Know Your P's and L's error?

[SozzledBoot]

This is from the Pre-school tutorial lesson entitled "Know Your P's and L's".

Dividing by an exchange rate and then later multiplying by that same rate cancels out the entire rate and just leaves you with whatever is left in the equation (in this case, the unit pip size).

In the case where the US Dollar is not quoted first and we want to get the US Dollar value, we have to add one more step.

EUR/USD:

1.2200

.0001 divided by exchange rate = pip value
so
.0001 / 1.2200 = EUR 0.00008196

but we need to get back to US dollars so we add another calculation which is

EUR x Exchange rate
So
0.00008196 x 1.2200 = 0.00009999

When rounded up it would be 0.0001 <---is this a unit pip?


Here's my question...

given:

0.0001 = 0.00008196
1.2200

if we multiply 0.00008196 on the right by 1.2200, isn't that the same thing as multiplying

0.0001 on the left by 1.2200?
1.2200

And doesn't a 1.2200 on the bottom cancel a 1.2200 on the top?

0.0001 X 1.2200 = 0.00008196 X 1.2200
1.2200

0.0001 X (1/1.2200) X 1.2200 = 0.00009999

0.0001 X (1.2200/1.2200) = 0.00009999

0.0001 X 1 = 0.00009999

0.0001 = 0.0001

Someone check the math for that.


ADDENDA ADDED NOVEMBER 20 2007:

Nothing to see here! Move along folks!

Pip value is only determined for the BASE currency.

As a formula, Pip value in the BASE currency = pip size (which is usually equal to 0.0001 but for the Japanese Yen is equal to 0.01) divided by the QUOTE currency's exchange rate.

But our take-home pay will eventually be given in US dollars regardless and so the pip value amount needs to be expressed in terms of the US dollar!

In cases where USD is the BASE currency, this presents no problem because the resulting pip value is 'already' expressed in the 'take-home' currency of the US dollar by the use of the formula above. However, in cases where USD is not the BASE currency it is a problem because, as I mentioned earlier, the pip value is determined for the BASE currency only.

So to express the BASE currency's pip value (where that BASE currency is not in USD) in the take-home currency of the US dollar, you must multiply that BASE currency's pip value amount by the US exchange rate.

It is merely a coincidence that multiplying by the US exchange rate to change the BASE currency pip value amount into a US dollar amount has the same 'mathematical effect' in the formula above as the cancellation of a term in an equation (leaving, of course, whatever is left, which in this case is the number 0.0001).

I was looking at the 'pure math' instead of the 'time-saving forex formula' being used.

I will flog myself in a self-made forex hell as punishment for my sins.