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[amibroker] OT: Re: Margin of Error



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Brian.

I don't get it... why don't you just post your thread on the Amibroker 
"trading systems" forum (amibroker-ts)? Tomasz has set this up explicitly 
for threads such as yours!  It takes 5 minutes to join it.  Honestly, that 
forum needs some traffic -- your ideas could really add to it!




----- Original Message ----- 
From: "brian.z123" <brian.z123@xxxxxxxxxxxx>
To: <amibroker@xxxxxxxxxxxxxxx>
Sent: Friday, November 10, 2006 7:40 AM
Subject: [amibroker] OT: Re: Margin of Error


> Hello Ton,
>
> Thanks to you and Keith for your support.
> Thanks also to QT who followed all the arguments.
> He can run rings around my stats.
>
> The files required to finish the project are not quite ready to post.
> Unfortunately some urgent business that I have to attend to
> personally has come up and so I will be out of the office and not in
> the forum for a couple of weeks.
> After that I will be taking some leave.
>
> When I get a chance to look at it I will probably talk to Tomasz
> privately about somewhere else to put them.
>
> Best wishes to all on both sides of the fence and the ones in the
> middle too.
>
>
> BrianB2.
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Ton Sieverding"
> <ton.sieverding@xxx> wrote:
>>
>> Brian, my opinion is that's Don's reaction is absurd. If he should
> not have a mirror at home, I will send him one. There is no reason
> to tell somebody that he is a 'over inflated educational guru who
> wants to see his writing in print'. If Don does not want to read
> your stuff, he is free to do so. Of all the emails I am getting, I
> am skipping 90%. But that's not a reason to give the sender of the
> emails such an answer. These kind of personal reactions on forums is
> wrong and not very constructive ...
>>
>> The question of course is, if this is the right place to post the
> kind of stuff you're writing ? For me as I already have told you,
> it's fine. For others as I understood not. So we have a conflict.
> Normally it's up to the forum manager to decide and solve the
> problem. Who is the forum manager ?
>>
>> Ton.
>>
>>
>>   ----- Original Message ----- 
>>   From: brian.z123
>>   To: amibroker@xxxxxxxxxxxxxxx
>>   Sent: Friday, November 10, 2006 7:51 AM
>>   Subject: [amibroker] OT: Re: Margin of Error
>>
>>
>>   Don,
>>
>>   Gentleman of the day.
>>
>>   Please don't post anymore on this issue.
>>   I have got the message.
>>
>>   I have already left the building.
>>
>>   I only checked in to confirm that it still wasn't going on to
> the
>>   detriment of the forum and others.
>>
>>   Don't drag Tomasz into it.
>>   He has enough to do and he does a brilliant job of managing a
> wide
>>   range of interests and all the various Ami platforms.
>>
>>   You have all had the last word and the last laugh.
>>
>>   Please do not post again and I won't have to ask you to stop
> again.
>>
>>   BrianB2.
>>
>>   --- In amibroker@xxxxxxxxxxxxxxx, "Don Lindberg" <dlindber@>
>>   wrote:
>>   >
>>   > Brian,
>>   > I am afraid I have to disagree with one of your statements,
> and I
>>   quote" The
>>   > reason I can do that is because my ego is not that large".
> This
>>   whole
>>   > educational guru" bit that your are on is nothing more than an
>>   over-inflated
>>   > ego that likes to see his words in print. I for one am getting
>>   tired of
>>   > seeing your never ending rants about something that 1) has
> little
>>   bearing on
>>   > this forum and 2) that you appear to know little about. Why
> don't
>>   you find a
>>   > soap box in some other park to preach from.I feel I am not
> alone
>>   in this
>>   > statement, and I do wish Tomasz would step in a put an end to
> this
>>   ABUSE of
>>   > our AmiBroker forum.
>>   > Sincerely,
>>   > Don Lindberg
>>   >
>>   > -------Original Message-------
>>   >
>>   > From: Fred
>>   > Date: 11/9/2006 8:49:36 PM
>>   > To: amibroker@xxxxxxxxxxxxxxx
>>   > Subject: [amibroker] OT: Re: Margin of Error
>>   >
>>   > Brian,
>>   >
>>   > At least have the courtesy to label your posts of this nature
> OFF
>>   > TOPIC ...
