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Money Management vs. % of Success in Trading Systems

  • #21
  • Sep 6, 2006 12:35pm Sep 6, 2006 12:35pm
Quoting miscon777
Adaptrade looks brilliant... haven't started the demo yet, but the articles alone are excellent - looks like just about everything you could want to know about money management, all in one place.

Decided to play a bit with the fixed fractional thing... whipped up a little spreadsheet to calculate lots required, balance growth, etc., at 25% and 33% success and 1:4 / 1:3 RRs. I made it fairly easy to alter so you can play around with it yourself - just change the blue fields in the first row of each sheet to match your system / account.

Once again, the actual $ balances shown at the bottom are not realistic... Just to make things fast and easy, to effect 25% success I just logged 3 losing trades followed by a single winning trade, and then repeated the pattern 25 times (100 total trades). This type of regular repitition would never happen in reality, and whatever patterns of wins and losses happened would completely change the running balance, and thus all the rest of the figures (most importantly, lots bought/sold per entry to achieve desired fractional loss). Same thing with the 33% Success shown on Sheet 2 - just two losers followed by one winner, repeated 33 times (99 trades).

I used a 1 pip = $1 dollar system (1:200 leverage, if I'm not mistaken), because 1:100 leverage required lot sizes of less than 1 (0.7, etc), and I don't believe that brokers allow for fractional lots. Perhaps someone can confirm or deny this?

You could easily use this to track your own trading to determine lot sizes on a running basis... which if I guess correctly, is just one of the features that Adaptrade's software would provide. Phil, perhaps you could fill us in?

Anyway, just playing around... let me know if I bungled any computations herein.


-miscon777
miscon,

Mike has written a series of great articles. They can be found by googling ""breakout futures" and then clicking free newsletter. I have read his work for quite some time before it occured to me that he was the author of the software as well.

Thank you for the work you put in the spreadsheet, it certainly proves your point about R:R and win%.


DS,

Thanks for your work as well. It's enjoyable to participate in a post as important as this one. One thing you didn't cover is the "D" word....drawdown. In most cases, profit and position size is severely cramped when you show respect for drawdown. For a typical system that I use the best fixed ratio independent of drawdown is around 10% of my account. When i limit drawdown to something reasonable like 20-30%, the fixed ratio drops to around 3%.

There are various money management algorithms which increase your fixed fraction (% account risked) as your win % goes up. And, this is logical...the more you consistently win, the more you should risk.

Phil
  • #22
  • Sep 6, 2006 12:56pm Sep 6, 2006 12:56pm
Excellent thread!

Darkstar, your examples are not the best because your systems have a completely different expectancy. The system with a 1:1 RR and 75% winning rate has 3 winners of x points each followed by a loser of x points. So out of 4 trades it wins 2x points. The system with a 4:1 RR and 25% winning rate has one winner of 4x points followed by 3 losers of x points each. So out of 4 trades it wins only x points. Obviously it has a much lower expectancy, so it performs worse in your tests, and the higher the position size the bigger the difference between the 2 systems. If the latter has RR = 5:1 instead of 4:1, then it also makes 2X, and then you can compare them. Or even better, just go to http://hquotes.com/tradehard/simulator.html and use that simulator to see what's going on.

All - I know that most people think that different orders of winners/losers in a series would lead to different outcomes. E.g. out of 10 trades you could have 6 wins and 4 losses, and it's intuitive to assume that your final equity is not the same if you have the 6 wins first, or the 4 losses, or some combination of those. In fact the order doesn't matter at all (assuming that you don't get a margin call if all losers come first of course). It is surprising, isn't it.
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  • #23
  • Sep 6, 2006 12:57pm Sep 6, 2006 12:57pm
Hi,
Great work done here. Money management does require a serious thought when it comes to trading. Unfortunately, it has become secondary to trading technical analysis.
I suppose one of the better books about Money management with respect to trading is "The Trading Game" by Ryan Jones. There is quite a lot of theory involved but it requires atleast a cursory glance even if you dont understand most of it.(let me know if any one wants it, I got the ebook)
Well, despite his own version of money management, apparently it is also not the best model for MM as per the legendary trader Larry Williams. He used a very simple formula for MM which he used during his trading career to make millions. The fact that he is presently a fugitive right now is not really my concern...lol!
If anyone is interested, I am sure I can dig it up to further see how much it will affect the outcome of this exercise.
He also mentions emphatically that the real keys to the kingdom is indeed MoneyManagement.
  • #24
  • Sep 6, 2006 12:58pm Sep 6, 2006 12:58pm
Quoting Darkstar
Now I’m no statistician, but the probability of hitting a 50% drawdown (8 consecutive trades) is SIGNIFICANTLY higher on a 25% system then it is on a 75% system, so the trader is all but forced to lower his risk-per-trade rate.

