Triangular Arbitrage

Triangular arbitrage refers to a method of trading wherein traders trade in currencies to register profits through discrepancies in the value of three currencies. The route to arbitrage is determinable by exchanging one currency for another to make profits from the differences in their market values.

The triangular arbitrage works on algorithms and advanced computer programs that can quickly determine these discrepancies and assist traders in registering profits. Such arbitrage of consecutive buying and selling of three currencies from one market to another and in large quantities allows traders to make low-risk profits through exchange rate discrepancies.

• Triangular arbitrage is a method of trading in currencies or other assets to book profits by raising the difference in the stated exchange rate and cross exchange rate of two currencies.
• The opportunity to make profits through triangular arbitrage is possible by calculating cross-exchange rates of two currencies against a third currency, i.e., the U.S dollar.  
• Triangular arbitrage opportunities arise and vanish quickly due to many competitive traders who detect discrepancies using algorithmic programs. Thus, a high demand leads to the adjustment of the overvalued currency. 

Triangular arbitrage refers to the discrepancies in the cross-exchange rate of currencies. It occurs when there is a sudden change in the exchange rates of currencies that do not match the cross-exchange rate, and the difference occurs. The cross-exchange rate is a method of valuing two currencies against a third currency.

The third currency in foreign exchange is usually the U.S Dollar, while the other two currencies are determinable against the dollar value. So, for instance, if three currencies are the Great Britain Pound (GBP), Euro, and U.S Dollar, then both GBP and Euro will be valued in terms of the U.S Dollar.

The discrepancies in the exchange rates usually occur due to the overvaluation of money in one market over another. Although, the differences in the prices of two currencies against a third currency are by a fraction of a cent, thereby encouraging traders to trade capital or money in large amounts to multiply their profits.

Thus, to book higher profits, the traders of currencies or assets determine the maximum price difference in the cross-exchange rate of two currencies. Thus, if the exchange rates of all three currencies do not align, it incentivizes the trader to convert one currency into another most profitable one.

Banks and individual investors engaging in foreign exchange or currency markets rely on fast-working algorithms and trading platforms. It allows them to automate certain trading processes and register profits even when exchange rate discrepancies occur for a few seconds.

However, like all other forms of trading in assets, triangular arbitration also comes with certain risks. For instance, hidden transaction costs might eat into the profits or reduce margins for the traders. Additionally, traders may lose money or be unable to lock in profits due to the difference in seconds.

Firstly, the triangular arbitrage calculation requires determining the difference between the stated value (€/£) and the cross-exchange value of two currencies, i.e., between $/£ and €/$. This formula helps determine the value of two currencies against per unit of the third currency. For instance, if there is an overvaluation of €/£, then the value of the euro (€) increases against the third currency or base currency, the U.S Dollar. 

Consequently, in foreign exchange markets today, traders tend to compare the changes in the values of the currencies against the U.S Dollar.

Therefore, in triangular arbitrage, opportunities are available for some of the most traded currencies in the world, such as euros, pounds, and Yen, against a third currency, i.e., the U.S dollar. However, opportunities for triangular arbitrage in forex markets rarely occur as many competitive traders seek to make huge profits from these discrepancies. 

Thus, it is extremely difficult to book profits due to incurring discrepancies due to the presence of an extremely large number of traders in the market, who use a triangular arbitrage algorithm to detect discrepancies and wish to take advantage of them. However, the discrepancies that also occur quickly disappear as the traders start to trade in the overvalued currency leading to high demand, thereby adjusting prices quickly. 

Thus, even before calculating or determining discrepancies in the exchange rates, these individual and institutional traders tend to do thorough background research. It helps these traders to dig for background information or policy changes that may lead to such discrepancies in the rates.

Let us look at a few examples to understand how triangular arbitration, with the help of cross-exchange rates,

Example #1

John is a trader in the U.S forex market and estimates an overvaluation in the present value of the euro (€) against the present value of the Great Britain Pound (GBP, £).

He calculates the discrepancies arising in the market through the cross-exchange rate formula by,

1. Multiplying the value of the euro per dollar with the pound per dollar will reveal the exchange rate difference between the euro and GBP,

• Euro/ Pound (€/£) = 1.17 x 1.69

                                          = € 1.9773

Thus, John tries to determine how he can exploit this slight increase in the value of the euro against the U.S dollar and earn profits by trading $ 1 million by applying the triangular arbitrage method. Let us look at the options available to John,

• John can convert $1million dollars into euros = $10,00,000 x 0.826 = € 826,000     
• He will then sell these euros and convert them into pounds at the new exchange rate,

= € 826,000/ 1.36

          = £ 607,352.94

• Thus, when he converts pounds back into U.S dollars, he receives = £ 607,352.94 x 1.69 = $1,026,426.468

Thereby, with this transaction route, a triangular arbitrage opportunity is possible that allows John to make gains worth = 1,026,426.468 - 10,00,000 = $ 26,426.468

Example #2

For instance, a Japanese trader sees a triangular arbitrage opportunity due to the rising difference between the stated exchange rate and cross-exchange rate of Japanese Yen (JPY) and Euros. Thus, he uses the third currency, i.e., the U.S dollar, to compare the cross-exchange rate.

Firstly, the trader calculates the cross-exchange rate by multiplying $/JPY with €/$. It helps him determine the difference between the exchange rate of the two as their values change against the dollar,

• €/JPY = $ 0.0096 x €1.05

           = € 0.01008

Thus, trader detects a rise in the value of the Japanese Yen against a devaluing Euro by a fraction. Hence, the Japanese trader converts a large sum, i.e., JPY 50,000, to multiply his profits by this slight difference. Thus, applying a triangular arbitration strategy aids the trader in earning higher returns from the overvaluing Yen.

• First, he converts the JPY into dollars = JPY 50,000 x $ 0.0096 = $ 480

• Then he converts $ into Euros = $480 x €1.05 = € 504

• Finally, the trader converts the euros into the initial currency, i.e., JPY, to cash profits = € 504 / 0.0068 = JPY 74,117.6470

Thereby, the Japanese trader will earn profits worth JPY 24,117.647 through triangular arbitrage on an initial investment worth JPY 50,000. 

This article has been a Guide to What is Triangular Arbitrage & its meaning. Here we explain how such arbitration works, along with the calculation and examples. You can also go through our recommended articles on corporate finance –

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