Triangular Arbitrage: Definition and Example

What Is Triangular Arbitrage?

Triangular arbitrage is the result of a discrepancy between three foreign currencies that occurs when the currency's exchange rates do not exactly match up. These opportunities are rare, and traders who take advantage of them usually have advanced computer equipment and/or programs to automate the process.

A trader employing triangular arbitrage, for example, could make the following series of exchanges—USD to EUR to GBP to USD using the EUR/USD, EUR/GBP, and USD/GDP rates, and (assuming low transaction costs) net a profit.

Key Takeaways

  • Triangular arbitrage is a form of low-risk profit-making by currency traders that takes advantage of exchange rate discrepancies through algorithmic trades.
  • To ensure profits, such trades should be performed quickly and should be large in size.
  • Because triangular arbitrage opportunities are regularly exploited, currency markets become more efficient.

Understanding Triangular Arbitrage

This type of arbitrage can result in a "riskless" profit if quoted currency exchange rates do not equal the market's cross-exchange rate. In other words, if two currencies also trade against some third currency, then the exchange rates of all three should be synchronized. Otherwise, a profit opportunity exists.

International banks, who make markets in currencies, exploit an inefficiency where one market is overvalued and another is undervalued. Price differences between exchange rates are only fractions of a cent, and for this form of arbitrage to be profitable, a trader must trade a large amount of capital.

Automated Trading Platforms and Triangular Arbitrage

Automated trading platforms have streamlined the way trades are executed, as an algorithm is created in which a trade is automatically conducted once specific criteria are met. Automated trading platforms allow a trader to set rules for entering and exiting a trade, and the computer will automatically conduct the trade according to the rules. While automated trading has many benefits, such as the ability to test a set of rules on historical data before risking capital, engaging in triangular arbitrage is only feasible using an automated trading platform.

Since the market is essentially a self-correcting entity, trades happen at such a rapid pace that an arbitrage opportunity can vanish within seconds of appearing. Automated trading platform are generally set to identify an opportunity and act on it before it disappears.

The speed of algorithmic trading platforms and markets can also work against traders. For example, a traders may not be able to lock in a profitable price before it moves past their desired position in less than a second, causing a loss.

Example of Triangular Arbitrage

Let's say you have $1 million and are provided with the following exchange rates: EUR/USD = 1.1586, EUR/GBP = 1.4600, and USD/GBP = 1.6939.

Now, you want to see if there is a triangular arbitrage opportunity, so you calculate the following:

  1. Sell dollars to buy euros: $1 million x 1.1586 = €1,158,600
  2. Sell euros for pounds: €1,158,600 ÷ 1.4600 = £793,561.64
  3. Sell pounds for dollars: £793,561.64 x 1.6939 = $1,344,214.06
  4. Subtract the initial investment from the final amount: $1,000,000 – $1,344,214.06 = -$344,214.06

From these transactions, you would receive a loss of $344,214.06 (assuming no transaction costs or taxes), so there is no triangular arbitrage opportunity. If the result had been positive, there would have been an arbitrage opportunity.

Arbitrage is buying one asset and selling it in another market for a profit. The technique can be used in many markets.

Converting Pairs

Converting currencies can be confusing. A mantra exists to help people remember—"left to right, divide; right to left, multiply," referring to the direction in which you read the exchange rate.

For example, using only the EUR/USD spot rate of $1.08 on 20 May, 2023 to convert €1,000,000 from EUR to USD and back (treat the backslash as a division symbol):

  • €1,000,000 ÷ $1.08 = $925,925.93
  • Multiply both sides of the equation by $1.08
  • €1,000,000 = $925,925.93 x $1.08

So, converting dollars to euros using the EUR/USD spot price requires multiplying, because you read the pair from right to left.

What Is the Triangular Arbitrage Algorithm?

A triangular arbitrage algorithm is an automated trading program that finds and executes triangular arbitrage opportunities.

Is Crypto Triangular Arbitrage Possible?

Triangular arbitrage identifies price differences for trading opportunities, so it might be possible to find three cryptocurrencies that allow you to use the strategy.

Is Triangular Arbitrage Illegal?

Buying and selling currency is legal. As long as all funds, information sources, and other practices are not against any laws, there is nothing illegal about the triangular arbitrage trading strategy.

The Bottom Line

Triangular arbitrage is a strategy where you find price discrepancies between three currencies and buy and sell them in a specific order to make a profit. Because of the constant and rapid fluctuation in exchange rates, it can be risky, so you need to be well-practiced to attempt it or use a proven automated trading method.

The comments, opinions, and analyses expressed on Investopedia are for informational purposes online. Read our warranty and liability disclaimer for more info. As of the date this article was written, the author does not use triangular arbitrage.

CorrectionMay 20, 2023: A previous version of this article incorrectly converted the three currency pairs.

Take the Next Step to Invest
The offers that appear in this table are from partnerships from which Investopedia receives compensation. This compensation may impact how and where listings appear. Investopedia does not include all offers available in the marketplace.