Triangular Arbitrage
Tue, Apr 15Triangular arbitrage is the method that guarantees all exchange rates are consistent with one another. For instance, if one U.S. dollar can be exchanged for one Australian dollar, and one Australian dollar can be exchanged for one British pound, then the GBP/USD rate should equal 1. If there is a discrepancy, it presents a chance to profit.
Consider the following exchange rates: Citibank quotes EUR/USD at 0.9045, Barclays quotes GBP/USD at 1.4443, and HSBC quotes EUR/GBP at 1.6200. The cross rate derived from Citibank and Barclays is calculated as ($1.4443 / $0.9045) = €1.5968. This cross rate differs from HSBC’s rate, indicating a potential for arbitrage profit among the three currency pairs.
A trader with $1,000,000 can exchange this amount with Barclays for £692,377 ($1,000,000 / $1.4443). These British pounds can then be sold to HSBC for €1,121,651 (£692,377 x €1.6200). Finally, the trader can convert these euros back to U.S. dollars at Citibank for $1,014,533 (€1,121,651 x $0.9045). This results in a risk-free profit of $14,533.
This form of Triangular Arbitrage will persist until the exchange rates reach equilibrium, meaning the cross rate aligns with the actual quote. The essence of triangular arbitrage lies in identifying and capitalizing on profitable opportunities arising from inconsistencies in exchange rates. Consequently, such discrepancies are quickly resolved through triangular arbitrage.
However, cross rates will only be approximately consistent due to the bid-ask spread associated with transaction costs, which helps maintain the overall structure as much as possible.
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