Triangular Arbitrage - Mechanics of Triangular Arbitrage

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. 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.

1. Citibank sells $5,000,000 to Deutsche Bank for euros, receiving €4,085,500. ($5,000,000 × 0.8171 €/$ = €4,085,500)
2. Citibank sells €4,085,500 to Crédit Agricole for pounds, receiving £3,430,311. (€4,085,500 ÷ 1.1910 €/£ = £3,430,311)
3. Citibank sells £3,430,311 to Barclays for dollars, receiving $5,025,406. (£3,430,311 × 1.4650 $/£ = $5,025,406)
4. 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.