Traingular Currency with Bid-Ask Spread

This is going to be a crappy question because I am using last year’s Schweser book. But one of the challenge questions (#13) asks for the arbitrage profit starting with $1 mil USD says:

USD:EUR: .7-.701

GPB:USD: 1.7-1.701

GBP:EUR: 1.2-1.201

So for this one the solution says to go from USD to GBP at the ask, then go from GPB to EUR at the bid, and then finally go back from EUR to USD at the ask. Fair enough, this makes sense to me.

But then there is an example within the Schweser text starting with 1 mil pesos:

AUD:USD .6-.6015

USD:MXN: 10.7-10.72

AUD:MXN: 6.3-6.3025

Now, when you go around the triangle, you buy AUD with MXN at the ask, you sell AUD for USD at the bid, but now you sell USD for MXN for at the bid.

The part I bolded, I just dont understand. In the end of chapter question, we had to buy USD from EUR to get to the back of the triangular. But now in the question in the text, we had to sell USD for MXN at the bid to get back to the top of the triangle. Why the difference? I feel like I can do the triangular arbitrage fine without the bid ask spread, but I just cannot seem to find a way to do it with a bid-ask spread, everytime I think I understand, I do it wrong. Any help is appreciated.

where do you end up with lower … that is the number to use.

1 AUD = 0.6 - 0.6015 USD

1 USD = 10 - 10.72 MXN

1 AUD = 6.3 - 6.3025 MXN

Start with 1 MXN

Buy AUD -> 1/6.3025

Buy USD -> multiplying by 0.6015 will give you more. So that is not the way to go. Use the 0.6

so now you have 1/6.3025 * 0.6 USD

Now you need MXN again. Again need to multiply by 10 otherwise you will end up with more.

1/6.3025 * 0.6 * 10 = 0.9520

Interesting tip, I will have to try it on a question to get comfortable with it. So the first move is always to buy at the ask, and then the next two moves are done at either the bid or the ask, depending on whichever one gives you a lower amount (but still makes an arbitrage profit)? What is the rationale as to why that would work? Thanks a ton!

even when you start - depends on which way you are going.

if you were in the above example going MXN to USD

Since 10 - 10.72 was the quote - buying USD with 1 Million Pesos would give you a lower amount when you divide by 10.72 not when you divide by 10. So again that rule applies.

If you had 1 Mill AUD - and were buying USD -> multiply by 0.6 would be the way to go there.

The reason for that is when someone wants to sell you - you lose in the process. That is how the exchange rates are set up.