So you want to understand triangular arbitrage...
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Triangular arbitrage is more simple than it sounds
A friend asked me about triangular arbitrage the other day, and I figured here was as good a place as any to explain what it is and how it works. Triangular arbitrage is a term used in currency trading, when you trade three currency pairs to generate a risk-free profit.
Arbitrage sounds great but is hard to do
This sounds like a great opportunity! Who doesn’t want a risk-free profit? The problem is that currency markets are very liquid, spreads are very small, and arbitrage opportunities are fleeting. So, though the profits are risk-free when the opportunity arises, don’t bet the bank (or your retirement accounts) on being able to pull this off. Generally these trading opportunities are only available to professional currency traders running sophisticated software on powerful computers with fast connections.
How it works
But the general concept isn’t hard to understand. Assume you have three currency pairs: Euro/USD, Euro/British Pounds, and USD/GBP. Assume also that the exchange rates are as follows:
EUR/USD: 1.01
EUR/GBP: 1.37
USD/GBP: 1.75
The first thing to note is that the third exchange rate, USD/GBP, is greater than the cross rate. The cross rate here is that exchange rate which does not include the USD, namely, the EUR/GBP exchange rate of 1.37. That relationship (third exchange rate is greater than the cross-rate) is what tells you that there is a triangular arbitrage opportunity.
And now the math
The math is pretty simple:
Assume you start with $1 million USD.
Sell dollars for euro: $1 million USD * 1.01 = 1,010,000 euro.
Sell euro for pounds: 1,010,000 euro / 1.37 = 737,226.28 pounds.
Sell pounds for dollars: 737,226.28 pounds * 1.75 = $1,290,145.99
Assuming no transaction costs and no taxes, your profit on that trade is $290,145.99.
The caveat: this is a contrived example!
It should be noted that this is a pretty contrived example, and that the actual profits available in a triangular trade are likely not to be close to $300,000 on a $1 million outlay.