# Triangle Arbitrage

Exhibit 2-1

USD:EUR 1.39 1.395 JPY:USD 82.9 82.945 EUR:JPY 115 115.1 Given the quotes, is there an opportunity and if John invests \$5,000,000, is there an expected profit? A. No. B. Yes, a profit of \$5,500. C. Yes, a profit of \$6,121.

Ok I must hav forgotten the whole up the bid down the ask thing, because I just can’t see how they got the answer.

We have EUR/ USD, JPY/EUR, and USD/ JPY, so going USD to EUR to JPY to USD we should be using the bid each time so 1/1.39 x 115 x 1/ 82.9 right? Or have I completely forgotten how to do these?

how comes 1 JPY gives you 82.9 USD

and 1 EUR gives u 115 JPY

and 1 USD gives you only 1.39 EUR… did you mess up your example?

i think you flipped EUR:USD

No that’s how it was in the problem, this almost has to be an error, it’s from the BSAS sample 2011, they said the answer is starting with USD go to JPY to EUR and back to USD

The rates they used were 82.9 , 115.1 , and 1.39, so essentially bid ask bid, but since you’re going DOWN shouldn’t it be ask for all of them?

well those rates make no sense. call BSAS and tell them summer says he is not happy with those rates

as summerside pointed out (with a typo), how can 1USD buy 1.39 EURO but buy less JPY than EURO can?

erratum.

Speaking on this topic-and dont mean to hijack the thread (thought it was about my question initially)… When faced with a Triangle Arbitrage questions, what is the easier/best way to tell right currency to start with?

The rates are absolutely wrong

Hi,

Matori> I’d go one round in the triangle in any direction (e.g. USD to JPY to EUR to USD). If I end up less money, go in the other direction. If I end up same amount of money, then, no arbitrage opportunity is present

I’m adjusting the rates (hopefully correctly) and attempts the question:

USD/EUR 1.39 1.395

JPY/USD 82.9 82.945

JPY/EUR 115 115.1

MissCleo, I can relate to bid/ask problem, I’m bad with bid and ask terms, but always remember that FX always gives you the lousier rates. I find that more helpful than memorizing ask, bid then ask etc. =)

1. John goes round the triangle:

a) John has 5 million USD. He goes to Japan and changes his money:

5000000 * (82.9 or 82.945?)

FX gives the lousier rate: 5000000* 82.9 = 414,500,000 JPY

b) John then goes to Europe.

414,500,000 JPY / (115 or 115.1?)

FX gives the lousier rate: 414.5 million JPY / 115.1 = 3.601 million EUR

c) John returns to USA

3.601 million EUR * (1.39 or 1.395)

FX gives the lousier rate: 3.601 million * 1.39 = 5.0054 million USD

Answer: B. John became richer by approx 5000 USD for travelling. =)

probably the easiest way without trying to remember anything more.