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# USD/JPY * EUR/USD = EUR/JPY always?

Discussion in 'Forex' started by CN2000, Jul 4, 2005.

1. ### CN2000

Hi! Could someone with a bit of experience in Forex clarify this?

Thank you.

2. ### Panurgo

If you can exchange 1 dollar for 100 Yen and 1 dollar for 2 Euros, than you can argue that 1 Euro can be exchanged for 50 Yen.

3. ### CN2000

Thanks Panurgo. The equation is USD/JPY * EUR/USD = EUR/JPY

100.00*2.00=200, and not 50

Any explanation why this happen and is it always like this or forex traders have an arbitrage trading opportunity?

Thanks

4. ### wpfund

Actually, Panurgo is right

5. ### CN2000

Ups!

Yep, 100.00*0.50=50.00

6. ### dodger fan

(1/100) * (1/.5) = 1/50

7. ### Fohat

There's no mystery in this fact, the proof is very simple,
from basic fractions math , we have:

a/c * b/a = ab/ca = b/c

If one substitutes , a=USD , b=EUR , c=JPY , the following equation follows:

USD/JPY * EUR/USD = EUR/JPY

8. ### CN2000

Ok guys, THANKS for all the math explanations.

The questions are:

does this happen all the time?
does the EUR/JPY have an independent quotation (sometimes) and therefore can a forex trader benefit from it?

To give an example, the USD/GBP * EUR/USD it's not equal to EUR/GBP.

9. ### jrkob

Yes it has.
So you are correct that in theory there are potential arbitrage opportunities.
The problem is that you will have to be super fast to take advantage of any distortion between the 3 markets (EUR/JPY, EUR/USD and USD/JPY). Banks, who benefit from faster connection than you and the tightest spread possible will, probably, take advantage of any distortion faster than you.

Remember also one thing: once you have initiated your 3 trades, you will have to reverse them at some point. God knows how long it will be before you can reverse the trades: remember you'll have to cross the spreads again. It seems to be a lot of work and risk for a very small potential proffit (not to mention the capital mobilized).

There has been dozen of threads on that very subject, you may want to refer to them.

You can also open a demo account with a broker and give it a try. Good luck. The FX desk in the bank I work for (as most of the banks in the world I guess) is doing that so I guess you'll be competing !

10. ### jrkob

You still get it wrong. Cable quotes the other way around.

#10     Jul 4, 2005
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