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: http://financialexamhelp123.com/triangular-arbitrage/
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:
- USD → EUR → AUD → USD
- 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.
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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.
why is it called a cross rate (or cross exchange rate)?
what is being crossed?
You’re crossing through JPY to get from CAD to EUR.
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