Can anyone please teach me how to calculate profit in triangular arbitrage?. I am not getting the concept of cross rates with bid ask spread.
Just imagine you have 1 of the starting currency, start translating it in the triangle until you get back to your starting currency. Remember, the broker always screws you, so take whichever quote (bid or ask) gives you less. If you wind up with a number less than 1 when you’re back to the starting currency, you went the wrong way.
I’m not sure what the CFA II says but i’m interested because I work in forex and this can be a confusing subject matter. In fact, it’s pretty much useless in practice with today’s electronic trading, but I’ll try to explain it as I learned it. Simplify this first by getting rid of bid/ask spreads. The first thing you have to look at is what currency pairs are involved. I’ll use one with both quoting conventions American/European. Where American is how many dollars buys the specific quantity while European is how much of a currency will buy 1 dollar. This can add to confusion though, so I’m sorry if I did, but European countries prior to the EUR were quoted how many of a currency would buy 1 dollar. i.e. How much Italian Lire would buy $1. Now it’s actually quoted in American terms, how many USD buys 1 EUR. In any case, if we take USD|CHF and EUR|USD, two DIFFERENT quoting conventions and let’s say USD|CHF = 1.5000 and EUR|USD = 1.5000… The left currency is the priced currency and the right currency is the pricing currency so… 1.5 CHF buys 1 USD and 1.5 USD buys 1 EUR In high school chemistry we used to do this all the time, you cancel out the fractions. (Note the difference between the slash and the straight line, the slash represents a fraction) 1.5CHF/USD * 1.5USD/EUR = 1.6900 CHF/EUR–>EUR|CHF Now to the arbitrage! let’s say a bank is quoting EUR|CHF at 1.60. Arbitrage is possible! (trust me, you don’t see this in practice) Conventional wisdom says to buy low and sell high, so that’s what you should do here. Since the bank quotes 1.60, BUY it. Therefore, buy the left and sell the right. BUY EUR and sell CHF. Here’s the steps if you’re a USD investor. Envision a triangle and start at the top where you begin with a USD amount of 10,000,000: 1. Buy CHF and sell USD @ 1.5 CHF per 1 USD (USD 10M) --> CHF 15M (sell USD|CHF) 2. Sell CHF and Buy EUR @ the MARKET 1.60 CHF per 1 EUR (CHF 15M) --> EUR 9.375M (buy EUR|CHF) 3. Buy USD and sell EUR @ 1.5 USD per 1 EUR (EUR 9.375M) --> USD 14.0625M That gets you back to the top of the triangle. You started short USD 10M when you bought CHF and ended up buying back USD 14.0625M netting 4.0625M, a substantial profit. If the rate was 1.75 instead, you would go the other direction on the triangle and still end up with USD. In that case, the bank’s pricing EUR|CHF too high so you’d sell EUR and buy CHF. Starting with USD though you’d be LONG 10M USD and sell EUR 6.6M @ 1.5 since it’s high, buy CHF 11.6 @ bank rate of 1.75 with that EUR, then Sell USD 7.77 @ 1.5. As far as the bid/ask… When you do a trade, the counterparty will take the better of the position. For example, if you’re selling EUR/ Buying USD, and using conventional quoting–American Terms–(how many USD buys EUR) then you’ll be selling EUR at the bid since: EUR|USD (Read Euro dollar where the left is the priced currency and the right is the pricing currency) * (USD/EUR rate [how many dollars for 1 EUR]). The bank won’t be giving you more USD for the amount of EUR you sell, so that’s why it’s the bid–multiplying by the smaller of the two rates. The other direction USD|CHF you’d be selling CHF and buying USD at the ask. It’s all about getting the conventions correctly. That’s a lot to take, let me know if you need further clarification.
you may also want to check the threads right before the exam in June. Multiple posts were made about this topic
Just do a bunch of the practice problems, then it clicks after a while. Sucks, but once you get it, you’ll be able to just look at them and know which way to go. Rip is right, it never happens in real life, so naturally CFAI wants you to learn it.
Long story short: Triangular arbitrage involves 3 parties. So draw a triangle, label the vertices A, B and C, with each edge having bidirection (A -> B and B -> A). Then for any distinct pair of party (A,B), you would be given a bid-ask spread. Without loss of generality, let’s say the rates are expressed as A : B = (p,q), where p is the bid and q is the ask. The rates are expressed in terms of B / A (note the notation here). Now for each directed edge in your triangle from A -> B, write down q. Similarly, for each directed edge from B->A, write down p. The trick here is to remember: up the bid, down the ask. In the previous case, when we go from A -> B, we are going from the denominator to the numerator (UP direction), so we use the bid rate §. Similarly, for B -> A, we are going from the numerator to the denominator (DOWN direction), so we use the ask rate (q). Fill in all the directed edges (all six of them) as above. Then beginning from a vertex (say A), you want to multiple the values when you traverse the directed edges in clockwise direction. Repeat the above step in the counter-clockwise direction. If any resultant values are greater than 1, you have an arbitrage opportunity. Backtrack the steps that you have taken and you get a series of steps to swap currency to earn that arbitrage. This is pretty straight forward once you got a pictorial view of the process. Consider yourself fortunate when you see a question like this on the exam.
I developed a fool-proof method for triangular arb. with bid-ask rates, but I need to be able to draw a quick diagram to show you. Just do a bunch of practice problems. You will get it.
Thanks guys for your help. Found lot of threads on this topic.
yeah, you’ll figure this out and feel really comfortable with it…and then you won’t see a single question on it on the exam.