Triangular arbitrage
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 currencies in the foreign exchange market.[1][2][3] 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 cross exchange rate is not aligned with the implicit cross exchange rate.[4][5] 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.[6]
Cross exchange rate discrepancies
Triangular arbitrage opportunities may only exist when a bank's quoted exchange rate is not equal to the market's implicit cross exchange rate. The following equation represents the calculation of an implicit cross exchange rate, the exchange rate one would expect in the market as implied from the ratio of two currencies other than the base currency.[7][8]
where
- is the implicit cross exchange rate for dollars in terms of currency a
- is the quoted market cross exchange rate for b in terms of currency a
- is the quoted market cross exchange rate for dollars in terms of currency b
If the market cross exchange rate quoted by a bank is equal to the implicit cross exchange rate as implied from the exchange rates of other currencies, then a no-arbitrage condition is sustained.[7] However, if an inequality exists between the market cross exchange rate, , and the implicit cross exchange rate, , then there exists an opportunity for arbitrage profits on the difference between the two exchange rates.[4]
Mechanics of triangular arbitrage
Some international banks serve as market makers 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.[5] 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 €0.8171 /$, 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 €1.1910 /£ (in other words it is willing to sell pounds at that price). While the quoted market cross exchange rate is €1.1910 /£, Citibank's trader realizes that the implicit cross exchange rate is €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.[5]
- Citibank sells $5,000,000 to Deutsche Bank for euros, receiving €4,085,500. ($5,000,000 × €0.8171 /$ = €4,085,500)
- Citibank sells €4,085,500 to Crédit Agricole for pounds, receiving £3,430,311. (€4,085,500 ÷ €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.
The reason for dividing the euro amount by the euro/pound exchange rate in this example is that the exchange rate is quoted in euro terms, as is the amount being traded. One could multiply the euro amount by the reciprocal pound/euro exchange rate and still calculate the ending amount of pounds.
Evidence for triangular arbitrage
Research examining high-frequency exchange rate data has found that
Tests for
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 platforms and 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.[9]
Profitability
Mere existence of triangular arbitrage opportunities does not necessarily imply that a trading strategy seeking to exploit currency mispricings is consistently profitable.
In the foreign exchange market, there are many market participants competing for each arbitrage opportunity; for arbitrage to be profitable, a trader would need to identify and execute each arbitrage opportunity faster than competitors. Competing arbitrageurs are expected to persist in striving to increase their execution speed of trades by engaging in what some researchers describe as an "electronic trading 'arms race'."
See also
References
- ISBN 978-0-324-52724-7.
- ISBN 978-1-4039-4837-3.
- ^ .
- ^ ISBN 978-0-324-36563-4.
- ^ ISBN 978-0-07-803465-7.
- ^ Ozyasar, Hunkar (2013). "Strategy for FOREX Triangulation". The Nest. Retrieved 2014-06-15.
- ^ ISBN 978-1-4292-0691-4.
- ISBN 978-0-415-30900-4.
- ^ .
External links
- Currency triangular arbitrage calculator on Android