Triangular Arbitrage

What is Arbitrage?

Arbitrage trading is an opportunity in financial markets when similar assets can be purchased and sold simultaneously at different prices for profit. Simply put, an arbitrageur buys cheaper assets and sells more expensive assets at the same time to take a profit with no net cash flow. In theory, the practice of arbitrage should require no capital and involve no risk. In practice, however, attempts at arbitrage generally involve both capital and risk.

According to the efficient markets hypothesis, arbitrage opportunities shouldn't exist, as during normal conditions of trade and market communication prices move toward equilibrium levels across markets. Conditions for arbitrage arise in practice, however, because of market inefficiencies. During these instances, currencies can be mispriced because of asymmetric information or lags in price quoting among market participants.[1]

In currency markets, the most direct form of arbitrage is two-currency, or "two-point," arbitrage. This type of arbitrage can be carried out when prices show a negative spread, a condition when one seller's ask price is lower than another buyer's bid price. In essence, the trader begins the trade at a profit. This circumstance is rare in currency markets but can occur on occasion, especially when there is high volatility or thin liquidity.

Additionally, it has become even more rare in recent years due to high-frequency trading, where computer algorithms have made pricing more efficient and reduced the time windows for such trading to occur.

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What is Triangular Arbitrage?

Triangular arbitrage (also known as three-point arbitrage or cross currency arbitrage) is a variation on the negative spread strategy that may offer improved chances. It involves the trade of three, or more, different currencies, thus increasing the likelihood that market inefficiencies will present opportunities for profits. In this strategy, traders will look for situations where a specific currency is overvalued relative to one currency but undervalued relative to the other.

Researchers have found that opportunities for triangular arbitrage arise up to 6% of the time during trading hours. One commonly traded trio of arbitrage currencies is EUR/USD, USD/GBP and EUR/GBP. However, any three or more actively traded pairs can be used.[2]

The process of completing a triangular arbitrage strategy with three currencies involves several steps:

  1. Identifying a triangular arbitrage opportunity involving three currency pairs,
  2. Identify the cross rate and implied cross rate
  3. If a difference in the rates from step 2 is present then trade the base currency for a second currency
  4. Then trade second currency for a third. At this stage, the trader is able to lock in a no-risk profit due to the imbalance that exists in the rates across the three pairs,
  5. Converting the third currency back into the initial currency to take a profit.

To identify an arbitrage opportunity, traders can use the following basic cross-currency value equation:

A/B x B/C x C/A = 1, where A is the base currency, and B and C are the two counter-currencies to be used in the arbitrage trade. If the equation does not equal one, then an opportunity for an arbitrage trade may exist.[3]

For an example of a trade, we can consider rates found on the following currency pairs: EUR/USD 1.1325, EUR/GBP 0.7805, GBP/USD 1.4528.

In the first step, the trader buys €10,000 at 1.1325 to obtain the equivalent of US$11,325. In the second portion of the trade, the trader sells €10,000 at 0.7805 to obtain £7,805. Finally, the trader uses the British pounds to buy dollars at a rate of 1.4528, yielding US$11,339.

Subtracting the amount obtained from the initial trade from the final amount (US$11,339 - US$11,325) would produce a positive difference of US$14 per trade.

As with other trades, however, attempts at arbitrage can be subject to risks. This includes execution risk, where the amount quoted is unable to be filled by a broker. If in the above trade, for example, the euro had moved to 0.7795 against the pound before the trader locked in a price, the action would produce a loss (US$11,324.58 – US$11,335) of about US$10.42 per trade.[4]


Arbitrage opportunities may arise less frequently in markets than some other profit-making opportunities, but they do appear on occasion. Economists, in fact, consider arbitrage to be a key element in maintaining fluidity of market conditions as arbitrageurs help bring prices across markets into balance. "According to the law of one price – a foundation of modern finance – arbitrage activity should ensure that prices of identical assets converge, lest unlimited risk-free profits may arise," economist Paolo Pasquariello noted in a study on financial market dislocations.[5]

The use of triangular arbitrage can be an efficient way to take profits when market conditions allow, and incorporating it into one's playbook of strategies may boost chances for gains. Traders, however, need to be aware that competition inherent in the forex market tends to correct price discrepancies very rapidly as they appear. As a result, the emergence of such opportunities may be fleeting—even as short as seconds or milliseconds. Because of this, anyone interested in adopting an arbitrage strategy will need to be have a system in place to monitor the market closely during extended periods in order to potentially take advantage of such opportunities before prices move to find an equilibrium.

Trading on margin carries a high level of risk and losses can exceed deposited funds.

Any opinions, news, research, analyses, prices, other information, or links to third-party sites are provided as general market commentary and do not constitute investment advice. FXCM will not accept liability for any loss or damage including, without limitation, to any loss of profit which may arise directly or indirectly from use of or reliance on such information.

FXCM Research Team

FXCM Research Team consists of a number of FXCM's Market and Product Specialists.

Articles published by FXCM Research Team generally have numerous contributors and aim to provide general Educational and Informative content on Market News and Products.



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