My Triangular Arbitrage Trick sat, remember, examples, process, struggled

BC_MBA_student

So I have always struggled with this but today I finally sat down and worked through a few examples and came up with this thought process to make sure I am always using the right rate at the right time.

These questions always start with the bid ask spreads from a lender. You have to remember that the rates are their bid and ask. Not yours. This example is #13 on page 323 of the Schweser text.

BID ASK
USD:EUR 0.7 0.701
GBP:USD 1.7 1.701
GBP:EUR 1.2 1.201

These questions will always give you an amount of money to start with. In this example we start with $1,000,000

The way I write it out to make sure I think it straight is as follows;

BUY GBP with USD @ Ask: $1,000,000 * 1/(1.701USD/GBP) = 587,889 GBP
BUY EUR with GBP @ Ask: 587,889 GBP *1/(1/1.2EUR/GBP) = 705,467 EUR
BUY USD with EUR @ Ask: 705,467 EUR * 1/(0.701EUR/USD) = 1,006,372

Profit = 1,006,372 - 1,000,000 = 6,372 USD


To some, that might look like a lot of inverting of the rate but my thought process is always saying I am buying X currency with Y currency at the ask. X:Y @ Ask

In the first line, GBP:USD 1.7-1.701 and the ask is 1.701USD/GBP. It will require the inverse but this ensures I will have the right rate.

I hope this helps clear this topic up for others as much as it helped me.

Chris

thecfawannabe

Thanks, I like this. Anything to help simplify triangular arbitrage is useful. Essentially you are saying 'up the ask, down the ask'. Just remember to invert the middle exchange and you're in good shape.



Edited 1 time(s). Last edit at Sunday, May 22, 2011 at 12:09PM by dapoopa.

xilinx_altera

"Given the bid ask quotes, the potential arbitrage profits from triangular arbitrage based on an initial position of 1m USD are closest to"
A 0 USD
B 7,212 USD
C 6,372 USD

I used 1.2 because GBP:EUR 1.2 1.201 is the bid ask spread. At this point, I have pounds and want to buy Euros. The bank is buying pounds for euros 1.2 and selling pounds for euros 1.201. We make the transaction at his asking price.

My way of thinking of it is that buy GBP for EUR at the ASK 1.201 but in this case we want to buy EUR with GBP, the other way around. so the inverse EUR:GBP 1/1.201 - 1/1.2 and then we want to BUY EUR with GBP at the ask (1/1.2)=0.8333GBP/EUR and we have 587,889 GBP so will have to inverse it again.

Maybe too much flipping for some but works for me.

ayodayo

I have seen questions that do not give the currency or amount you need to start with. But, what is cool about triangular arb is that you can start with any amount in any of the three currencies and earn the same % arbitrage profit, as long as you go the same direction around the tree.

ayaz_mahmud369

I do the same thing as CFA Chap, write out all the bids as x USD/EUR, y EUR/GBP etc and then invert all of the asks to 1/x EUR/USD, 1/y GBP/EUR. That way you just multiply across. I find it is less confusing and saves time as you move down each starting currency

WarrenB1

dapoopa - actually, it's "up the bid, DOWN the ask". easy to remember - saying "up the ask" dust doesn't sound right.