# FX Arbitrage Triangles

Hello all,

I have a problem with FX arbitrage triangles. I can’t get the same arbitrage that I get clockwise, as when I go counter clockwise. This may have something to do with the bid-ask spreads, or maybe I’m just missing something.

How do I know which currency to go to first to get the right answer?

Note, the answers are only off by a few hundred dollars when a million is being converted, but nevertheless it worries me. Thanks.

I have the same question…I end up getting losses with the 1 Million triangular arb situation.

Do you have an example?

Not sure where exactly you’re tripping up, but remeber that with a direct quote, if you are buying, use the bid (Bid and Buy both start with B, if this helps you remember). If your spreads are quoted indirectly, convert them to a direct quote.

Edited to convert to million:

USD:EUR: 0.7000- 0.7010 GBP:USD: 1.7000- 1.7010 GBP:EUR: 1.2000- 1.2010 I can’t seem to get the same amount. I must be using the wrong quote. USD to EUR --> \$1x 0.7= 0.7; EUR to GBP --> 0.7/1.201 =0.58285 GBP to USD --> 0.58285 x 1.7 = 0.9908 \$1M x 0.9908= 990,800 (down 9,200) USD to GBP --> 1/1.701 = 0.58789 GBP to EUR --> 0,58789 x 1.2 = 0.70545 EUR to USD --> 0.70545/0.701=\$1.00635 \$1M x 1.00635 = 1,006,350 (up 6,350) Those numbers don’t seem to line up to me. I guess my questions is, if my math is accurate, if I go the ‘wrong way’ first, do I just try again going the other way?

This is my way:

Sell 1 mil USD to buy GBP =1/10701 =589.7k GBP

Sell GBP to buy EUR = 589.7k *1.2 =705.5k EUR

Sell EUR to buy back USD = 705.5/0.701 = 1006.419

Due to the round up, my approx arbitrage profit = 6.419 k USD

My answer to your question is, if you go the wrong way first, you have to go back the other way for sure.

this is my way to remember better…

this is my strategy for direction…100% guarantee success cos i tried it multiple times…

Third currency ----> Overvalued currency —> Undervalued Currency ----> Third Currency

1. start with the third currency (say \$)

2. then the overvalued currency , pound. you can use (Bid (third currency ) cos you will be selling to buy the overvalued currency, pound ) or Ask (overvalued Currency cos you will be buying pound)

3. Then undervalued currency, Yen… the same way (either bid (overvalued currency pound ) or ask (undervalued Currency) Yen)

4. then original third currency (either bid ( undervalued currency) or ask (third currency))

I put in either cos there are some bid and ask that are not mentioned and you need to change according to what they give.