# Triangular Arbitrage: Definition and Example

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> **Definition**
>
> Triangular arbitrage is a type of forex trading that involves exchanging one currency for a second, then trading it for a third, and then finally exchanging it back into the original currency.

## What Is Triangular Arbitrage?

Triangular arbitrage is a type of foreign exchange ([forex](https://www.investopedia.com/best-brokers-for-forex-trading-4587882)) trading that involves exchanging one currency for a second, then trading it for a third, and then finally exchanging it back into the original currency. The goal of this trading pattern is 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.

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. If the transaction costs are low, the trader could net a profit from this exchange.  

### Key Takeaways

*   Triangular arbitrage involves buying and selling currencies across three different currency pairs, ending up back in the original currency.
*   It is a form of low-risk profit-making by currency traders who exploit exchange rate discrepancies through algorithmic trades.
*   To be profitable, trades using triangular arbitrage should be large and performed quickly.
*   Exploiting triangular arbitrage opportunities can lead to more efficient markets.

## Understanding Triangular Arbitrage

Triangular arbitrage is used in [foreign exchange](https://www.investopedia.com/terms/f/foreign-exchange.asp) trading to exploit differences in exchange rates across different markets. It involves three trades: an initial currency is exchanged 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.”

> **Important**
>
> Arbitrage is a trading strategy in which an asset is bought in one market and simultaneously sold in another market. The goal is to profit from small differences in price across the two different markets.

Exchange rates should synchronize across all currency pairs, but because of market inefficiencies, they sometimes do not. These can be caused by:

*   Delays in moving market information
*   Differing levels of liquidity across markets
*   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. These forex traders use sophisticated technology capable of instantaneously identifying and acting on arbitrage opportunities.

## Converting Currency Pairs

Currency pair conversion is a fundamental concept in the forex market: the value of one currency is quoted in terms of another currency. Each [currency pair](https://www.investopedia.com/terms/forex/f/foreign-currency-pairs.asp) 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 trader's first step is to check the exchange rate for EUR/USD. These rates might be:

*   **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. 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

## Example of Using Triangular Arbitrage

Triangular arbitrage takes this a step further by quickly converting between three currency pairs, such as the pairs of USD (U.S. dollars), EUR (euros), and GBP (British pounds). 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 x 0.70 = 0.595

The implied exchange rate indicates that 1 USD should be exchangeable for 0.595 GBP.  

### Step 3: Compare With the Actual Exchange Rate

The actual exchange rate for GBP/USD is 2.00, which is equal to:

> 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 trader would buy EUR with 100,000 USD at the 0.85 rate:

> 100,000 x 0.85 = 85,000 EUR

The trader would then 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, the trader would then 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.

## Automated Trading Platforms and Triangular Arbitrage

In the above example, the trade would actually be executed by the algorithmic trading platform that the trader was using, rather than by the individual trader, to take advantage of these price discrepancies before they are corrected.

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](https://www.investopedia.com/articles/trading/11/automated-trading-systems.asp) allow a trader to set rules for entering and exiting a trade, and the computer will automatically conduct the trade without the trader needing to take additional action.

Engaging in triangular arbitrage is only feasible using this type of 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.  

> **Warning**
>
> The speed of algorithmic trading platforms and markets can also work against traders. For example, 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.

## What Is the Triangular Arbitrage Algorithm?

A triangular arbitrage algorithm is an automated trading program that finds and executes triangular arbitrage opportunities. This is the only way to effectively make this kind of trade, since market discrepancies are usually resolved too quickly for manual trades to take advantage of them.

## Is Crypto Triangular Arbitrage Possible?

Triangular arbitrage identifies price differences for trading opportunities. It is possible that trading three cryptocurrencies would 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, this type of trade is only feasible using a proven automated trading method. It should only be used by experienced traders.  

> **Article Sources**
>
> 1.  R. Dubil. "An Arbitrage Guide to Financial Markets." John Wiley & Sons, 2019. Pages 110-111, 129-130.