Before you trade you need a predefined timeframe where you should be consistently profitable. This is the only way to trade for a living- to take home a paycheck every single week for food and rent.
Let's say you choose a week as your interval. At the end of each week you look at your results to see if your system is performing normally or not. Abnormal and normal must be based on preset levels of profit or else it will become an emotional decision to cut a system off after a drawdown.
I created a stochastic model of net weekly trading results to find out the required profit factor, winning percentage, and trade frequency to be confident, with statistical certainty, that a system will not lose money. I encourage you to go to the end of the post if you are interested in the math- I uploaded my detailed notes and an Excel table of the results.
Below are a few tables taken from my model. n is the number of trades per week (or other timeframe), p is the winning percentage, and r is the profit factor (avg profit/avg loss). This first table shows that you can still have a good system even if average profit=average loss (r=1), you just have to make accurate calls. The gray boxes are where it is impossible to turn a profit with the given r and p.
| r = | 1.0 |
| n | p |
| 1 | 95% |
| 1 | 90% |
| 1 | 85% |
| 2 | 80% |
| 3 | 75% |
| 4 | 70% |
| 8 | 65% |
| 17 | 60% |
| 71 | 55% |
| 99999 | 50% |
| 99999 | 45% |
| 99999 | 40% |
| 99999 | 35% |
| 99999 | 30% |
| 99999 | 25% |
| 99999 | 20% |
| 99999 | 15% |
| 99999 | 10% |
| 99999 | 5% |
| 99999 | 0% |
If we can increase our profit factor to r=2, so we win an average of twice what we lose, then the table is a little different, in fact we can lose most of our trades as long as we trade very frequently:
| r = | 2.0 |
| n | p |
| 1 | 95% |
| 1 | 90% |
| 1 | 85% |
| 1 | 80% |
| 1 | 75% |
| 2 | 70% |
| 2 | 65% |
| 3 | 60% |
| 4 | 55% |
| 7 | 50% |
| 13 | 45% |
| 39 | 40% |
| 581 | 35% |
| 99999 | 30% |
| 99999 | 25% |
| 99999 | 20% |
| 99999 | 15% |
| 99999 | 10% |
| 99999 | 5% |
| 99999 | 0% |
Finally, I'll show you the table of r=10. From it you can see that it is possible to turn a consistent weekly profit even with 9/10 trades ending in a loss. However it is going to be nearly impossible to create a system that can find so many positions with such high potential every single week:
| r = | 10.0 |
| n | p |
| 1 | 95% |
| 1 | 90% |
| 1 | 85% |
| 1 | 80% |
| 1 | 75% |
| 1 | 70% |
| 1 | 65% |
| 1 | 60% |
| 1 | 55% |
| 2 | 50% |
| 2 | 45% |
| 2 | 40% |
| 3 | 35% |
| 4 | 30% |
| 6 | 25% |
| 10 | 20% |
| 26 | 15% |
| 772 | 10% |
| 99999 | 5% |
| 99999 | 0% |
This chart summarizes the three tables, adding in r=1.5 and r=5 so you can visually compare all three variables:

Finally, here are my detailed notes of how I derived the model and the Excel worksheet of the calculations. They are both in Word 2007 format but I am happy to convert them if anyone asks. I advise reading the document before going into the spreadsheet since the table of three variables might be a little hard to understand. Document, Worksheet
Please don't hesitate to ask any questions, this is a little more mathematical than usual.
4 comments:
Hi Max,
Good work, I like the statistical approach.
Similar sort of stuff to Acrary's work on ET many years ago.
Have you look at his thread on systems development? http://www.elitetrader.com/vb/showthread.php?s=24b00f5ee572b16e84c53a237937683c&threadid=33654&perpage=6&pagenumber=1
He took it one step further and considered how many noncorrelated systems with N profit factor you would need trade to be confident of being profitable xx% of periods (he used 99% and monthly, so he accepted only one loss every 8 years!)
I haven't used anything like this in my trading as yet as I don't draw an income, but I can see myself going down this path in the future.
If it's okay with you, I might post something similar on my blog (I will acknowledge the work) after I read the document and spreadsheet.
Nizar.
(thetrendfollower.blogspot.com)
Thanks Nizar, of course feel free to reference anything, it's an honor.
Acrary's thread was very useful.
Regards,
Max
Hi Max,
Can you please convert the documents to Office 2003 format?
Thanks.
Nizar.
Nizar,
This plugin to view the 2007 format should help- http://www.microsoft.com/downloads/details.aspx?familyid=941b3470-3ae9-4aee-8f43-c6bb74cd1466&displaylang=en
Regards,
Max
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