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# Cumulative Loss Formula

Discussion in 'Risk Management' started by dima777, Oct 2, 2008.

1. ### dima777

Hi!
I was curious if there is a formula that will calculate the number of trades required to reach a specific cumulative loss from a series of losses if you give it the number of trades,the amount risked per each trade and the target loss. I attached the workbook which shows that it is necessary to have 70 losses in a row to lose 50% if you risk 1 percent per trade.
Thanks

3. ### MGJ

Yes, there is such a formula. To derive it yourself, observe that "a 1% loss" leaves you with 99% of (your original bankroll). Observe that "two 1% losses in a row" leave you with 99% of (99% of (your original bankroll)). Proceed by induction.

By the way, sixty nine (not 70) 1% losses in a row, leave you with 49.9837% of your original bankroll. Whereas sixty eight 1% losses in a row, leave you with 50.4886% of your original bankroll. You can use these facts as "test cases whose correct answers are known in advance" to convince yourself that your formula is getting the right answer.

And here is one more: 100 losses in a row, where each loss is 2%, leaves you with 13.2620% of your original bankroll.

4. ### dima777

I will certainly try to deduce this formula but it would be great if you could share it with me - because you sound like you know it...

try:

CL = Cumulative loss

6. ### dima777

thanks but this formula doesn't work on other numbers -try 30% - it should give you 37 - while it gives 119...the working formula:

A1 = Individual loss (1), B2 = Target cumulative loss (50%)

=CEILING(LOG(1-B1,(100-A1)/100),1)+1

Should a useful addition to the money management toolkit of any trader..

_________________________________
No, I'm pretty sure the formula I derived is correct.

If you are compounding as in the prior examples on the thread, 37 losses in a row will not give you 30% of your initial value; 119 losses will.

8. ### MTE

It's a simple compounding formula:

FV=PV*(1+r)^n

n is you number of trades.
r is your return on each trade, which will be negative since it's a loss (e.g. -0.01 if you are risking 1% per trade)
PV is your starting capital and FV is your ending capital, which you can set to a 100 and whatever level you target, respectively.

Then it is just a simple mathematical manipulation to get n:

n=ln(FV/PV) / ln(1+r)

9. ### dima777

thanks. But I might be confusing something here but the results are conter-logical:

Why getting to 50% will take you only 70 trades while to 30% -120? I am using my worksheet as a reference...to check the results...

10. ### dima777

thanks...will check it in a bit

#10     Oct 3, 2008
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