Economics Arb question

I’m stuck on arb triangles and when to use bid or ask, and which way to go around the triangle to profit on an arb opportunity. I was hoping somebody might be able to explain this simply to me. eg. Bid-ask quotes: USD:EUR 0.7-0.701 GBP:USD 1.7-1.701 GBP:EUR 1.2-1.201 Start with 1m USD… I realise that the cross rates mean that there is an arb opportunity. The answer is that you: 1) convert the 1m USD to GBP at the ask 2) convert the GBP to EUR at the bid 3) convert the EUR into USD at the ask and make 6,372 USD profit. I understand that the bid-ask is what the broker buys and sells currency is, respectively - right? But, as we’re the ones changing the currency, aren’t we always buying and hence using the ask price? Also, how do you know which way around the triangle to go to start with? I realise that these might be simple questions, and would greatly appreciate any help. Thanks.

The concept behind triangular arbitrage is simple, but if they throw bid-ask spreads at you in the problem, it’s going to be a bear to solve, and quite honestly it’s going to take some luck in choosing the right pair to analyze in the right direction to solve it quickly. More likely, they will ask you the problem without bid/ask rates, which simplifies the problem, and the penalty for choosing the wrong pair to start with (mostly a luck issue) is about 10 seconds, rather than 30.

Try to think it through like you’re actually executing the trade. “I am selling dollars for Pounds” Every time you calculate it use the number that results in less. So if you’re buying Pounds, it costs 1.701 dollars. If you’re selling Pounds for Euros, you get the lower one - 1.2 euros. Just remember, the bid-ask spread screws you, so always choose the number that will result in making you the least money.

I haven’t looked at one of these in months and wanted to see if I could still do it without referencing any notes. It was still as easy it was then b/c of a system I developed to remember how to do this: 1. If you hold the base currency (ie. the USD in USD:EUR) use the bid. Otherwise use the ask 2. Always multiply by the bid and divide by the ask That’s it! use that info and work the problem one way, if that doesn’t work go the other way.

Thank you all!