Lose/Win Percentage for a Good Trading System

[growltiger]

My point was that this formula could be used as a basis for calculating expectation of maximum drawdown (expected consecutive losses) for any trading system with a known win rate.

Isn't the point that you want to know the distribution of runs of n consecutive losses in a sequence of 100 trades, or 1000 trades, or whatever. On its own, starting at an arbitrary point, the chances of n successive losses must be (1-win rate) to the power of n. So if n=5, and the win rate is 50%, the chance of my losing 5 times in a row will be 1/32. But I cannot summon to mind the piece of statistical theory which would then say how many n-fold losses I should expect in a given run of trades.

 

[TheBramble]

Both pieces of information are useful.

1. What's my most likely longest number of consecutive losses?

2. How often is this run likely to occur?

My initial point was that by using (1) we can establish what our maximum drawdown is likely to be with any given trading system where the win/lose probability is known.

 

[rog1111]

Hi TheBramble

That's an interesting formula. Is it based purely on observations of the results posted on this forum/thread ? Or is there any other statistical basis for it ? JonnyT's FX systems were mentioned in another post & I have backtested a bunch of them for EUR:$ for 1 year. I guess that the longer the time period the better chance that the formula would apply. Anyway, after seeing the formula, I thought I'd check it against the backtested results (not real results).

conseclosers 11 11 9 8 7 7 5 5 9 6 10 6 6 4 6 5 9 9 10 10 7 4 6 4
Prob Win 0.43 0.45 0.44 0.46 0.52 0.52 0.55 0.54 0.41 0.41 0.42 0.40 0.48 0.51 0.52 0.53 0.41 0.45 0.40 0.43 0.50 0.50 0.50 0.49
Formula c/losers 11 11 11 11 10 10 9 9 12 12 12 12 10 10 10 9 12 11 12 11 10 10 10 10


I'm not quite sure what this is telling us, although the most divergence between the formula's predicition and actual consec losers was found with the best performing systems (as measured by PL and PL to Drawdown ratio - not shown here), so maybe this shows that these better systems were really just lucky statistical abberations, and therefore unlikely to continue ? This might then alter one's choice of which backtested system to trade for real. All very interesting.....

rog1111

Playing around with some stats in relation to this thread and I have a possible correlation between Probability of a Win and Max Drawdown (in terms of average consecutive number of losses) which lends itself to a formula.

I don't keep stats on my trades (as mentioned above), but if anyone else could confirm/reject my hypothesis based on their own data:-

In any trading system, where Pw is the probability of a Win (and is expressed 0.01-1.00)

Average Number of Consecutive Losses = 20*(1-Pw).

Obviously, if you're using a fixed stoploss and if this formula is reasonably valid, it's possible to determine your max drawdown to within one std.dev.

 

[TheBramble]

I'm not quite sure what this is telling us,

I'm using a Monte Carlo generator for the lmost likely max losses calculations.

I'm using the formula GrowlTiger mentioned to calculate the frequency of the max loss string occurring.

If I'm interpreting your data correctly it's saying that the back-tested data falls within the predicted maximum number of consecutive losses.

The variable Pw confuses things a bit, but with the range given (0.40 - 0.54):- (using mcl for max consecutive losses)

Where Pw=0.40 - mcl=12 and occurs every 459 trades.
Where Pw=0.54 - mcl=9 and occurs every 1084 trades.

The fact that the maximum loss string has not yet been reached may be due to the large number of trades required for it to (statistically) manifest itself.

Naturally enough, we have to assume in any randomly initiated test of this nature, the start date of the test can be considered to be slap bang in the middle of the distribution. So if your data was based on trading days (250/year) we could be quite close to the maximum string occurring. In theory....!

 

[Matt321]

Thanks for all the stats and info you've all posted,I'll try and do the calculations later.
Rog 1111 have you got the average amount of winning pips and average amount of losing pips.
so I can apply the "expectancy test " to Jonny Ts Fx system.
Taken from your figures above the average Pw = 44.875% which I feel is not very good unless your
losses are small and winnings are rather large.
I think for a worthwhile system it should be above the 50% mark,especially an intraday system,if it was a trending system over a few days or weeks then you could get away with less than 50% wins.

 

[JonnyT]

Hi Matt321,

A 40% win ratio with the average win > than twice the average loss is excellent.

50%+ win ratio's are highly unlikely for any mechanical day trading system. (I have yet to see one)

Unfortunately your statement lacks true substance.

JonnyT

 

[frugi]

A spreadsheet formula for calculating likely max consecutive losers based on number of trades and probability of winning each.

=ROUND(LN(total number of trades)/-LN((1-chance of winning each trade)),0)

where the chance of winning each trade is between 0 and 1.

Possibly useful?

 

[Matt321]

Hi Jonny glad you turned up as you seem to know what your talking about from experience,we were
just doing calculation from backtests.In fact I did ask for the average winner and average loser in order
to do an "expectancy test" .I also did say the winner would have to be large.
As I'm looking for a system I have been trying yours out the last couple of days on the £/$ got 46pips yesterday and lost 72 today.Today it went about 5 pips above the range,I then put the bet on. and it reversed back down and in the red all day,still nevermind another day tomorrow.

 

[JonnyT]

What do you mean lost 72?

It lost 35 today as that is the stop loss I specified!

Monday was also a 40 pip+ day...

JonnyT

 

[rog1111]

TheBramble

Your logic seems sound. The number of trades for each system varies from 57 to 280, although I have realised that in some cases results are given for 2004 only. Also, although stops are fixed. not every loser is due to being stopped out on price, as there are time stops too, so some losers could be less than the max. Hmm, this is a new angle for me to consider. Good post !

rog1111

I'm using a Monte Carlo generator for the lmost likely max losses calculations.

