Expert: Josh - 10/17/2008

Question
Hello:

I have a question that pertains to a calculation used in the currency trading markets.
Can you try to explain to me the mathematical reason for this calculation?

I read the following for determining the value of one pip, which equals 0.0001 for most currency pairs: divide 0.0001 by the exchange rate.
Why is this done since the 1/10,000 place in the rate of 1.5250 has the value of 0/10000 of $1.00?  

Here is an example:

USD/CHF = 1.5250
0.0001 divided by exchange rate = pip value 0.0001 / 1.5250 = 0.0000655

I found this information at the following URL:
http://www.babypips.com/school/know_your_ps_and_ls.html

If you go to this site you may get a better understanding to question.


I thank you for any helpful explanation that may be sent to me.

Answer
Hi Kenneth,

I guess it all comes down to common practice rather than mathematical justification as you could probably tell from the tone of the passage  at the quoted website.

Why choose 0.00001? It's just a matter of convenience (or convention) to the stock broker. You are right saying that 0.00001 is 1/100000 (ten parts per million).

Note: the quoted "USD/JPY 119.90" exchange rate is really saying one US dollar buys 119.90 Yen. Similarly, "EUR/USD 1.193" means one euro buys 1.193 US dollar. Written as a fraction, the ratio 1.193 should have units in [USD]/[Euro]. Now, dividing one pip (0.00001) by 1.1930 simply gives us a small amount (8.3822 parts per million) in units of [Euro]/[USD].

If you read on, the next paragraph is much ado about nothing.
Quote  "EUR/USD at an exchange rate of 1.1930
(.0001 / 1.1930) X EUR 100,000 = EUR 8.38 x 1.1930 = $9.99734 rounded up will be $10 per pip"

You notice that equality does NOT follow. The notation is really sloppy, with conversion factors being added at various places. The exchange rate will cancel out in the end no matter what.

Looking at "(.0001 / 1.1930) X 100,000", we could have rewritten this as (.0001 x 100,000) /1.1930. The first part evaluates to "$10 per pip" whatever it means, this is the message the author wants to get across. An exchange rate of 1.1930 [USD/Euro], then appears mysteriously, to cancel out with 1/1.1930 [Euro/USD]. It is just a mess all round. He should not bother with all this and just give as a matter of definition $10 per pip. The 9.997... etc is just numerical error. It should be 10.

I suggest not studying the "so called" formula so carefully, because there's a fair bit that cancels out in the end. Use the formula only if you find it convenient, see the "How the heck do I calculate profit and loss?" section, and in particular,
"(.0001/1.4550) x $100,000 = $6.87 per pip x 20 pips = $137.40"

If it confuses you, then don't use it. We can work it out from first principle.

Given the exchange rates
USD/CHF 1.4525 / 1.4530 and
USD/CHF 1.4550 / 1.4555

The movement is (1.4550-1.4530)=0.002 (we could have called this 20 pip, but we don't need to use this whatsoever).

Initially, you used Swiss Franc to buy US dollar (CHF -> USD). Now, the US dollar strengthened, so you want to buy back the Swiss Franc (USD -> CHF). The margin 0.002 is relative to the CHF.

To find the gain you made per US dollar, simply multiply 0.002 by (1/1.4550) [USD/CHF]. Your net profit is 0.002/1.4550 = $0.0013746 per dollar.

Now, you can multiply this by however many lots (or dollar) you initially purchased. Assuming you purchased a single unit at 10,000, you have earned 0.0013746*10000 = $137.46 in USD.

This uses good old maths with no funny units.