# Triangular arbitrage

Triangular arbitrage is one of the most basic and firstly explained forex trading strategy. The underlying intuition holds that similar products have to sell for the same price. This should hold no matter how they are achieved, either directly or indirectly. If then this means that there’s a (triangular) arbitrage present. As a result, market participants that have detected this can make a (almost) risk free profit by converting one currency into another. This action will push prices back towards each other until the inefficiency has disappeared. As such, these actions by markets participants guarantee that market remain efficient.

## Triangular arbitrage cross rate

To be more specific, suppose you’re looking for a triangular arbitrage opportunity by spotting 3 different currencies: USD, EUR and GBP. Suppose that 1 EUR is worth 1,0910 USD, 1 EUR is worth 0,7413 GBP and 1 USD is worth 0,6794 GBP as shown in the provided Excel spreadsheet below. The EUR-GBP cross rate equals 0,7412 which does not equals the direct EUR-GBP exchange rate of 0,7413. Intuitively, this means that an investor that want to converts EUR to GBP is better of by exchanging directly. An investor willing to convert GBP to EUR better sells his GBP for USD and then USD for EUR since the cross rate is more advantages than.

## Triangular arbitrage example

To check for a triangular arbitrage opportunity, it is required to check whether a profit can be made based on of the 2 trade combinations. The first combination sells USD for EUR, than EUR for GBP and lastly GBP for USD. The second combination sells USD for GBP, GBP for EUR and EUR for USD.As indicated above, the way to exploit a possible inefficiency is to sell EUR for GBP and than exchanging the received GBP back to EUR based on the cross rate.

## Triangular arbitrage bid-ask spread

In practice however, it is not possible to just trade at the midquote price. Investors that want to buy or sell a currency for another need to pay the ask price in case of a buy order, or will only receive the bid price in case of a sell. The difference between the ask and bid price is called the bid-ask spread and serves as a compensation for liquidity providers. As a result, it could be the case that the midquotes don’t fully match. Yet on this apparent mispricing is not exploitable due to the presence of a transaction cost: the bid-ask spread.

## Summary

Triangular arbitrage is a basic forex trading strategy that tries to find and exploit mispricings among currencies. Due to its simplicity, algorithms are continuously looking and exploiting for this profit opportunity and contributes to efficient markets.

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### Triangular arbitrage

Need to have more insights? Download our free Excel file: Triangular arbitrage.