/S0378-4371(02)00799-9| arxiv = cond-mat/0202391 | bibcode = 2002PhyA..310..467A }}</ref> A triangular arbitrage strategy involves three trades, exchanging the initial currency for a second, the second currency for a third, and the third currency for the initial. During the second trade, the arbitrageur locks in a zero-risk profit from the discrepancy that exists when the market [[exchange rate|cross exchange rate]] is not aligned with the implicit cross exchange rate.<ref name="Madura 2007">{{Cite book | title = International Financial Management: Abridged 8th Edition | author = Madura, Jeff | year = 2007 | publisher = Thomson South-Western | ___location = Mason, OH | isbn = 978-0-324-36563-4}}</ref><ref name="Eun & Resnick 2011">{{Cite book | title = International Financial Management, 6th Edition | author = Eun, Cheol S. | author2 = Resnick, Bruce G. | year = 2011 | publisher = McGraw-Hill/Irwin | ___location = New York, NY | isbn = 978-0-07-803465-7}}</ref> A profitable trade is only possible if there exist market imperfections. Profitable triangular arbitrage is very rarely possible because when such opportunities arise, traders execute trades that take advantage of the imperfections and prices adjust up or down until the opportunity disappears.<ref name="Ozyasar 2013">{{Cite news | title = Strategy for FOREX Triangulation | author = Ozyasar, Hunkar | date = 2013 | publisher = The Nest | url = http://budgeting.thenest.com/strategy-forex-triangulation-21257.html | accessdate = 2014-06-15}}</ref>

==Cross exchange rate discrepancies==

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==Evidence for triangular arbitrage==

Research examining high-frequency exchange rate data has found that [[mispricing]]s do occur in the foreign exchange market such that executable triangular arbitrage opportunities appear possible.<ref name="Fenn et al. 2009">{{Cite journal | title = The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market | journal = International Journal of Theoretical and Applied Finance | volume = 12 | issue = 8 | year = 2009 | pages = 1105–1123 | author = Fenn, Daniel J. | author2 = Howison, Sam D. | author3 = McDonald, Mark | author4 = Williams, Stacy | author5 = Johnson, Neil F. | url = http://www.worldscinet.com/ijtaf/12/1208/S0219024909005609.html | accessdate = 2011-07-06| doi = 10.1142/S0219024909005609 | arxiv = 0812.0913 }}</ref> In observations of triangular arbitrage, the constituent exchange rates have exhibited strong [[correlation]].<ref name="Aiba et al. 2002" /> A study examining exchange rate data provided by [[HSBC Bank (Europe)|HSBC Bank]] for the [[Japanese yen]] (JPY) and the [[Swiss franc]] (CHF) found that although a limited number of arbitrage opportunities appeared to exist for as many as 100 seconds, 95% of them lasted for 5 seconds or less, and 60% lasted for 1 second or less. Further, most arbitrage opportunities were found to have small magnitudes, with 94% of JPY and CHF opportunities existing at a difference of 1 [[basis point]], which translates into a potential arbitrage profit of $100 USD per $1 million USD transacted.<ref name="Fenn et al. 2009" />

Tests for [[seasonality]] in the amount and duration of triangular arbitrage opportunities have shown that incidence of arbitrage opportunities and mean duration is consistent from day to day. However, significant variations have been identified during different times of day. Transactions involving the JPY and CHF have demonstrated a smaller number of opportunities and long average duration around 01:00 and 10:00 [[UTC]], contrasted with a greater number of opportunities and short average duration around 13:00 and 16:00 UTC. Such variations in incidence and duration of arbitrage opportunities can be explained by variations in [[market liquidity]] during the trading day. For example, the foreign exchange market is found to be most liquid for Asia around 00:00 and 10:00 UTC, for Europe around 07:00 and 17:00 UTC, and for America around 13:00 and 23:00 UTC. The overall foreign exchange market is most liquid around 08:00 and 16:00 UTC, and the least liquid around 22:00 and 01:00 UTC. The periods of highest liquidity correspond with the periods of greatest incidence of opportunities for triangular arbitrage. This correspondence is substantiated by the observation of narrower bid-ask spreads during periods of high liquidity, resulting in a greater potential for mispricings and therefore arbitrage opportunities. However, market forces are driven to correct for mispricings due to a high frequency of trades that will trade away fleeting arbitrage opportunities.<ref name="Fenn et al. 2009" />