This statement is absolutely correct. I've attached a chart that some might find useful. It is based on a 50 trade sequence with win % on the right and consecutive losses across the top.

This brings up another issue that hasn't been discussed yet. The human factor.

Since we are using some extremes for examples I'll continue (it's appropriate imo anyway).

On paper a system with an inverse R:R and a high win % can have positive expectancy. Say 30 pip stop with a 10 pip target and a 90% win rate. But make one mistake in 10 trades and you cut your profit in half.

Likewise (as has already been demonstrated) a system with a 4:1 R:R and a 25% win rate can be positive. For instance, consider a 10 pip s/l and 40 pip target (yes I know extreme like the last example but I actually know people who trade like this, or try anyway). At 10 pips of s/l on a pair like cable you have very little room for error. Factor in spread, which will hurt your R:R, and it's even worse.

Both extremes are subject to a fair amount of damage if mistakes are made (the human factor). Unless you trade completely automated you will make mistakes. I know I'm human and I make my fair share.

Understanding the relationship between each of these factors including the human factor and trade frequency (which hasn't been discussed yet) is the key to saf(er) trading and a nice equity curve.

My rule of thumb when evaluating systems looks like this. If the average R:R is 3:1 then the breakeven win% is 25%. I want my win rate to be double that. That's before breakeven filters. If it's not then I keep evaluating changes or dump it all together. All in all I usually reject the extremes. A method has to be consistently tradeable (fairly easy to execute) or it's all just academic.
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Secret Identity: Bill Sullivan
  • #25
  • Sep 6, 2006 1:21pm Sep 6, 2006 1:21pm
Quoting LazyPawn
Excellent thread!


All - I know that most people think that different orders of winners/losers in a series would lead to different outcomes. E.g. out of 10 trades you could have 6 wins and 4 losses, and it's intuitive to assume that your final equity is not the same if you have the 6 wins first, or the 4 losses, or some combination of those. In fact the order doesn't matter at all (assuming that you don't get a margin call if all losers come first of course). It is surprising, isn't it.
LazyPawn,

Your assumption couldn't be further from the truth. Below are two identical images. They consist of 378 trades. The only difference between the two is the sequence of the order in which these trades occurred. One went bust and one lived happily ever after.
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  • #26
  • Sep 6, 2006 1:28pm Sep 6, 2006 1:28pm
Quoting LazyPawn
Excellent thread!

Darkstar, your examples are not the best because your systems have a completely different expectancy. The system with a 1:1 RR and 75% winning rate has 3 winners of x points each followed by a loser of x points. So out of 4 trades it wins 2x points. The system with a 4:1 RR and 25% winning rate has one winner of 4x points followed by 3 losers of x points each. So out of 4 trades it wins only x points. Obviously it has a much lower expectancy, so it performs worse in your tests, and the higher the position size the bigger the difference between the 2 systems. If the latter has RR = 5:1 instead of 4:1, then it also makes 2X, and then you can compare them. Or even better, just go to http://hquotes.com/tradehard/simulator.html and use that simulator to see what's going on.
I see what your saying. Like I said I'm no probability expert. Anyway, at 5:1 w/25% winrate the return is still only 30%. Thats a little less then half the 75% winrate system.

Also as was outlined in the consecutive losses probability table that Captain supplied, you run a much higher possibility of blowing up your account at high leverage, so you have to scale back the position size. Risking 2% at 5:1 yields an ~11% return.

