Triangular arbitrage: Difference between revisions

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==Mechanics of triangular arbitrage==

[[File:Triangular-arbitrage.svg|thumb|right|A visual representation of a realistic triangular arbitrage scenario, using sample bid and ask prices quoted by international banks]]

Some international banks serve as [[market maker]]s between currencies by narrowing their [[bid–ask spread]] more than the bid-ask spread of the implicit cross exchange rate. However, the bid and ask prices of the implicit cross exchange rate naturally discipline market makers. When banks' quoted exchange rates move out of alignment with cross exchange rates, any banks or traders who detect the discrepancy have an opportunity to earn arbitrage profits via a triangular arbitrage strategy.<ref name="Eun & Resnick 2011" /> To execute a triangular arbitrage [[trading strategy]], a bank would calculate cross exchange rates and compare them with exchange rates quoted by other banks to identify a pricing discrepancy.

For example, [[Citibank]] detects that [[Deutsche Bank]] is quoting dollars at a [[bid price]] of 0€0.8171 €/$, and that [[Barclays]] is quoting pounds at a bid price of $1.4650 $/£ (Deutsche Bank and Barclays are in other words willing to buy those currencies at those prices). Citibank itself is quoting the same prices for these two exchange rates. A trader at Citibank then sees that [[Crédit Agricole]] is quoting pounds at an [[ask price]] of 1€1.1910 €/£ (in other words it is willing to sell pounds at that price). While the quoted market cross exchange rate is 1€1.1910 €/£, Citibank's trader realizes that the implicit cross exchange rate is 1€1.1971 €/£ (by calculating 1.4650 × 0.8171 = 1.1971), meaning that Crédit Agricole has narrowed its bid-ask spread to serve as a market maker between the euro and the pound. Although the market suggests the implicit cross exchange rate should be 1.1971 euros per pound, Crédit Agricole is selling pounds at a lower price of 1.1910 euros. Citibank's trader can hastily exercise triangular arbitrage by exchanging dollars for euros with Deutsche Bank, then exchanging euros for pounds with Crédit Agricole, and finally exchanging pounds for dollars with Barclays. The following steps illustrate the triangular arbitrage transaction.<ref name="Eun & Resnick 2011" />

# Citibank sells $5,000,000 to Deutsche Bank for euros, receiving €4,085,500. ($5,000,000 × 0€0.8171 €/$ = €4,085,500)

# Citibank sells €4,085,500 to Crédit Agricole for pounds, receiving £3,430,311. (€4,085,500 ÷ 1€1.1910 €/£ = £3,430,311)

# Citibank sells £3,430,311 to Barclays for dollars, receiving $5,025,406. (£3,430,311 × $1.4650 $/£ = $5,025,406)

# Citibank ultimately earns an arbitrage profit of $25,406 on the $5,000,000 of capital it used to execute the strategy.

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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. | 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 US$100 USD per US$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" />

Researchers have shown a decrease in the incidence of triangular arbitrage opportunities from 2003 to 2005 for the Japanese yen and Swiss franc and have attributed the decrease to broader adoption of [[electronic trading platform]]s and [[algorithmic trading|trading algorithms]] during the same period. Such electronic systems have enabled traders to trade and react rapidly to price changes. The speed gained from these technologies improved trading efficiency and the correction of mispricings, allowing for less incidence of triangular arbitrage opportunities.<ref name="Fenn et al. 2009" />