# Triangular Arbitrage Confusion

Hi Everyone! First time poster, glad to join the ranks.

Reading 13 EOC Question 15 is a triangular arbitrage problem with two dealers. One is told they have to convert pounds to pesos in order to pay an invoice. After all the calculations, you are left with the following:

The question asks if an arb op exists.

The solution to the problem states that there is no arb op because although one can purchase from Dealer A at a lower price, one must sell to both dealers at the same price.

My question is how is it not profitable to use fewer pounds to get the same amount of pesos regardless of the sales price?

Thank you!

This really isnâ€™t triangular arbitrage, because there are only two currencies involved, not three.

Starting with GBP, there are four possibilities:

• GBP â†’A MXN â†’A GBP
• GBP â†’A MXN â†’B GBP
• GBP â†’B MXN â†’A GBP
• GBP â†’B MXN â†’B GBP

Here, â†’_i_ means exchanging through dealer i.

Start with GBP 1,000,000 (or whatever), try each of these conversions, and see if you end up with more GBP than you started with. If so, thereâ€™s an arbitrage opportunity. If not, there isnâ€™t.

(Note: you can start with MXN if you prefer, but the results will be the same.)

I see, thank you S2000magician. I stopped at the comparison of the two sets of numbers. Had I continued down the path, I would have realized that one side of the spread never comes into play. Tricky trickyâ€¦

Youâ€™re welcome.

If the situation is :