Quoting LazyPawn
All - I know that most people think that different orders of winners/losers in a series would lead to different outcomes. E.g. out of 10 trades you could have 6 wins and 4 losses, and it's intuitive to assume that your final equity is not the same if you have the 6 wins first, or the 4 losses, or some combination of those. In fact the order doesn't matter at all (assuming that you don't get a margin call if all losers come first of course). It is surprising, isn't it.
I actually had no idea! Thanks for that fascinating piece of data!
  • #27
  • Sep 6, 2006 1:31pm Sep 6, 2006 1:31pm
Quoting Captain Piptastic
I've attached a chart that some might find useful. It is based on a 50 trade sequence with win % on the right and consecutive losses across the top.
I just tacked it up on my wall. Thanks for the extremly useful chart.
  • #28
  • Sep 6, 2006 1:32pm Sep 6, 2006 1:32pm
Quoting philmcgrew
LazyPawn,

Your assumption couldn't be further from the truth. Below are two identical images. They consist of 378 trades. The only difference between the two is the sequence of the order in which these trades occurred. One went bust and one lived happily ever after.

I don't think so. If we are using a fixed fraction (same %) or equity it doesn't matter. I don't know what you have in those 2 images, but please give me a concrete example if you have one. Or an excel file. So if I first lose 4% of my equity, then I win 3% of the new equity, I have the same equity at the end as with a 3% win followed by a 4% loss. Please check and see for yourself, I attached a random example in my previous post, as an example.
  • #29
  • Sep 6, 2006 1:40pm Sep 6, 2006 1:40pm
Quoting LazyPawn
I don't think so. If we are using a fixed fraction (same %) or equity it doesn't matter. I don't know what you have in those 2 images, but please give me a concrete example if you have one. Or an excel file. So if I first lose 4% of my equity, then I win 3% of the new equity, I have the same equity at the end as with a 3% win followed by a 4% loss. Please check and see for yourself, I attached a random example in my previous post, as an example.
Your assumptions are that wins and losses are equally distributed. In real life, they are not. You can experience a series of wins and losses. Captain Piptastics's spreadsheet shows the probability of this happening quite well.

If you drawdown your account by 50% you have to make 100% to get back to your starting balance. That is not the same as starting off with a few wins and then a loss.

If the images don't make sense let me know and i'll discuss them with you.
  • #30
  • Sep 6, 2006 1:41pm Sep 6, 2006 1:41pm
Quoting LazyPawn
Excellent thread!

Darkstar, your examples are not the best because your systems have a completely different expectancy. The system with a 1:1 RR and 75% winning rate has 3 winners of x points each followed by a loser of x points. So out of 4 trades it wins 2x points. The system with a 4:1 RR and 25% winning rate has one winner of 4x points followed by 3 losers of x points each. So out of 4 trades it wins only x points. Obviously it has a much lower expectancy, so it performs worse in your tests, and the higher the position size the bigger the difference between the 2 systems. If the latter has RR = 5:1 instead of 4:1, then it also makes 2X, and then you can compare them. Or even better, just go to http://hquotes.com/tradehard/simulator.html and use that simulator to see what's going on.
Right, but, that's kind of the point. The higher win percentage, coupled with the lower WL ratio results in a different expectancy. Take a sampling of 100 trades and you get the same result. Try 1000, and it will be the same - using Darkstar's figures, of course.

What's really interesting to me is what the right formula would be for finding the optimal WL ratio for a given winning percentage. I think what you would need, in addition to the basic system figures, is a sampling of the maximum runs a trade goes. I have that information already in my database for my system. I know my winning percentage, a risk rate (max SL), and the maximum each trade would have gone. Based on all that data, though, I'd love to know what the average TP should be on my system to maximize my average profits. I think that kind of exercise is what moves this kind of information into practical use.
  • #31
  • Sep 6, 2006 1:43pm Sep 6, 2006 1:43pm
If my current equity is E and I win p1 (a percent of E), the the new equity is E(1+p1). Example> current equity 10000, I have a 2% winner, the new equity would be 10000*(1+0.02). Then if I have a p2 trade, the new equity would be [E*(1+p1)](1+p2) ... and so on. So the general formula is E*(1+p1)*(1+p2)*...*(1+pn). Obviously the order of those factors doesn't matter, since a*b*c is the same as a*c*b.
  • #32
  • Sep 6, 2006 1:47pm Sep 6, 2006 1:47pm
Quoting philmcgrew
Your assumptions are that wins and losses are equally distributed. In real life, they are not. You can experience a series of wins and losses. Captain Piptastics's spreadsheet shows the probability of this happening quite well.

