Triangular arbitrage looks to profit from discrepancies among three foreign currencies when their exchange rates across markets don't match up. These opportunities are rare, and traders usually employ sophisticated programs to automate finding these differences. It involves exchanging one currency for a second, then trading it for a third, and then finally exchanging it back into the original currency.

A trader using triangular arbitrage, for example, could make a series of exchanges—U. S. dollar (USD) to euros (EUR) to the British pound (GBP) to USD using the EUR/USD, EUR/GBP, and USD/GBP rates, and, if the transaction costs are low, net a profit.

Understanding Triangular Arbitrage

Triangular arbitrage is used in foreign exchange trading to exploit differences in exchange rates across different markets. It involves three trades, exchanging an initial currency for a second, the second currency for a third, and finally, the third currency back to the initial currency, ideally at a profit. Hence the name “triangular.”

Exchange rates should synchronize across all currency pairs, but because of market inefficiencies, they sometimes are not. These can be caused by delays in moving market information, differing levels of liquidity across markets, or rapid changes in market conditions. Prospects for triangular arbitrage are typically fleeting, existing for only a few seconds or less, as the market quickly corrects the mispricing. Therefore, automated trading systems capable of executing trades at high speed are used to exploit the momentary difference.

To be successful, arbitrage trades have to offer returns greater than the transaction costs involved, including bid-ask spreads and trading fees. The potential profit must outweigh these costs for the arbitrage to be profitable. Also, triangular arbitrage is more feasible in currency pairs with high liquidity since this reduces the influence of the trade on the market price and minimizes the cost of trading.

In practice, triangular arbitrage opportunities are rare and are exploited mainly by institutional traders with sophisticated technology capable of instantaneously identifying and acting on these opportunities.

Automated Trading Platforms and Triangular Arbitrage

Automated trading platforms have streamlined how trades are executed since an algorithm can be created to trade 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. While automated trading has many benefits, such as the ability to test potential rules on historical data before risking capital, engaging in triangular arbitrage is only feasible using an automated trading platform.

Since the market is thought to be self-correcting, trades happen so rapidly that an arbitrage opportunity can vanish within seconds of appearing.

Example of Triangular Arbitrage

Suppose we're working with three currencies: USD, EUR, and GBP. The key to triangular arbitrage is exploiting discrepancies in the currency exchange rates.

Step 1: Identify the exchange rate discrepancy

Let's say the current market exchange rates are as follows:

• USD/EUR = 0.85
• EUR/GBP = 0.70
• GBP/USD = 2.00

These currency rates mean that 1 USD equals 0.85 EUR, 1 EUR equals 0.70 GBP, and 1 GBP equals 1.50 USD.

Step 2: Calculate the implied cross exchange rates

To determine if there's an arbitrage opportunity, the implied USD/GBP exchange rate needs to be calculated and compared with the actual USD/GBP exchange rate. The implied rate can be found by multiplying the USD/EUR and EUR/GBP rates. This is done as follows:

• Implied USD/GBP = USD/EUR x EUR/GBP = 0.85*0.70 = 0.595

Based on the above, 1 USD should be exchangeable for 0.595 GBP for an arbitrage opportunity.

Step 3: Compare with the actual exchange rate

The actual exchange rate for GBP/USD is 2.00, which is equal to a USD/GBP rate of 1/2.00 = 0.5. This is lower than the implied rate of 0.595. Thus, there is the potential for triangular arbitrage.

Step 4: Execute the arbitrage

Let's say the trader has 100,000 USD. The execution of the trades would be as follows:

• Buy EUR with 100,000 USD at the 0.85 rate:

100,000 x 0.85 = 85,000 EUR

• Use the 85,000 EUR proceeds to buy GBP at the 0.70 rate.

85,000 x 0.70 = 59,500 GBP

• With the 59,500 GBP, purchase USD at the 2.00 rate.

59,500 x 2.0 = 119,000 USD.

Step 5: Calculate the profit

The trader began with 100,000 USD and ended with 119,000 USD. Thus the profit is 119,000 - 100,000 = 19,000. Thus, the trader received a triangular arbitrage of 19,000.

Converting Pairs

Currency pair conversion is a fundamental concept in the currency market: the value of one currency is quoted in terms of another currency. Each currency pair represents the exchange rate between two currencies and is used in forex trading to speculate on the relative strength of one currency against another.

The first currency listed in a currency pair is known as the “base currency”; it’s the currency being bought or sold. The second currency is the “quote currency,” which indicates how much is needed to buy one unit of the base currency. In forex trading, buying a currency pair implies buying the base currency and selling the quote currency. Conversely, selling the pair means selling the base currency and buying the quote currency. A direct quote occurs when the foreign currency is the base currency, while an indirect quote is when the domestic currency is the base currency. The bid price is what buyers are willing to pay for the base currency, and the ask or offer price is what sellers are willing to accept. The difference between these prices is the spread. Understanding currency pair conversion is crucial for forex traders since it helps them make informed decisions about buying and selling currencies based on their assessments of market conditions and economic indicators.

Example of Converting Pairs

Suppose a trader wants to convert 10,000 USD to EUR. The example below illustrates the basic process of converting from USD to EUR, taking into account exchange rates and bid-ask spreads. These factors are important for understanding how much foreign currency will be received and for making cost-effective decisions when converting currencies.

Step 1: Check the exchange rate

The trader's first step is to check the exchange rate for EUR/USD. The rates are assumed to be as follows:

• Bid Price: 0.92937 EUR for 1 USD
• Ask Price: 0.93023 EUR for 1 USD

The trader will sell the USD at the bid price, and the trader will pay for EUR at the ask price.

Step 2: Calculate the conversion

Since the trader is buying EUR, the ask price will be used for the calculation. To determine how many euros the trader will receive for 10,000 USD, you'll need to do the conversion as follows: Amount in USD x Exchange Rate (Ask Price) = 10,000 x 0.93023 = 9,302.30 EUR

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 experienced to try it or use a proven automated trading method.