A Primer On Cross Currency Triangulation

The major significance and importance of cross currency triangulation is due to the fact that many spot currency cross pairs are not traded against each other in the interbank market as standard pairs. 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. 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.

Notice that none of the base currencies in these pairs is a nation that has adopted the Maastricht Treaty, and therefore rejected adoption of the euro. With the European Union's implementation of Rule 1103/97 on Sept. 11, 1997, a formal legality existed for calculating conversions to euros. This rule also established convertibility to six, then three, decimal places and the adoption of triangulation as the legal norm for transacting business in the eurozone. What this legality gave to investors, traders and bankers was a new means to trade currencies, with a whole host of new profit opportunities. For this article, the focus will be about triangulation as a means to trade and profit. (For background reading, check out our Forex Tutorial.)

How Triangulation Changes the Process
Before triangulation existed, a company in the U.K., selling 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 a means to take advantage of bid-ask spreads in the interbank market.

Well-capitalized investors and traders can always find discrepancies, on a daily basis, 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. 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. (To learn more, see Arbitrage Squeezes Profit From Market Inefficiency.)

Example Number One
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.

Example Number Two
Suppose that we have a three-pair triangulation opportunity such as GBP/CHF, EUR/GBP and EUR/CHF, where 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.

Example Number Three
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 paces in between. Yet, 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. (To learn more, read Forex Currencies: Currency Cross Rates.)

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.

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, in terms of 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 option trades. The same opportunities exist for each one of these markets.

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