Triangular arbitrage made extremely easy

let’s say you are given three bid-ask quotes as given below 1) a/b 2) b/c 3) a/c (suppose if last one is c/a you can easily convert it to a/c by taking new bid = 1/ask & new ask =1/bid. Remember that finally we should have 1 * 2 = 3 format i.e. a/b * b/c = a/c format) Step-1 find cross currency rate from 1 & 2 quote. As i have mentioned above if 1 * 2 = 3 then a/c bid-ask quotes are simply bid1 * bid2 - ask1*ask2 Step 2: now compare your calculated quote (step1) with the given quote (3). Remember that we can sell at bid and buy at ask so use the following formula to calculate triangular arbitrage profit. ((Max bid / Min ask) - 1) x principal i hope this will help someone to get easy marks. I found it somewhat difficult so i tried to come out with this simple approach. Good thing is that this will always work irrespective of whether you use 2 * 1 = 3 or 1 * 3 = 2 !! I may not get time to get back to this thread again so please do not feel bad. BTW This is my first post to this forum & i am posting this from mobile so not sure if it will come in right format. Best of luck for exams.

BTW one can test this on one of the mock test question which asks you to calculate arbitrage profit. :slight_smile:

I’m sticking to the worse off method. If I get it wrong, I get it wrong. Not worth the time and effort especially at this stage.

yes, there is no time but this may help in future to some one who want to check his answer using alternate method.

“Up the bid and down the ask.” Lay out path you want to follow, say USD->AUD->MXN->USD Lay out the 3 currency pairs that achieve this. You can do it as given in the item set, say: USD/AUD -> MXN/AUD -> MXN/USD Don’t even try to start flipping them around. Use what is given exactly as given. Now follow the path you originally laid out. - Since you want to go from USD -> AUD and since the USD is “on top”(USD/AUD) you use the ask price(“down the ask”) - Next you want to go from AUD to MXN and since the AUD is on the bottom and you want to go up to MXN(MXN/AUD), you use the bid price(“up the bid”) - Lastly, since you now want to convert your MXN back to USD, and since the MXN is on top, you use the ask price. (“down the ask”) Now you can compare to the original amount to see what the profit is. If none, go the other way (USD->MXN->AUD->USD) and see if you get a profit that way. Steps will be the reverse: MXN/USD -> MXN/AUD -> USD/AUD -> - “Up the bid”, use the bid price on MXN/USD(going “up” from USD to MXN) - “Down the ask”, use the ask price on MXN/AUD(going “down” from MXN to AUD) - “Up the bid”, use the bid price on USD/AUD(going up from AUD to USD) If none of the 3 answers is “no profit”, you know one path will give you the right answer. If “no profit” is a choice, and you don’t get one either way you know that’s the answer. Another tip to that helps is if what you have at each current step is in the numerator, use the ask price. Remember you want to go to the currency in the denominator(“down”). Reverse if what you have is in denominator. You use the bid price because the currency you want to go to is in the numerator(“up”) Once I learned that method it’s really simple. I’ve tried them all, the benefit of this one is you don’t need to manipulate the bid/asks as given in the item set. They could flip the quotes in any form and as long as you remember up the bid, down the ask you have your approach already completed. You’ll know what price to use and assuming you know whether to multiply or divide by the rate(the easy part) you’ll get the answer hopefully on the first path you chose. Once you start getting into flipping ask quotes to bid quotes, etc that’s where you get lost and make mistakes. That’s why I couldn’t mess with the approach in the OP. Search for it on the board if my explanation wasn’t clear enough. I wasn’t about to give away the easy points. I hope this helps someone.

This works if you are given USD/AUD, but what if you are given AUD:USD in bid-ask form. How do you convert that bid-ask quote into a USD/AUD bid-ask qoute? Also, just to confirm when you “up-the-bid” you multiply and divide when you “down-the-ask”? Thanks!

USD/AUD = AUD:USD if you’re confused on that you might want to re-read the opening piece of forex… that’s the basics… You probably do want to get into the older format if they use that FC:DC stuff on the exam. Will make it easier to follow the steps. If you mean what if you’re given AUD/USD in the above example, follow same path initially: USD->AUD->MXN->USD You’re given the following pairs(only change is I flipped opening one based on your question) AUD/USD -> MXN/AUD -> MXN/USD You start with USD: - You want to go up from USD to AUD, so “up the bid” - You now want to go from AUD to MXN so “up the bid” - Last step, you want to go from MXN to USD so “down the ask” If you compare to my opening example, I only changed the first step. This is the beauty of this method. They could give you a combination that will make your head spin if you try to start flipping bid/asks around. Try it yourself flipping all 3 rates. For your second question, I honestly have not tried to remember that step. You might be right but I’d rather lay out what prices to use first and the rest I can figure out on the fly. It will be obvious once you have the correct price in front of you. Try it with a few examples.

USD/AUD = AUD:USD, i understand that, but my point was more if you are given: AUD:USD = $1.2210-20 how do you convert that to USD/AUD bid-ask quote?

Isn’t AUD:USD = $1.2210-20 the exact same as USD/AUD = $1.2210-20 ? It’s only the notation that changes. Now if you wanted USD:AUD(aka AUD/USD) you’d take the inverses of the bid/ask and then flip them so 0.8183-90 Try it out and confirm. This is why I say don’t even bother. You’re already adding an unecessary step and can get confused.

usd/aus = aus:usd - it is the same exact bid ask spread, the only thing that changes is the notation.


I have made a youtube video explaining triangular arbitrage in a very straightforward and simple way. Check it out here, and let me know what you guys think and if you found it useful.

I cant post links but search for this vid: CFA Level 2 - Economics | Arbitrage Triangle Explained

Kind Regards

This reply comes about 10 years too late to be of practical value.