# Price inequalities in Forex?

My understanding of forex is limited so please bear with me.

I believe foreign currency rates are traded in pairs, e.g. USD vs GBP at a price set by supply and demand.

Does this mean that it can lead to inequalities? For example if we have GBP,USD and EUR. If 1 GBP = 2 USD, and 1 USD = 2 EUR.. then logically 1 GBP should equal 4 EUR.

However if they are traded pairwise, this need not necessarily be the case. I imagine it tends towards that price as an equilibrium, but in practice there must be a lot of the time when you have this inequality.

Then the question is, is this property exploited for financial profit?

Such inequalities only exist for very short periods of time, precisely because people make money exploiting them. Read up on arbitrage.

• If by short periods of time, you mean milliseconds at best, I agree. Too short a time for you or me to exploit the pricing. Commented Sep 26, 2011 at 19:24
• Heh, only read your comment after posting, I happened to choose similar wording again. Commented Sep 27, 2011 at 9:57

You are right, if by "a lot of time" you mean a lot of occasions lasting a few milliseconds each. This is one of the oldest arbitrages in the book, and there's plenty of people constantly on the lookout for such situations, hence they are rare and don't last very long. Most of the time the relationship is satisfied to within the accuracy set by the bid-ask spread.

What you write as an equality should actually be a set of inequalities. Continuing with your example, suppose 1 GBP ~ 2 USD, where the market price to buy GBP (the offer) is \$2.01 and to sell GBP (the bid) is \$1.99. Suppose further that 1 USD ~ 2 EUR, and the market price to buy USD is EUR2.01 and to sell USD is EUR1.99. Then converting your GBP to EUR in this way requires selling for USD (receive \$1.99), then sell the USD for EUR (receive EUR3.9601). Going the other way, converting EUR to GBP, it will cost you EUR4.0401 to buy 1 GBP. Hence, so long as the posted prices for direct conversion are within these bounds, there is no arbitrage.

• This would easily be the best answer if you provided an example of those inequalities. Someone without knowledge of bid/ask spreads might not understand how that arbitrage would work Commented Sep 29, 2011 at 0:34