Triangular Arbitrage

Does anyone have any methods or techniques for remembering how to solve these problems? These seem really confusing. The bid-ask quotes for the US Dollar, GBP, and SF are * SF per USD: 1.6500-10 *USD per GBP: 1.2000-10 *SF per GBP: 2.0000-10 What are the potential arbitrage profits from an initial position of 1 million dollars?

schweser has an amazing strategy create a triangle from the 3 currencies, each has a corner, then go around the circle converting from one currency to the next, if you end up with more money then you started out with you have just made profit using triangular arbitrage, if not, then go around the other way, get it?

viktorv Wrote: ------------------------------------------------------- > schweser has an amazing strategy > > create a triangle from the 3 currencies, each has > a corner, > > then go around the circle converting from one > currency to the next, if you end up with more > money then you started out with you have just made > profit using triangular arbitrage, if not, then go > around the other way, get it? I saw that. But there is as problem. They say “bid up” and “ask down”. But doesn’t this depend on how the quotes are given?? So if they gave us inconsistent quotes this strategy would not work… Am I mistaken?

I have a strategy that takes two minutes to do the whole thing. Its too bad I didn’t have the opportunity to test it on the exam last June.

Correct me if I am wrong, but I think the strategy would be 1. Start off with USD$1million 2. Convert the USD to GBP. (USD1m/1.2010=GBP832639.4671) 3. Convert the GBP to SF(GBP832639.4671*2=SF1665278.94) 4. Convert the SF to USD(SF1665278.94/1.6510=USD 1008648.66, > USD1m)

Looks easy, but how do you know when to use the bid and when to use the ask? I get hopelessly confused if I try to do it in my head.

Make the triangle. Write the bid and ask on arrows going from curr to curr. If the rate is USD to EU, and you have a bid ask, then the bid goes with the arrow that goes from usd to eu, and ask on the arrow from EU to USD. Then take a currency amount UP the Bid all around the triangle and see if you end up flat. If not, go aroundt he ASKS. It’s easy to remember, because UP the ASK would be painful (insert Peter Griffin Family Guy Laugh). If there’s a problem in LII that isn’t worth worrying about, this is it. THey haven’t asked it in at least 3 years, it’s too easy.

I find that triangle a bit difficult. Could you explain where to put those exchanges rates and what goes up/down in that mnemonic “bid up ask down”? ================================= I tried to make up some sort of mnemonic: I want to take SEK Amt * GBP/SEK * IDR/GBP * SEK/IDR Given: SEK/GBP: 12.5476-12.9485 IDR/SEK: 1496.98-1340.86 IDR/GBP: 18930.67-16982.30 Rewritten on the form I need …| bid …| ask … GBP/SEK | 1/12.9485 | 1/12.5476 IDR/GBP | 18,930.67 | 16,982.30 SEK/IDR | 1/1340.86 | 1/1496.98 GBP/SEK (bid) X IDR/GBP (bid) X SEK/IDR (bid) = 1/12.9485 * 18930.67 * 1/1340.86 = 1.0903428

Danteshek Wrote: ------------------------------------------------------- > Looks easy, but how do you know when to use the > bid and when to use the ask? I get hopelessly > confused if I try to do it in my head. First, think of your target currency. Which currency are you trying to BUY here [If u remember, if you want to BUY a certain currency, the conversion rate to use shld be the ASK rate since this is what the bank charges you to buy that particular currency] Using the example above, say you started off with dollar and you wanted to convert it to SF(I…e sell , bUY SF), u shld use the the bid rate. The ASK rate would be the figure to take if you wanted to SELL SF, buy . I normally think of it this way, since u can view the ASK-quote as posted above as the cost in SF terms needed for you to purchase 1USD. If you can make this identification, it shld be clear…

I use the same method as the post above, I dont try to figure this out mathematically but attempt to make sense of the conversion i.e. bid when selling, ask when buying

This is how I think of it. In order to calculate arbitrage currency needs to be stated in such a way that multiplied they reduce themselves one way to do it is 1 mil usd* gbp/usd*sf/gbp *usd/sf so now you have to restate the quotes and remember this is dealer perspective so usd/ gbp is 1.2000-1.2010 then gbp/usd is 1/1.201-1/1.200 remember you need to switch because dealer buys cheap and sells expensive and same usd/sf 1/1.651 -1/1.650 Now that we restated the quotes you can proceed calculating We sell Us for Gbp at lower rate - 1/1.201 We sell Gbp for SF at lower rate - 2.000 We sell Sf for Usd at lower rate -1/1.651 then 1/1.201*2*1/1.651=1.008648 - multiply that by 1 mil As client you sell at the bid price and buy at ask

The easiest way to do this is the following: In converting from one currency to another, If what you HAVE is in the DENOMINATOR of the quote, use the BID. If what you HAVE is in the NOMINATOR of the quote, use the ASK. This way you can go around both ways and don’t have the construct the triangle.

Yes, Danteshak,what you said looks right, since by using this method, you’d definitely get the smaller of both figures you’d obtain if you used both the Bid and Ask rate. In general you should be taking the smaller figure.

I agree, this is confusing as well. Like you all have said, Schweser’s strategy is to remember the phrase “Up the bid, down the ask.” This means that for the bid, the currency that is in the denominator is the currency that you give to the foreign exchange dealer and you get the currency that is in the numerator. For the ask quote, you give the dealer the currency that is in the numerator and get back the currency that is in the denominator at that rate. When working the triangular arbitrage problem, draw a triangle with each of the three currencies as each corner. Then, figure out the rates for converting each currency into the other currencies, then work your way around the triangle in both directions, and if you end up with more money, then arbitrage is possible. Schweser says there is no way to determine which way (clockwise/counter clock wise) to go around the triangle first to determine if arbitrage exists. You have to go around both ways and see what happens.

according to Stalla: Sales are on the bid side Buys are on the ask side determine whether you are buying or selling and then that should tell you whether you are dividing (sells) or mulitplying (buys)