>>   >
>>   > This is my last post in this thread ...
>>   >
>>   > I usually let most of your posts go by because for the most
> part
>>   > They're too lengthy with very little meat to bother with but
> at
>>   the
>>   > same time they are also usually innocuous. However, your posts
> on
>>   > this topic are anything but innocuous ... There's
> no "training"
>>   going
>>   > on, just diarhea of the keyboard and as far as critqiuing your
>>   posts
>>   > go, we did so you just chose to ignore them or more likely
> didn't
>>   > understand the critique. I'm sorry if you were offended, but I
>>   find
>>   > your posts offering to "teach" others about something you
>>   obviously
>>   > know very little about to be highly offensive to the point
> where I
>>   > feel I must step in and say so before you drive the lemmings
> to
>>   the
>>   > sea.
>>   >
>>   > PS ... My comment about your one reply being absurd was not my
>>   > colorful way of disagreeing ...
>>   >
>>   > --- In amibroker@xxxxxxxxxxxxxxx, "brian.z123" <brian.z123@>
> wrote:
>>   > >
>>   > > Hello Paul,
>>   > >
>>   > > The IT revolution has brought in a whole new set of
> paradigms.
>>   > > It is all relatively new.
>>   > > I don't believe any of us fully understand where it will all
> go.
>>   > > I also think we are only scratching the surface and that we
> are
>>   not
>>   > > using what is available to us now to its full extent.
>>   > >
>>   > > That applies to this forum.
>>   > >
>>   > > I am not one of the *internet kids* and they should be
> lapping
>>   me
>>   > > several times over, but they are not.
>>   > > The fact is I am a way more radical than most of the kids
> who
>>   are
>>   > > half my age.
>>   > >
>>   > > In the brave new world of internet forums, what is training,
> who
>>   is
>>   > > the teacher, who is the student and what format should it
> take?
>>   > > Who says the teacher has to know what subject we are going
> to
>>   > learn,
>>   > > have all the answers or even give them all to you if he/she
> does?
>>   > >
>>   > > As Fred said, *it is all floating around in my head*, where
> else
>>   do
>>   > > I need it to be?
>>   > > I don't need to write it all down for my own benefit.
>>   > > I already know the answer.
>>   > > I am only researching the subject further to put the fancy
> icing
>>   on
>>   > > the cake.
>>   > >
>>   > > Sometimes in the forum I can change from being the teacher
> to
>>   the
>>   > > student and back again in three posts.
>>   > > The reason I can do that is because my ego is not that large
>>   that I
>>   > > can't turn it to my purposes.
>>   > >
>>   > > As a radical person I don't sit on the sidelines.
>>   > > I actively participate.
>>   > > I have attempted two *internet culture* experiments within
> the
>>   forum
>>   > > (keep in mind that I am naive to the ways of forums which
> most
>>   of
>>   > > you understand inside out).
>>   > >
>>   > > In the first I took on a pro-active role and offered to do a
>>   little
>>   > > free admin on the files section.
>>   > > I got absolutely hammered.
>>   > > That is the nature of experiments.
>>   > > I have no regrets.
>>   > > The results of the experiments are safely tucked away in my
>>   > research
>>   > > lab.
>>   > >
>>   > > This time I tried a pro-active discussion with a light
>>   structured
>>   > > theme behind it.
>>   > > I was sensing that the experiment was failing so in those
>>   > > circumstances it is not hard for me to end the experiment.
>>   > >
>>   > > Don't blame me; the forum is just not up to it.
>>   > > Rest assured the underlying process was spot on, albeit very
>>   avante
>>   > > garde as a training method.
>>   > > It was all too quantum for the forum.
>>   > > The mean member wants Newtonian billiard balls.
>>   > >
>>   > > I would have been delighted if the forum could or would have
>>   > > critiqed the real points in the topics.
>>   > > Not one single person challenged my propositions that the
>>   > > optimisation phase might not qualify as a system test
> because it
>>   > > involves making subjective judgements, or my silly
> suggestion
>>   that
>>   > > the number and frequency of signals in a test sample, or
> changes
>>   > > there-in, might be a symptom of over-fitting.