I'm using the formula GrowlTiger mentioned to calculate the frequency of the max loss string occurring.

If I'm interpreting your data correctly it's saying that the back-tested data falls within the predicted maximum number of consecutive losses.

The variable Pw confuses things a bit, but with the range given (0.40 - 0.54):- (using mcl for max consecutive losses)

Where Pw=0.40 - mcl=12 and occurs every 459 trades.
Where Pw=0.54 - mcl=9 and occurs every 1084 trades.

The fact that the maximum loss string has not yet been reached may be due to the large number of trades required for it to (statistically) manifest itself.

Naturally enough, we have to assume in any randomly initiated test of this nature, the start date of the test can be considered to be slap bang in the middle of the distribution. So if your data was based on trading days (250/year) we could be quite close to the maximum string occurring. In theory....!

 

[rog1111]

Frugi - thanks for posting your formula

I have tried it out, and I must say that it corresponds quite well to my consec losers in 1 year backtesting for all 24 systems (it's actually the same type of system with different time criteria and stops). The correlation is somewhat better than the 20*(1-Pw) formula, but this might be because it takes into account the number of trades ?

rog1111

A spreadsheet formula for calculating likely max consecutive losers based on number of trades and probability of winning each.

=ROUND(LN(total number of trades)/-LN((1-chance of winning each trade)),0)

where the chance of winning each trade is between 0 and 1.

Possibly useful?

 

[rog1111]

matt32

Since the system has 24 different sets of criteria for which backtesting was carried out, there are 24 sets of average winners and losers. The ave winner is larger in all cases, sometimes more than double.

rog1111

Hi Jonny glad you turned up as you seem to know what your talking about from experience,we were
just doing calculation from backtests.In fact I did ask for the average winner and average loser in order
to do an "expectancy test" .I also did say the winner would have to be large.
As I'm looking for a system I have been trying yours out the last couple of days on the £/$ got 46pips yesterday and lost 72 today.Today it went about 5 pips above the range,I then put the bet on. and it reversed back down and in the red all day,still nevermind another day tomorrow.

 

[TheBramble]

A spreadsheet formula for calculating likely max consecutive losers based on number of trades and probability of winning each.

=ROUND(LN(total number of trades)/-LN((1-chance of winning each trade)),0)

where the chance of winning each trade is between 0 and 1.

Possibly useful?

I did give that a whirl Frugi, but I found it a bit 'lumpy' in the transitions from one Pw value to another.

Besides, I've got a vested interest in my Monte Carlo Generator (...keep your eyes open for it - very soon (but don't order yet...) on Commercial Trading Systems )

 

[TheBramble]

Also, although stops are fixed. not every loser is due to being stopped out on price, as there are time stops too, so some losers could be less than the max.

It doesn't matter why you stop out or how often you trade/don't trade. Price stops, time stops - doesn't matter. Your system is your system and it has its own Pw derived from precisely the way you trade.

I agree. if your stops are not of a constant size it makes it more difficult to determine absolute (financial) drawdown, but makes no difference to the mcl or their likely distribution.

 

[Matt321]

If average Pw = 45% then average win needs to be one and half times averages loss if its double then your laughing on paper anyway.My first statement was that winnings have to be rather bigger than losses.
That is full of substance,don't get so defensive stick to the facts.

 

[rog1111]

Also I could get 9 straight losers, 1 winner, then another long run of losers, so the overall drawdown would be far more devastating than just the initial max consec run of losers. Still, it's useful to know what we could reasonably expect over time - thanks.

rog1111

It doesn't matter why you stop out or how often you trade/don't trade. Price stops, time stops - doesn't matter. Your system is your system and it has its own Pw derived from precisely the way you trade.

I agree. if your stops are not of a constant size it makes it more difficult to determine absolute (financial) drawdown, but makes no difference to the mcl or their likely distribution.

 

[TheBramble]

If average Pw = 45% then average win needs to be one and half times averages loss if its double then your laughing on paper anyway.My first statement was that winnings have to be rather bigger than losses.
That is full of substance,don't get so defensive stick to the facts.

Matt, who was that aimed at?

 

[TheBramble]

Also I could get 9 straight losers, 1 winner, then another long run of losers, so the overall drawdown would be far more devastating than just the initial max consec run of losers.

Absolutely!

You could get an infinite number of consecutive losses - in theory.

I agree that it is an interesting area of exploration - distribution of win/loss.

But ultimately, providing your losses are WAY smaller than your wins, your max risk per trade is minuscule (less than 1% of trading capital) and your system is giving you at least a 50/50 success rate - you'll do OK.

 

[Matt321]

Sorry Tony didn't mean to upset you,its good to be all friends together,one 4 all and all 4 one.
I was wondering if the Nationwide housing stats that came out today would affect the £/$ or even the Euro dollar on an intraday basis.
I'm just digging some more great formulas to test your trading systems ,I know I have them jotted down somewhere,you are all great sounding boards for my ideas so stick around.
Rog 1111 I have been trying to download that backtesting system but with no success even though
I put the security setting as low as poss,what 4 christ sake is wrong with it.
Case you wonder where I am,I'll be out jogging,I,m also installing a lot body workout gear as well so I can keep fit while watching the screen,particular in view of the news of GB being the worst country for obesity in the EU,so far I have lost 8lb in 2 weeks.

 

[chump]

"so far I have lost 8lb in 2 weeks"..LOL...what is your stop loss ?

I've been a little inactive through injury lately,but I have a speed ball and punchbag in my gym/office for those special little moments of inaction....