## Three Way (Triangular) Arbitrage in Forex : Does it Work ?

One of the most interesting ideas in forex trading comes from what would seem to be a fundamental market inefficiency that would seem very easy to exploit by most market participants. Three way arbitrage is a trading technique that seeks to exploit inconsistencies in exchange rates arising from trading activity, inconsistencies that supposedly lead to tradable market inefficiencies. On today’s article I will write a little bit about three way arbitrage, what it is, how it is traded and what the potential rewards may be. I will tell you why I think this cannot be done successfully by regular retail traders and why the rewards – if any – would be much lower than those of a regular long term profitable trading system.
When we have a large group of currencies and all their combinations are available as different currency pairs there is a basic consequence that leads to the trading of several pairs being equivalent to the trading of some crosses. For example if you are buying 1 lot EUR/JPY it would supposedly be equivalent to going long an equivalent on the EUR/USD and going long one equivalent on the USD/JPY. The idea is that your profits are dependent on the EUR/USD and the USD/JPY exchange rates such that the USD exposure is canceled and your net exposure comes from the indirect relationship of the EUR with the JPY. The below graph better explains this idea (using the EUR/USD, GBP/USD and EUR/GBP) (the graph was taken from here, where the concept is also further explained).

The three way arbitrate inefficiency now arises when we consider a case in which the EUR/JPY exchange rate is NOT equivalent to the EUR/USD/USD/JPY case so there must be something going on in the market that is causing a temporary inconsistency. If this inconsistency becomes large enough one can enter trades on the cross and the other pairs in opposite directions so that the discrepancy is corrected. Let us consider the following example :

EUR/JPY = 107.86
EUR/USD = 1.2713
USD/JPY = 84.75

The exchange rate inferred from the above would be 1.2713*84.75 which would be 107.74 and the actual rate is 107.86. What we can do now is short the EUR/JPY and go long EUR/USD and USD/JPY until the correlation is reestablished. Sounds easy, right ? The fact is that there are many important problems that make the exploitation of this three way arbitrage almost impossible.

The first problem is the trading cost. This three way arbitrage is based on taking very small profits from the market and as such it becomes extremely vulnerable to spread variations. A bad spread means that you will lose most of the profitability or that you will need to search for very large arbitrage gaps which are rare and often fall in line with news events when trading spreads are much higher and trading becomes much harder.

The second and biggest problem is execution. Not only will it be extremely hard to get into these orders without any slippage (since your profitability depends on it) but getting out might be even harder as you will be trying to squeeze a very small amount of profit from the market. These arbitrage opportunities are also searched by funds with ultra fast computers and direct connections to banking feeds and therefore the liquidity related to them will dry up terribly fast.