Triangular Arbitrage

Can any one explain a relatively simple was to do a triangular arbitrage problem?

up-the-bid - multiply

down-the-ask - divide

use the starting points provided in the answers

fairly straight forward once you get the hang of it

I wrote an article on this:

It’s easiest to learn with an example. Suppose that you’re given these quotes:

  • EUR/USD 0.8911/0.8929
  • AUD/EUR 1.5183/1.5213
  • AUD/USD 1.3586/1.3614

We want to see if there’s an arbitrage opportunity and, if so, what trades we need to make to earn a profit.

Let’s start with USD1,000,000. (The starting currency makes no difference.) We’ll try two both directions:

  1. USD → EUR → AUD → USD
  2. USD → AUD → EUR → USD

For each exchange, keep two ideas in mind:

  • The new currency is in the numerator in the exchange rate
  • We choose the exchange rate that gives us fewer of the new currency; i.e., either multiply by the smaller number or divide by the larger number

Here we go:

USD1,000,000 × EUR0.8911/USD1.0 × AUD1.5183/EUR1.0 ×USD1.0/AUD1.3614 = USD993,798

We lose money that way, so let’s try the other way:

USD1,000,000 × AUD1.3586/USD1.0 × EUR1.0/AUD1.5213 ×USD1.0/EUR0.8929 = USD1,000,170

We make money that way, so that’s the way to go: sell USD for AUD, sell AUD for EUR, and sell EUR for USD.

If you’re getting confused about what to multiply by and what to divide by, just remember that a dealer will always be looking to screw you (to generate their spread). Therefore they will want to multiply by a number and divide by a bigger number.

There: that looks better.

If you can remember that dealers are cheapskates, you’ll always get this one correct.

Thanks for the pick up s2000.

My pleasure.

sir, you are simply a cfa magician, so simple and effective method!

You’re very kind.