If you drawdown your account by 50% you have to make 100% to get back to your starting balance. That is not the same as starting off with a few wins and then a loss.

If the images don't make sense let me know and i'll discuss them with you.
Trust me, the distribution does NOT matter if you are using the same % of equity. Please read the previous post and formula, it's very easy to understand. If I lose 50% first then win 50%, I have only 75% of my original equity. But if I win 50% first, then lose 50%, isn't it exactly the same? Still 75% of the original equity.
  • #33
  • Sep 6, 2006 1:49pm Sep 6, 2006 1:49pm
Quoting LazyPawn
If my current equity is E and I win p1 (a percent of E), the the new equity is E(1+p1). Example> current equity 10000, I have a 2% winner, the new equity would be 10000*(1+0.02). Then if I have a p2 trade, the new equity would be [E*(1+p1)](1+p2) ... and so on. So the general formula is E*(1+p1)*(1+p2)*...*(1+pn). Obviously the order of those factors doesn't matter, since a*b*c is the same as a*c*b.
That works well as long as you never take a loss. Good luck with that. The sequence of events absolutely matters.

I do admit that you understand the associative law of mathematics but that has nothing to do with money management.
  • #34
  • Sep 6, 2006 1:52pm Sep 6, 2006 1:52pm
Quoting LazyPawn
Trust me, the distribution does NOT matter if you are using the same % of equity. Please read the previous post and formula, it's very easy to understand. If I lose 50% first then win 50%, I have only 75% of my original equity. But if I win 50% first, then lose 50%, isn't it exactly the same? Still 75% of the original equity.
This is quite true and it that's your point you win. If you step into the real world on non-normal distrubutions you are in for a rude awakening.
  • #35
  • Sep 6, 2006 1:54pm Sep 6, 2006 1:54pm
Quoting philmcgrew
That works well as long as you never take a loss. Good luck with that. The sequence of events absolutely matters.

I do admit that you understand the associative law of mathematics but that has nothing to do with money management.
I hope you understand that p1, p2 etc. can be positive or negative. p2 can be -3%, right...

If you are talking about the psychological aspect of trading, then I agree. Some people would be tempted to quit if they happen to start with a few losses, or modify their risk percentage for each trade. But that's another story. If you keep trading, and keep using the same risk percentage-wise, the order of winners/losers has no impact on your final equity.
  • #36
  • Sep 6, 2006 1:59pm Sep 6, 2006 1:59pm
By the way, don't you find it unfair that having a 2% loss followed by a 2% win, or having a 2% win followed by a 2% loss both lead to a loss overall?! It means that if the system we are using has a 50% expectancy and we use a fixed ratio position size we are in fact losing money. Ugly :-(
  • #37
  • Sep 6, 2006 2:19pm Sep 6, 2006 2:19pm
As I see it and Calculate it.

If I'm wrong, I'm gonna be busy recoding shi#.
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  • #38
  • Edited 2:30pm Sep 6, 2006 2:19pm | Edited 2:30pm
Quoting LazyPawn
I hope you understand that p1, p2 etc. can be positive or negative. p2 can be -3%, right...

If you are talking about the psychological aspect of trading, then I agree. Some people would be tempted to quit if they happen to start with a few losses, or modify their risk percentage for each trade. But that's another story. If you keep trading, and keep using the same risk percentage-wise, the order of winners/losers has no impact on your final equity.
Read this short article with an open mind. I hope that it can help explain the concept a little better.

http://www.adaptrade.com/Articles/article-mc.htm

http://www.traders.com/Documentation...nt/Bryant.html

Phil
  • #39
  • Sep 6, 2006 2:41pm Sep 6, 2006 2:41pm
Quoting Bemac
As I see it and Calculate it.

If I'm wrong, I'm gonna be busy recoding shi#.
Bemac,

The good news is that you don't have to recode. The bad news is that your "system" does not have a positive expectancy and as such, money management principles can not be applied.

Ryan Jones explains this concept on pages 15 & 16 of his book The Trading Game.

Phil
  • #40
  • Sep 6, 2006 2:51pm Sep 6, 2006 2:51pm
Hi Phil,

Now it has a + expectancy.

I don't have Mr. Jones' book. If there is a breife explanation that you could post I would appreciate that.
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