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Hi
Carl,
<FONT face=Arial color=#0000ff
size=2>
Thanks
for the detailed description. With this explanation, I can create an
excel spreadsheet to calculate the numbers.
***** Erika ***** :-)
<FONT face=Tahoma
size=2>-----Original Message-----From: topos8
[mailto:topos8@xxxxxxx]Sent: Tuesday, August 27, 2002 8:28
AMTo: realtraders@xxxxxxxxxxxxxxxSubject: [RT] Re: Help
needed in mathematicsYes, there is a formula, but it
is difficult to describe via e-mail.The main thing to remember is that
since you have so many "observations", i.e., hypothetical trades, the
profit numbers for all these trades follow a normal distribution law (as
you observed).The key parameters that determine the normal
distribution are the mean and the standard deviation. You already know the
mean, namely $144 profit per trade. The standard deviation is the square
root of the average, squared deviation from the mean.To calculate
the standard deviation here is what you do. For each trade,
calculate the profit on that trade, then subtract 144 (the answer here can
be a negative number!) and then square the result. Having done this for
each trade, add up all the resulting answers and divide the sum by the
number of trades. Finally, take the square root of this last number.
This is the standard deviation.The significance of the standard
deviation is this. 66% of the trades will show a profit within 1
standard deviation (either way) of the average profit ($144). 90% of the
trades will show a profit within 2 standard deviations of the average
profit.Now what happens if you look at groups of trades instead of
individual trades?To take an example, suppose you look at groups
of 100 trades because that is the average number of trades your system
makes in a month. As it happens, the average profit on groups of 100
trades will also follow a normal distribution. In this example the mean of
this distribution will be 100 x $144 = $14,400. What about the standard
deviation? Well, suppose that D was the standard deviation you
calculated above for the distribution of individual trades. Then
the standard deviation on groups of 100 trades would be the square root of
100 times D,i.e., 10 x D. Notice that the standard deviation goes up much
more slowly than does the mean as you increase the number of trades in a
group. This means that as the number of trades in a group goes up, the
probability that there will be a profit on the group of trades taken as a
whole also goes up.The way you calculate these probabilities is to use
the normal distribution tables found in statistical reference books.
These tables are tabulated for normal distributions with mean 0 and
standard deviation 1. To use them you have to convert your total
profit on a group of trades into a number that has a normal
distribution with mean 0 and standard deviation 1.So let us say
that P symbolizes the profit on a group of N trades and that the standard
deviation on individual trades (which we calculated above ) is
D.Then [(P - (N x $144)) / (square root of N)x D ] will be a quantity
than follows a normal distribution with mean 0 and standard deviation
1. Let's call this quantity A.Then the profit P on a group
of N trades will be greater than 0 if and only if A is greater than
the number (-144 N)/ (D x square root of N). So if you look up this last
number in the statistical tables for the normal distribution with mean 0
and standard deviation 1 you will find next to it the probability that a
group of N trades in your system will show a net
profit.Carl--- In realtraders@xxxx, "Erika Toth Fluke"
<erika@xxxx> wrote:> Hi Carl,> > > Thanks
for the explanation.> > Is the square root relationship changing
if look at the monthly or quarterly> numbers (125, 355
trades)?> > Can this relationship be expressed in a
formula?> > Thanks again,> ***** Erika *****
:-)> > > -----Original
Message-----> From: topos8
[mailto:topos8@xxxx]> Sent: Monday, August 26, 2002 5:53
PM> To: realtraders@xxxx> Subject: [RT]
Re: Help needed in mathematics> > > The
answer to your question is a standard exercise in
probabilty> theory.> > The reason
that the probability of a profitable week is higher
that> the probability of a profitable trade is simple.
There are 28 trades> per week and each trade on average
makes $144. So if you divide the> total weekly profit
by the number of trades that week you will get a>
number whose average is again $144 but whose variablity is much
lower> (by a factor proportional to the square root of
28) than the> variability of the profit on a single trade.
So you are much more> likely to make money in a typical
week of many trades than you are to> make money on a
single trade.> > The same phenomenon explains why
owning a casino is the sure road to> wealth: On any
give roll of the dice or deal of the cards the casino>
has only a small advantage over the customer. But when you look
at> the casino's results over millions of dice rolls
etc, it is a sure> winner.> >
Carl> > > --- In realtraders@xxxx, "Erika
Toth Fluke" <erika@xxxx> wrote:> >
HI,> >> > I'm trying to prove that
a 422 sample win/loss distribution's>
profitability> > will increase if I look at the
weekly, monthly etc. data.> >> >
The original dataset gives 45% win/loss on the trade by trade
basis> and> > 71.6% on the weekly
basis (about 28 trades/week).> >>
> The data has the characteristics of the normal distribution,
where> the> > average trade wins:
$144> > standard deviation is:
$1266.34> >> > Can somebody point
it out why the weekly profitability increases so> >
significantly or show me a formula that can be used to calculate
the> > increase in profitability depending on the time
frame?> >> > The result is there
but, somehow I'm just not getting it.>
>> > Thanks for your help.>
>> > ***** Erika ***** :-)> >
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