What is a Triangular Arbitrage?

Also known as triangle arbitrage, triangular arbitrage refers to a process by which a trader takes advantage of a mismatch between the exchange rates of three different currencies. By buying and selling these particular currencies, the trader makes a risk-free profit. Such a mismatch usually only lasts for seconds because there is a large number of traders actively looking for such an opportunity, so only sophisticated traders with advanced equipment usually are able to take advantage of it.

An opportunity for a triangular arbitrage occurs when exchange rates between three currencies are not in balance. A trader who notices this imbalance uses Currency A to buy Currency B, which he or she then changes into Currency C. He or she finally converts the money back into Currency A and ends up with a profit.

For example, a trader has $1,000 US Dollars (USD) and notices that the exchange rates are as follow: Japanese yen (JPY)/USD = 100; USD/Great Britain pound (GBP) = 1.60; JPY/GBP = 140. Calculating the first two quotes, the JPY/GBP exchange rate should be 100 X 1.60 = 160, so the quote undervalues the GBP against the JPY. There is an exchange rate mismatch and an opportunity for a triangular arbitrage in this case.

The trader uses his or her $1,000 USD to buy Japanese yen, getting ¥100,000 JPY. He or she converts it again into Great Britain pounds, getting £714.29 — because GBP/JPY = 1/140 = 0.0071429. Finally, the trader sells the GBP for USD and gets $1,142.86 USD. The trader, therefore, gains a risk-free profit of $142.86 USD — the amount of the final trade minus the original investment of $1,000 USD = $142.86 USD from the triangular arbitrage.

Because many traders are looking for such an opportunity, a triangular arbitrage opportunity usually lasts only for a few seconds. The trader has to conduct these transactions at the same time or within a very short period of time. If the trader takes too long to complete these transactions, the exchange rates could change before he or she finishes the triangular arbitrage process. In such a case, the trader would face a risk, turning the process into a pseudo-arbitrage. Traders who conduct triangular arbitrages need sophisticated computer equipment and software to finish the transactions quickly.

By conducting triangular arbitrages, traders alter supply and demand patterns in the foreign exchange rate. They change the prices of different currencies and bring the exchange rates into balance. In this way, triangular arbitrages help restore equilibrium in the foreign exchange market.