Triangular arbitrage -- which direction to go?

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rockmania

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1 million USD investor is trying for an arbitrage profit and is given the following bid-ask quotes for the USD, GBP and EUR.
USD:EUR: 0.7000 - 0.7010
GBP:USD: 1.7000 - 1.7010
GBP:EUR: 1.2000 - 1.2010
There is an arbitrage opportunity here. The given USD:EUR is under quoted. I tried in the following way
USD –> EUR –> GBP –> USD? I got -ve value
USD –> GBP –> EUR –> USD? I got correct value.
How do we start with which direction to go? I am afraid I will loose time, if I hit the wrong direction.
Thanks in advance.
 
1. Find out the theoretical price
2. Then Alway remember Buy Low and Sell High
3. I will discuss you a problem tomorrow
 
can you post the answer and the USD:EUR under quoted?
that would help to help you
 
1) The quoted USD:EUR: 0.7000 - 0.7010
To find out if arbitrage opportunity exists, I calculated the same currency pair using GBP:USD and GBP:EUR and resulted in 0.7055 - 0.7065. So there is an arbitrage opportunity here.
2) The answer for the arbitrage profit is $6372
USD –> EUR –> GBP –> USD? (0.7000/1.2010) x 1.7000 = $0.9908, I have a loss here.
USD –> GBP –> EUR –> USD? (1.2000/1.7010) x (1/0.7010) = $1.006372. I have a gain $6372
 
your process is good in both ways.
you have to ask youserlf in term of the domestic currency USD ,which one will give you more in term of the other currency when your are looking at the misspriced quote :
you can get it directly 700 000Eur with the direct quote 0.7000 - 0.7010
or you can get 705 500Eur by strating up with GBP and doing the triangle 0.7055 - 0.7065
so you always want to get more. if the quote was over quote, then you would start with the one that pays more. which would be the direct quote and do the inverse triangle
 
summerside182 wrote:
then you would start with the one that pays more. which would be the direct quote and do the inverse triangle
Click to expand...
I think this answers it. I never focused on the the inverse triange value 0.7055 - 0.7065, except to find out if arbitrage is possible or not. So I know upfont now, that I am getting 0.7055 EUR/USD using the inverse triangle. If the inverse quote is less (say 0.6055 - 65), then I should avoid this route and start with 0.7000 - 0.7010.
Thanks for your help. +1
 
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