>>   > >
>>   > > Not even the *Great Fred*, brought the full force of his
>>   intellect
>>   > > to bear on the facts and arguments presented.
>>   > >
>>   > > Incidentally Fred, it is not curve-fitting, which is a valid
>>   > > mathematical method, it is over-fitting.
>>   > >
>>   > > I was not offended by your *absurd* comment; that is just a
>>   > > colourful way of saying you disagree with the argument.
>>   > > Some of your behaviours and the behaviour of others in the
> forum
>>   is
>>   > > however deeply offfensive to me.
>>   > >
>>   > > As always some lovely people joined the topic(s) and
> generously
>>   > > shared some good information.
>>   > >
>>   > > If anyone who expressed interest in the subject privately or
>>   > > publically or who participated constructively in the topics
>>   wants
>>   > > some further info please email.
>>   > >
>>   > > Sometime in the next month or two I will probably email some
>>   extra
>>   > > notes out to that group to honour the commitment I made when
> the
>>   > > project commenced.
>>   > > I doubt if they will be as extensive or as conclusive as
> they
>>   could
>>   > > have been.
>>   > >
>>   > > I will be overseas on holiday for a while so I am not sure
> on
>>   the
>>   > > timing.
>>   > >
>>   > > Please don't engage in any acrimonious debate amongst
>>   yourselves;
>>   > > that is the very thing I abhor most.
>>   > >
>>   > > BrianB2.
>>   > >
>>   > >
>>   > >
>>   > > --- In amibroker@xxxxxxxxxxxxxxx, "Paul Ho" <paultsho@>
> wrote:
>>   > > >
>>   > > > I agree, there are plenty of other forums to post it to,
> AB-TS
>>   or
>>   > > even
>>   > > > elitetraders. and probably get more thorough examination
>>   there. I
>>   > > think the
>>   > > > concept presented needs thorough examination and is
> nowhere
>>   near
>>   > > ready for
>>   > > > "Training" as the originator espoused.
>>   > > > This is not the right place as Fred has said.
>>   > > >
>>   > > >
>>   > > > _____
>>   > > >
>>   > > > From: amibroker@xxxxxxxxxxxxxxx
>>   > [mailto:amibroker@xxxxxxxxxxxxxxx]
>>   > > On Behalf
>>   > > > Of Fred
>>   > > > Sent: Friday, 10 November 2006 12:12 PM
>>   > > > To: amibroker@xxxxxxxxxxxxxxx
>>   > > > Subject: [amibroker] Re: Margin of Error
>>   > > >
>>   > > >
>>   > > >
>>   > > > What's the big deal ... Post it in AB-TS where those who
>>   aren't
>>   > > > interested don't have to read it ... The main forum is
> where
>>   for
>>   > > the
>>   > > > most part newbies come to learn about how to make things
>>   happen
>>   > > using
>>   > > > the product and not so newbies come to discuss new
> features
>>   and a
>>   > > > variety of other things realted to the product, as opposed
> to
>>   > > hearing
>>   > > > newbies spout off about concepts they can't quite put
> together
>>   > > that
>>   > > > have nothing to do with the product or its use.
>>   > > >
>>   > > > I'd be happy to participate unless of course you think
>>   differing
>>   > > > points of view are for some reason dangerous.
>>   > > >
>>   > > > --- In amibroker@xxxxxxxxx <mailto:amibroker%
>>   40yahoogroups.com>
>>   > > ps.com,
>>   > > > Keith McCombs <kmccombs@> wrote:
>>   > > > >
>>   > > > > BrianB2 --
>>   > > > > I, for one, am very disappointed by your decision to
>>   > discontinue
>>   > > > > "Project Based Training". I was looking forward to
> further
>>   > > > > installments. Trading is definitely a statistical
> endeavor,
>>   > your
>>   > > > first
>>   > > > > submission on Margin of Error was, in my opinion,
> extremely
>>   > well
>>   > > > written
>>   > > > > and "ON Topic".
>>   > > > >
>>   > > > > As for your apology, I will not accept it. It is not
> due.
