FX Arbitrage Triangles

CFA Level II Economics
#1

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.

#2

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

#3

Do you have an example?

#4

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.

#5

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?

#6

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

#7

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

:slight_smile:

#8

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.