Financial Maths question - arbitrage

Hi - does anyone know the answer to this for me please?

Does the existence of quadrilateral arbitrage between 4 currencies necessarily imply the existence of triangular arbitrage? Justify.

I understand all about arbitrage in FX markets - but am slightly unsure whether arbitrage between 4 currencies would always imply arbitrage between 3 of them?

Any ideas, anyone?

Reply 1

generalebriety

I think I speak for everyone when I say: what the buggery is arbitrage?

This is more of an economics(?) question than a maths question, I think...

Reply 2

takeonme79

I haven't studied this but I'm guessing it doesn't.

I've nicked the following from wikipedia:

Consider the three foreign exchange rates among the Canadian dollar, the U.S. dollar, and the Australian dollar. Triangular arbitrage will produce a profit whenever the following relation does not hold:

CD$/US$ * AU$/CD$ = AU$/US$

for example if

the Canadian Dollar (CD$) and the US dollar (US$) is CD$1.13/US$1.00 in Canada (1 USD gets you CD$1.13)
the Australian Dollar (AU$) and the US dollar (US$) is AU$1.33/US$1.00 in Australia (1 USD gets you AU$1.33)
the Australian Dollar (AU$) and the Canadian Dollar (CD$) is AU$1.18/CD$1.00 (1 CD gets you AU$1.18)
1.13 * 1.18 = 1.3334 > 1.33

Now let's extend this by taking an example where

1.1*1.2*1.3 = 1.716 > 1.71

If you remove any of the items from the left hand side of the equation, the inequality doesn't hold so your arbitrage disappears.
So you just need to write this up into a counterexample to disprove the conjecture.