A Primer on Cross Currency Triangulation

The major significance of cross-currency triangulations–in which foreign money exchanges do not involve the U.S. dollar–results from the fact that many currencies are not typically traded against each other in the interbank market. Major companies, importers and exporters, governments, investors, and tourists, all needed a method to simultaneously transact business in euros while allowing for money and profits to repatriate back to their home currencies. With a realignment of the currency markets due to the adoption of the euro, cross-currency pairs such as the EUR/JPY, GBP/CHF, GBP/JPY, and EUR/GBP, as well as many other cross-currency pairs, developed over time, for many reasons.

Notice that none of the base currencies in the pairs listed above is a nation that has adopted the Maastricht Treaty, and therefore rejected the adoption of the euro. With the European Union’s implementation of Rule 1103/97 on Sept. 11, 1997, formal legality existed for calculating conversions to euros. This rule also established convertibility to six decimal places (rather than just three) and the adoption of triangulation as the legal norm for transacting business in the eurozone. This legality gave investors, traders, and bankers a new means to trade currencies, with a whole host of new profit opportunities. This article will focus on triangulation as a means to trade and profit. 


  • Cross-currency triangulation takes advantage of the discrepancies in the bid-ask spread between non-U.S. dollar exchange rates in order to turn a profit.
  • The most popular triangular opportunities are usually found with the CHF, EUR, GBP, JPY, and U.S. dollars in order to convert from euros to home currencies. 
  • The basic cross exchange rate formula is A/B x B/C = C/B.

How Triangulation Changes the Process

Before triangulation existed, a company in the U.K. selling products in Switzerland and receiving Swiss francs had to sell Swiss francs for U.S. dollars and then sell U.S. dollars for British pounds. Before cross currencies existed, repatriations occurred by triangulating pairs with U.S. dollars. Therefore, triangulation with crosses gave us the means to take advantage of the bid-ask spreads in the interbank market.

On a daily basis, well-capitalized investors and traders can always find discrepancies between bid-ask spreads through the many cross pairs that exist today, thanks to the inclusion of euros. Although these arbitrage opportunities may last for as little as 10 seconds, many capitalize on these differences to turn a profit. Fortunately, computers linked directly to the interbank market can easily meet this challenge and profit through bid-ask spreads around the world from banks that make markets in currencies. 

Cross Exchange Rate Formula

The basic formula always works like this: A/B x B/C = C/B. The cross rate should equal the ratio of the two corresponding pairs, therefore, EUR/GBP = EUR/USD divided by GBP/US, just like GBP/CHF = GBP/USD x USD/CHF.

Cross Exchange Rate Formula Example

For example, suppose we know the bid and offer of AUD/USD and NZD/USD, and we want to profit from AUD/NZD.

AUD/NZD bid = AUD/USD bid divided by NZD/USD offer = a certain rate
AUD/NZD offer = AUD/USD offer divided by NZD/USD bid = a rate

The product of the rate through the bid-ask spread will determine whether a profit opportunity exists.

Three-Pair Triangulation Example

Suppose that we have a three-pair triangulation opportunity such as GBP/CHF, EUR/GBP, and EUR/CHF, in which GBP/CHF is quoted from EUR/GBP and EUR/CHF. Notice the base currencies within EUR/GBP and EUR/CHF; they equal the GBP/CHF, but we must make our euro conversions in order to achieve our objective.

GBP/CHF bid = EUR/CHF bid divided by EUR/GBP offer = a certain rate
GBP/CHF offer = EUR/CHF offer divided by EUR/GBP bid = a certain rate calculated in euros

Whether you earned a profit in this example would depend on exchange rates. Notice the conversion of euros from GBPs and CHFs; triangulating currencies usually involves either euro or U.S. dollar conversions.

Triangulation Example With U.S. Dollar

Suppose we triangulate a U.S. dollar conversion from CHF/JPY; CHF/JPY is simply USD/CHF and USD/JPY. The bid equals the division of the bid of the cross rate terms currency (top), by the offer of the base (bottom). To find the offer, divide the offer of the terms currency by the bid of the base.

If the USD/CHF rate is 1.5000-10 and USD/JPY is 100.00-10 for a CHF/JPY cross rate, the bid would be 100.00 divided by 1.5010 or 66.6223 JPY/CHF; the offer would be 100.10 divided by 1.5000 or 66.7337 JPY/CHF.

Why Triangulate?

In most instances, triangulation involves profiting from exchange rate disparities. This can be accomplished in many ways. For example, suppose you institute two buys on a certain pair and one sell, or you sell two pairs and buy one pair. Any number of triangulation opportunities exist every day from banks in Tokyo, London, New York, Singapore, Australia, and all the places in between. These same opportunities may exist around the world, trading the exact same pair. The most popular triangular opportunities are usually found with the CHF, EUR, GBP, JPY, and U.S. dollars, in order to convert from euros to home currencies. 

What is noticeable, more and more, is that many brokers, including retail currency brokers, are including cross currency pairs in their dealing rates section of their trade stations. One can now trade the GBP/USD as easily as the USD/GBP, and the EUR/USD as easily as the USD/EUR. The difference between the interbank market and the retail side of trading is the spot market. Many may want to transact their business through the spot market where they know their trade will be executed because prices in the interbank market are so ephemeral.

Traders can easily transact any triangular arbitrage opportunities with two or three currency pairs crossed by many nations, as well as take advantage of any other bid-ask spread opportunities. For the small retail trader with limited funds, this would probably work. However, for the well-capitalized trader, it may not because the spot market doesn’t always reflect exact exchange rates. Larger traders may have to wait on certain spot prices before transacting their business–a wait they may not be willing to risk when it comes to profits.

The Bottom Line

Many opportunities exist for the arbitrage and triangular traders, that don’t always include exchange rate arbitrages. Traders may want to capitalize on merger and acquisition opportunities through the currency markets, swap trades, forward trades, yield curve trades, and options trades. The same opportunities exist for each one of these markets. 

Leave a Reply

Your email address will not be published. Required fields are marked *