What Is Cross-Currency Triangulation?
Cross-currency triangulation is the process of converting one currency into another by using a third currency as an intermediary, often because the two original currencies are not actively traded against each other.
This method helps achieve efficient pricing and execution in global markets and is widely used in international trade, finance, and investing. Triangulation became especially important as more currencies gained prominence, such as the euro, reducing reliance on the U.S. dollar but still ensuring smooth currency conversion when direct exchange rates are unavailable or inefficient.
Key Takeaways
- Cross-currency triangulation converts currencies through a third common currency, often bypassing the U.S. dollar.
- It leverages bid-ask spread discrepancies to present profit opportunities in currency exchanges.
- Triangular arbitrage involves trading three currencies to exploit exchange rate differences quickly.
- Major currencies like EUR, GBP, and JPY frequently participate in these opportunities.
- Triangulation often benefits well-capitalized traders using computerized trading systems to exploit momentary arbitrage chances.
Exploring the Mechanics of Cross-Currency Triangulation
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 return to their home currencies.
The euro’s adoption led to the creation of cross-currency pairs like EUR/JPY, GBP/CHF, GBP/JPY, and EUR/GBP. Other cross-currency pairs developed over time for a variety of economic reasons.
Fast Fact
The most frequently traded currencies in the world are:
- USD: United States dollar
- EUR: Euro
- JPY: Japanese yen
- GBP: British pound
- CHY: Chinese yen
- AUD: Australian dollar
- CAD: Canadian dollar
- CHF: Swiss franc
With the European Union’s implementation of Rule 1103/97 of June 17, 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.
Before triangulation, a UK company selling in Switzerland had to convert Swiss francs to USD, then to British pounds. Before cross-currencies existed, repatriations occurred by triangulating pairs with U.S. dollars. Triangulation with crosses gave businesses and traders the means to take advantage of the bid-ask spreads in the interbank market.
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 mere 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.
The cross rate should equal the ratio of the two corresponding pairs. Therefore:
EUR/GBP = EUR/USD ÷ GBP/USD
and
GBP/CHF = GBP/USD × USD/CHF
The basic formula always works like this:
A/B ÷ C/B = A/C
or
A/B * B/C = A/C
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 ÷ NZD/USD offer
AUD/NZD offer = AUD/USD offer ÷ NZD/USD bid
The product of the rate through the bid-ask spread will determine whether a profit opportunity exists.
How Three-Pair Triangulation Works in Currency Trading
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 quote currencies within EUR/GBP and EUR/CHF; they equal the GBP/CHF, but we must make our euro conversions to achieve our objective.
You can find the first exchange rate:
GBP/CHF bid = EUR/CHF bid ÷ EUR/GBP offer
And then calculate that rate in euros:
GBP/CHF offer = EUR/CHF offer ÷ EUR/GBP bid
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.
Demonstrating Triangulation Using U.S. Dollar Pairs
Most U.S. dollar (USD) pairs will hold the USD as the base currency. However, the pair could also be quoted as a European or reciprocal quotation, and the USD would not be considered the base.
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 JPY/USD is 100.00-10, then for a CHF/JPY cross rate, the bid would be:
100.00 x 1.5010 = 115.01 JPY/CHF
The offer would be:
100.10 x 1.5000 = 115.115 JPY/CHF
Practical Uses of Cross Currency Triangulation in Finance
In most instances, triangulation involves profiting from exchange rate disparities. This can be accomplished in many ways.
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.
Important
The most popular triangular opportunities are usually found with the CHF, EUR, GBP, JPY, and USD, in order to convert from euros to home currencies.
Many brokers, including retail currency brokers, now include cross-currency pairs in the dealing rates section of their trade stations. It’s possible to trade GBP/USD as easily as USD/GBP, and EUR/USD as easily as USD/EUR. The difference between the interbank market and the retail side of trading is the spot market. Traders often use the spot market to ensure trade execution, as interbank prices are fleeting.
Traders can capitalize on triangular arbitrage with multiple currency pairs, utilizing 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 work 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.
Many opportunities exist for arbitrage and triangular traders that don’t always include exchange rate arbitrage. Traders may want to capitalize on merger and acquisition opportunities through:
- Currency markets
- Swap trades
- Forward trades
- Yield curve trades
- Options trades
The same opportunities exist for each one of these markets.
Why Does Cross Currency Triangulation Exist?
Cross currency triangulation exists because major companies, importers and exporters, governments, investors, and tourists needed a method to simultaneously transact business in euros while allowing for money and profits to repatriate back to their home currencies.
How Does Including Euros Help Cross Currency Triangulation?
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. The arbitrage opportunities may only last for seconds, but many capitalize on these differences to turn a profit.
How Does Triangular Arbitrage Work?
Triangular arbitrage is used when trading foreign currency pairs to make a profit by exploiting small differences in exchange rates. It involves trading currencies three times. An initial currency is traded for a second currency, the second for a third currency, and the third back to the initial currency. Because these trades must be done quickly, they are usually performed by automated trading software.
The Bottom Line
Cross-currency triangulation converts one currency into another through a third when the two aren’t actively traded against each other, improving pricing and execution. Used across major currencies like EUR, JPY, GBP, and USD, it can also create brief arbitrage opportunities for traders and help businesses efficiently settle international transactions.