>>   Nor
>>   > do
>>   > > > I
>>   > > > > want an apology from those on the forum who were so rude
> to
>>   you
>>   > > and
>>   > > > to
>>   > > > > the forum as a whole. I just wish they had acted in a
> more
>>   > civil
>>   > > > manner
>>   > > > > and allowed you to continue with your presentation.
> Their
>>   > > comments
>>   > > > were
>>   > > > > rarely constructive (except perhaps to their own egos).
> If,
>>   for
>>   > > > some
>>   > > > > ideological reason, they didn't agree with you, couldn't
>>   they
>>   > > just
>>   > > > have
>>   > > > > skipped your posts, with no harm done?
>>   > > > >
>>   > > > > Perhaps, after a few days, you can reconsider. Please,
> if
>>   > > > possible, try
>>   > > > > to block out the noise and continue on with your
>>   presentation.
>>   > > > >
>>   > > > > I am sure that there are others like myself who would
> love
>>   to
>>   > > > hear "the
>>   > > > > rest of the story".
>>   > > > > -- Keith
>>   > > > >
>>   > > > >
>>   > > > > brian.z123 wrote:
>>   > > > > >
>>   > > > > > This topic was part of OT:Project Based Training which
>>   > > actually is
>>   > > > > > not an OT subject.
>>   > > > > > I put it under OT to be extra polite.
>>   > > > > > It was all part of a project that involved
> demonstrating
>>   the
>>   > > > > > principles under discussion in AmiBroker at the end of
> the
>>   > > > > > discussion.
>>   > > > > >
>>   > > > > > The topic(s) are within both the guidelines for the
> forum
>>   and
>>   > > OT
>>   > > > > > subjects in the forum.
>>   > > > > >
>>   > > > > > Main topics of discussion:
>>   > > > > > - Trading techniques (using AmiBroker to implement the
>>   > > technique)
>>   > > > > >
>>   > > > > > Allowable off-topic discussion:
>>   > > > > > - Trading in general
>>   > > > > >
>>   > > > > > The project had no more to do with TS than it does,
> say,
>>   AT.
>>   > > > > > It had everything to do with trading in general.
>>   > > > > >
>>   > > > > > However I am removing it from the forum on two counts.
>>   > > > > > Firstly, I am customer orientated and I am responding
> to
>>   the
>>   > > > > > requests of forum members.
>>   > > > > > I don't agree with your arguments in anyway but I am
>>   > complying
>>   > > > with
>>   > > > > > your request.
>>   > > > > >
>>   > > > > > Secondly, and more importantly, some members of the
> forum
>>   have
>>   > > > > > breached my personal code of conduct.
>>   > > > > > The environment (of this project) has been made
> unpleasant
>>   > for
>>   > > me
>>   > > > > > and is not conducive to any further effort.
>>   > > > > >
>>   > > > > > That doesn't rule out my participation in other topics.
>>   > > > > >
>>   > > > > > Thanks to the people who contributed.
>>   > > > > > I apologise to anyone who was benefitting from the
>>   discussion
>>   > > and
>>   > > > > > who will now miss out on the rest of the *project*
>>   components.
>>   > > > > >
>>   > > > > > The decision was out of my hands.
>>   > > > > >
>>   > > > > > BrianB2.
>>   > > > > >
>>   > > > > > --- In amibroker@xxxxxxxxx <mailto:amibroker%
>>   > > 40yahoogroups.com> ps.com
>>   > > > <mailto:amibroker%
>>   > > > 40yahoogroups.com>,
>>   > > > > > "brian.z123" <brian.z123@>
>>   > > > > > wrote:
>>   > > > > > >
>>   > > > > > > Part1 of Project Based Training No1.
>>   > > > > > >
>>   > > > > > > The objective of the project is to introduce new
> traders
>>   to
>>   > > the
>>   > > > > > main
>>   > > > > > > concepts of system design/testing and demonstrate
> their
>>   > > > > > application
>>   > > > > > > in AmiBroker.
>>   > > > > > > At the same time it is hoped that the ideas
> presented
>>   will
>>   > > > provoke
>>   > > > > > > discussion and provide trading stimulation.
>>   > > > > > >
>>   > > > > > > All of the stages in the design process will not be
>>   > > demonstrated
>>   > > > > > as
>>   > > > > > > most have already been covered elsewhere in the
>>   AmiBroker
>>   > > > support
>>   > > > > > > material.
