John

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John

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:-

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.

For 2003 - 04

max drawdown was in march this year at 141 the usual is circa 50 points

max consecutive losses 1

For Jan 2002 - April 2003

win ratio 86%

Av win 237 points

Av loss 50.05 points

max consecutive losses 3 in 2002

yesterdays trade +176 points

your formula work out like so.

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).

20 (100% -55%)

20 (45%) = 9

I have probably made a pigs ear of it,as I don't fully understand it.

Trades

1 -4

2 4

3 6

4 -3

5 -2

6 4

7 5

8 3

9 -5

10 4

11 6

12 -5

13 -4

14 -5

15 4

16 -2

17 4

18 6

19 4

20 -5

Wins 11

Losses 9

Ratio 55

Average win 4.55

Average loss 3.88

Pw (Aw) - Pl (Al)

=0.55 x (4.55) - 0.45(3.88)

=2.50 - 1.75 = 0.75

Update:

If the last number turns out to be(ie -0.75) a minus then your system is losing,although the one above is positive.

There is no backtesting system I know of, you just get a calculator and your broker's statement.

The ratio is really a %,The way I did it was divide 20 trades into a 100= 5 then 11wins X 5 = 55 then 9 x 5 = 45 so thats your ratio or % of winners55%/losers45%.

You can also juggle figures around and play the "what if game" ie: if I had a closer stop

losses it would mean more losses but smaller ones etc the different combinations are endless,but it can help your tweak your system up.Try swopping the losers for winners

so you have 45% winners 55% losers the answer should be if i haven't got it wrong -2.15

bad news.

Average Number of Consecutive Losses = 20*(1-Pw) [where Pw is expressed 0.01-1.00]

So, if your trading system has a win rate of 65% the calculation will be:-

20 * (1 - .65) = 7

So trading a system with a 65% win rate you**must expect ** on average to get strings of 7 consecutive losses.

You will get strings of less and greater numbers of consecutive losses, but this is the average you can**expect **.

Not only does this make it (slightly) more bearable when it occurs, it also means you can manage your position size accordingly.

Of course, the beloved 'Black Swan' may well float into the picture at any moment so it still makes sense to keep your max risk per trade within minuscule limits in relation to your trading capital.

BTW - This formula when applied to DC2000's trading systems stats (come on man, we all want to know...!) indicates he can expect on average, strings of just 3 consecutive losses.

So, if your trading system has a win rate of 65% the calculation will be:-

20 * (1 - .65) = 7

So trading a system with a 65% win rate you

You will get strings of less and greater numbers of consecutive losses, but this is the average you can

Not only does this make it (slightly) more bearable when it occurs, it also means you can manage your position size accordingly.

Of course, the beloved 'Black Swan' may well float into the picture at any moment so it still makes sense to keep your max risk per trade within minuscule limits in relation to your trading capital.

BTW - This formula when applied to DC2000's trading systems stats (come on man, we all want to know...!) indicates he can expect on average, strings of just 3 consecutive losses.

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So trading a system with a 65% win rate you must expect on average to get strings of 7 consecutive losses.

You will get strings of less and greater numbers of consecutive losses, but this is the average you can expect .

What does average mean??

I think on average if you have a 65% system 7 consecutive losses although certainly possible

are quite rare. Occuring less than once per 1000 trades.

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Stew

Looking back over some the posts I was wondering what happen to "3rddawn" and "Jonny Ts" Forex trading system he was using.Is he laying on a beach somewhere sunning himself or did he go broke.

donaldduke said:What does average mean??

I think on average if you have a 65% system 7 consecutive losses although certainly possible

are quite rare. Occuring less than once per 1000 trades.

DD - average wasn't the best term to use, but I'm struggling with how best to describe this.

In any trading run, there could of course be an infinite number of consecutive losses. Mathematically improbable, but possible.

By 'average' I meant that the

You are correct - a relatively rare event, as it would occur approximately once every 1554 trades, but as you approach this number of trades - the probability of this sequence being produced increases.

But that wasn't my point.

My point was that this formula could be used as a basis for calculating

In DC2000's system with a win rate of 89%, the most liekly number of consecutive losses is 3 and he can expect then to occur every 751 trades.

TheBramble said:My point was that this formula could be used as a basis for calculatingexpectationof 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.

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.

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

TheBramble said: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.

rog1111 said: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....!

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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.

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