Triangular Arbitrage

I thought I understood this the first time around, however upon review it’s just not clicking with me. What is your approach to constructing the triangle? How do you know which rate (bid or ask) should go on the internal or external triangle when drawing it? For some reason I’m struggling with this and the CFAI books don’t seem to use the same approach. Thanks.

The helpful gimmick I picked up from Schweser is Up the BID, Down the ASK. So if you are quoted \$2.01/GBP BID and 2.02/GBP ASK, you use the bid price going from GBP to and the ask price going from \$ to GBP. That being said, I usually put the ASK amounts on the inside of the triangle and the bids on the outside.

I actually just figured it out. For example, if the quote is Sf per , the arrow going from Sf to uses the ask rate. Then the arrow going from \$ to Sf uses the bid rate. Clearly it’s too early in the morning…

one way i remember is…you’re always getting the worst deal when you’re buying a currency… so if there is a quotation of Bid - Ask of 120 Yen/USD - 140 Yen/USD if you have USD and you’re buying Yen…you’ll take the 120 Yen/USD rate if you have Yen and you’re buying USD…you’ll take the 140 Yen/USD rate remmeber…the bank/other party always gets the better deal…

DO : Draw a triangle DO NOT: Draw an Octagon

The way Schweser/Stalla ask their questions, you end up having to work the triangle four times, and I always violate the three minutes per q rule on these problems. How long does it take everyone else here to work one of these Q’s?

Draw the triangle and mark each corner with a currency. Write both exchange rates between each point along the side. Pick whatever currency they are answering in (usually dollars). Start with \$1 and then go around the triangle in either direction; don’t think about bid/ask, like mumukada said it is the rate that is always going to screw you (the currency dealer makes his living on the spread)…so if you are exchanging dollars for pounds use the exchange rate that will give you the fewest pounds. So start with the dollar and exchange it for the next currency; take that new amount in the new currency and exchange it for the next currency, and finally repeat and bring yourself back to your starting point. If you arrive back with exactly 1 there is no arbitrage, if you end up with more than a dollar you've discovered the correct arb opportunity per unit of starting currency (again usually ), if you end up with less than a dollar there is an arb opportunity you just have to do the same process going the opposite direction. Like I said I start with 1 unit of currency as it is easy to just multiply it by the nominal amount they ask (say 1,000,000)…just easier to keep the numbers manageable. Do a few of them the way I just described and I assure you that you’ll be praying there is a tri-arb problem.

Just assume the worst. If you are buying a currency, you pay the ask. If you are selling it you receive the bid.

Sponge bob you just connected the dots piece for me - if you go around one way and the value is greater than \$1, there is your arbitrage. I hadn’t considered the fact that doing the reverse would get you a negative value. That saves a step.

The one thing to remember if you get the negative value is to do it over again the other direction. DON’T just take loss amount and assume it would be the arb to save time…it will give you a slightly wrong answer, but you can be sure that CFAI will gladly offer you a slightly wrong option as an answer.

Haha of course they will. Thanks for the clarification on this one Bob!

I just go one way and see if I end up with more money. If I don’t, I go the other way. While I’m traveling, I use the rate that gives me a bad deal compared to the deal that the banker is getting.