>>   > > > > > >
>>   > > > > > > A basic understanding of the application of some
>>   statistical
>>   > > > > > methods
>>   > > > > > > to the trading environment is a pre-requisite.
>>   > > > > > > The opening topics address this need.
>>   > > > > > >
>>   > > > > > > To those who find the subject matter new *the
> project*
>>   will
>>   > > be a
>>   > > > > > > workbook .
>>   > > > > > > To those who have experience in the subject it will
> be an
>>   > > > > > > opportunity to workshop.
>>   > > > > > >
>>   > > > > > > I would like to acknowledge my indebtedness to the
>>   academic
>>   > > > > > > community .
>>   > > > > > > I often refer to the material so generously
> interpreted
>>   for
>>   > > the
>>   > > > > > > layperson and made available at websites by academic
>>   > > > specialists,
>>   > > > > > > particularly those associated with Universities.
>>   > > > > > >
>>   > > > > > >
>>   > > >
>>   >
> *******************************************************************
>>   > > > > > > Margin of Error.
>>   > > > > > >
>>   > > > > > > Back-testing of historical data provides traders
> with a
>>   > > sample,
>>   > > > > > > typical of the trade they are testing. From that
> sample
>>   > they
>>   > > > make
>>   > > > > > > inferences about the larger group, or population, of
> all
>>   > past
>>   > > > > > trades
>>   > > > > > > and future trades, of the same type, that were not
>>   included
>>   > > in
>>   > > > > > their
>>   > > > > > > test window.
>>   > > > > > > Despite the fact that the people who teach them to
> back-
>>   > test
>>   > > > also
>>   > > > > > > teach them that the past can not predict the future,
>>   some
>>   > > > continue
>>   > > > > > > to act as if it can.
>>   > > > > > >
>>   > > > > > > If the past can't predict the future. How can anyone
>>   trade
>>   > > with
>>   > > > > > > confidence?
>>   > > > > > >
>>   > > > > > > The answer is that while the future can't be
> predicted,
>>   the
>>   > > > > > > likelihood of some mathematically defined outcomes
> can be
>>   > > > > > predicted
>>   > > > > > > with a degree of confidence.
>>   > > > > > > Statistics is the mathematical discipline that
> manages
>>   that
>>   > > very
>>   > > > > > > well.
>>   > > > > > >
>>   > > > > > > The caveat is that to apply statistical methods to
>>   trading
>>   > > > > > samples,
>>   > > > > > > the assumption is made that they are the result of a
>>   random
>>   > > > > > process.
>>   > > > > > > Where the trading system chosen is biased to non-
> random
>>   > > > behaviour
>>   > > > > > it
>>   > > > > > > will be prone to failure if the market acts contrary
> to
>>   > that
>>   > > > bias.
>>   > > > > > >
>>   > > > > > > For that reason system traders are faced with a
> choice
>>   > > between
>>   > > > > > > attempting to define market behaviour e.g. a trend,
> and
>>   > pick
>>   > > a
>>   > > > > > > system to suit that, or search for a universal
> signal
>>   that
>>   > is
>>   > > > > > > consistent irrespective of any assumed market bias.
>>   > > > > > >
>>   > > > > > > If statistics can predict the likelihood of future
>>   trading
>>   > > > > > outcomes,
>>   > > > > > > how accurate will it be?
>>   > > > > > >
>>   > > > > > > *Standard error* or *margin of error* offers traders
> a
>>   > > solution
>>   > > > > > but
>>   > > > > > > they are not subjects that are often discussed.
>>   > > > > > >
>>   > > > > > > In his book ,*Design, Testing, and Optimisation of
>>   Trading
>>   > > > > > Systems*
>>   > > > > > > (John Wiley & Sons, 1992), Robert Pardo raises the
> issue
>>   of
>>   > > the
>>   > > > > > > accuracy of trading *predictions* based on the size
> of
>>   the
>>   > > > sample
>>   > > > > > > used:
>>   > > > > > >
>>   > > > > > > * The sample size must be large enough to allow the
>>   trading
>>   > > > system
>>   > > > > > > to generate a statistically significant sample of
> trades.
