Triangular arbitrage

From Wikipedia, the free encyclopedia

Triangular arbitrage (sometimes called triangle arbitrage) refers to taking advantage of a state of imbalance between three foreign exchange markets: a combination of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices.

Triangular arbitrage offers a risk-free profit (in theory), so opportunities for triangular arbitrage usually disappear quickly, as many people are looking for them, or simply never occur as everybody knows the pricing relation.

[edit] Example

Consider the three foreign exchange rates among the Canadian dollar, the U.S. dollar, and the Australian dollar. Triangular arbitrage will produce a profit whenever the following relation does not hold:

CD$/US$ * AU$/CD$ = AU$/US$.

For example if you can trade at these exchange rates

the Canadian Dollar (CD$) against the US dollar (US$) is CD$1.13/US$1.00 (1 US$ gets you CD$1.13)
the Australian Dollar (AU$) against the US dollar (US$) is AU$1.33/US$1.00 (1 US$ gets you AU$1.33)
the Australian Dollar (AU$) against the Canadian Dollar (CD$) is AU$1.18/CD$1.00 (1 CD$ gets you AU$1.18)

1.13 * 1.18 = 1.3334 > 1.3300, thus mispricing has occurred.

To take advantage of the mispricing, starting with US$10,000 to invest:

1st buy Canadian Dollars with his US Dollars: US$10,000 * (CD$1.13/US$1) = CD$11,300
2nd buy Australian Dollars with his Canadian Dollars: CD$11,300 * (AU$1.18/CD$1.00) = AU$13,334
3rd buy US Dollars with his Australian Dollars: AU$13,334 / (AU$1.33/US$1.0000) = US$10,025
Net risk free profit: US$25.00

A profit maximizing trader presented with these prices will trade up to the maximum size possible, or equivalently do the trade as many times as possible, until one of the traders on the other side of one of the deals changes his price. In practice currencies are quoted with a bid ask spread, so a trader should be careful that he is actually buying at the quoted ask price, and selling at the quoted bid price. Other transaction costs, such as commissions, might also invalidate the apparent free lunch.