# Triangular Arbitrage

Triangular Arbitrage is the process of ensuring that all exchange rates are consistent with each other.

For example, if 1 US dollar is exchanged for 1 Australian dollar, and 1 Australian dollar is exchanged for 1 British pound, then GBP/USD should be equal to 1.

If different, then there is an opportunity for profit.

Assume the quote is as follows:

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

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

This cross exchange rate is different from HSBC’s.

The opportunity exists to profit from arbitrage between three currency pairs.

This is called Triangular Arbitrage.

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

The pounds can then 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 rate equilibrium is re-established (cross rate equals actual quoted price).

The process of triangular arbitrage is exactly the process of finding and taking advantage of profit opportunities when exchange rates are inconsistent.

This inconsistency will be eliminated quickly due to triangular arbitrage.

However, taking into account the bid-ask spread associated with transaction costs, the cross-rate will only be roughly consistent