Triangular arbitrage is the process that ensures that all exchange rates are mutually consistent.

For example, one U.S. dollar exchanges for one Australian dollar, and one Australian dollar exchanges for one British pound, then the GBP/USD should equal 1.

If it differs, then there is an opportunity to make a profit.

Suppose the following exchange rates are quoted:

  • Citibank quotes EUR/USD at 0.9045.
  • Barclays quotes GBP/USD at 1.4443.
  • HSBC quotes EUR/GBP at 1.6200.

The cross rate between Citibank and Barclays is ($1.4443 / $0.9045) = €1.5968.

This cross rate is not the same as HSBC’s.

An opportunity exists to profit from arbitrage among the three currency pairs.

This is known as Triangular Arbitrage.

A trader with $1,000,000 can sell to Barclays for £692,377 ($1,000,00 / $1.4443).

Then these British pounds can be sold to HSBC for €1,1121,651 (£692,377 x €1.6200).

Finally, the trader can sell these euros to Citibank for $1,014,533 (€1,121,651 x $0.9045).

The result is a risk-free profit of $14,533.

This type of Triangular Arbitrage will continue until exchange rates equilibrium is re-established (cross rate equals the actual quote).

The process of triangular arbitrage is exactly that of finding and exploiting profitable opportunities in such exchange rate inconsistencies.

As a result of triangular arbitrage, such inconsistencies will be eliminated rapidly.

Cross rates, however, will only be roughly consistent given the bid-ask spread associated with transaction cost