How triangular arbitrage works in currency markets

Currency prices are linked to each other. If the links get out of line, even for a moment, a trader can loop through three currencies and end up with more money than they started with. This is triangular arbitrage. This page explains how it works and why it is rare.

Quick answer

Triangular arbitrage is a trading method that takes advantage of a price mismatch between three currencies. A trader converts currency A into B, B into C, and C back into A. If the three exchange rates are not consistent with each other, the trader ends with more of currency A than at the start. Such gaps are tiny and close within moments, so it is mostly done by fast computer systems.

Key takeaways

• Triangular arbitrage loops through three currencies.
• It works only when cross rates are out of line.
• The profit on each loop is very small.
• Gaps close within moments, so speed is critical to it.
• Costs like spreads often remove the gain for ordinary traders.

What is triangular arbitrage?

Arbitrage means buying and selling the same thing in different places or forms to earn from a price difference. In this form, the 'thing' is money in three currencies, and the different forms are the three exchange rates between them.

In an efficient market, the rate between any two currencies should match what you get by going through a third currency. This implied rate is called the cross rate. When the quoted rate and the cross rate differ, an arbitrage chance appears.

A simple example

Suppose the rates are: 1 US dollar = 84 rupees, 1 euro = 1.10 US dollars and 1 euro = 93 rupees. Using the first two rates, the cross rate for the euro should be 84 x 1.10 = 92.40 rupees. But the market quotes 93 rupees. The gap is the opportunity.

A trader starts with 92,400 rupees and buys 1,100 US dollars. They use those dollars to buy 1,000 euros. Then they sell the 1,000 euros at 93 rupees each and get 93,000 rupees. The loop gives a gain of 600 rupees before costs.

Why are such chances rare?

Banks and trading firms run computer programs that watch thousands of prices every second. When a gap appears, they trade at once, which pushes the rates back in line. Most gaps last only fractions of a second.

In real markets, the numbers are also much smaller than in the example. Bid-ask spreads, fees and the time taken to place three trades can easily remove the gain. This is why the strategy is mainly used by firms with very fast systems.

Is it relevant in India?

In India, retail currency trading is allowed only in permitted contracts on recognised exchanges, such as rupee pairs and certain cross-currency pairs in the NSE currency derivatives segment. Trading with unauthorised forex platforms is not allowed under RBI rules.

The idea is still useful for understanding how currency prices stay linked. It also shows how arbitrage, by many traders, helps keep markets efficient. Arbitrage does not guarantee profit once costs and timing risk are counted.

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