>>   > > > > > > A sample of one trade is certainly insignificant,
>>   whereas a
>>   > > > sample
>>   > > > > > > of 50 trades or more is generally adequate.*
>>   > > > > > >
>>   > > > > > > He uses Standard Error as a measure of significance:
>>   > > > > > >
>>   > > > > > > StdError = = 1/SquareRoot(sample size),
>>   > > > > > >
>>   > > > > > > 1/SqRt(50) = = 14.1%.
>>   > > > > > >
>>   > > > > > > There is little by way of further explanation
> provided.
>>   > > > > > >
>>   > > > > > > Applying the formula to a greater number of samples:
>>   > > > > > >
>>   > > > > > > Where N = = the number of trades in the sample
>>   > > > > > >
>>   > > > > > > StdError factor = = 1/SqRt(N)
>>   > > > > > > StdError% = 1/SqRt(N) * 100
>>   > > > > > >
>>   > > > > > > If N = = 2500 the StdError% = = 1/SqRt(2500) * 100 =
> =
>>   +/-
>>   > 2%
>>   > > > > > > If N = = 10000 the StdError% = = 1/SqRt(10000) * 100
> = =
>>   +/-
>>   >
>>   > > 1%
>>   > > > > > >
>>   > > > > > > A trade sample of 10000 to provide statistical
> accuracy
>>   of
>>   > > 1% is
>>   > > > > > not
>>   > > > > > > easily achievable for traders, although a lot easier
> than
>>   > > > > > accurately
>>   > > > > > > surveying the eye colour of Polar Bears.
>>   > > > > > >
>>   > > > > > > Pardos equation is in fact, a rounding of the
> StdError
>>   > > equation
>>   > > > > > for
>>   > > > > > > a 95% level of confidence:
>>   > > > > > >
>>   > > > > > > Margin of error at 99% confidence = = 1.29/SqRt(N)
>>   > > > > > > Margin of error at 95% confidence = = 0.98/SqRt(N)
>>   > > > > > > Margin of error at 90% confidence = = 0.82/SqRt(N)
>>   > > > > > >
>>   > > > > > > Later in the project I will use a basic random
> number
>>   > > generator,
>>   > > > > > > within Xcel, to provide a visual aid that traders
> can
>>   use to
>>   > > > > > > understand the *sample* concept and decide for
>>   themselves
>>   > > what
>>   > > > > > > constitutes an adequate sample.
>>   > > > > > >
>>   > > > > > > Wikipedia provides some additional clarity on the
>>   subject:
>>   > > > > > >
>>   > > > > > > http://en.wikipedia
>>   > > <http://en.wikipedia.org/wiki/Margin_of_error>
>>   > > > .org/wiki/Margin_of_error
>>   > > > > > <http://en.wikipedia
>>   > > <http://en.wikipedia.org/wiki/Margin_of_error>
>>   > > > .org/wiki/Margin_of_error>
>>   > > > > > >
>>   > > > > > > *The margin of error expresses the amount of the
> random
>>   > > > variation
>>   > > > > > > underlying a survey's results. This can be thought
> of as
>>   a
>>   > > > measure
>>   > > > > > > of the variation one would see in reported
> percentages
>>   if
>>   > > the
>>   > > > same
>>   > > > > > > poll were taken multiple times. The larger the
> margin of
>>   > > error,
>>   > > > > > the
>>   > > > > > > less confidence one has that the poll's reported
>>   > percentages
>>   > > are
>>   > > > > > > close to the "true" percentages, that is the
> percentages
>>   in
>>   > > the
>>   > > > > > > whole population.*
>>   > > > > > >
>>   > > > > > > *An interesting mathematical fact is that the margin
> of
>>   > error
>>   > > > > > > depends only on the sample size and not on the
>>   population
>>   > > size,
>>   > > > > > > provided that the population is significantly larger
>>   than
>>   > the
>>   > > > > > sample
>>   > > > > > > size, and provided a simple random sample is used.
> Thus
>>   for
>>   > > > > > > instance.......the running example with 1,013 random
>>   > > > samples......would
>>   > > > > > > yield essentially the same margin of error (4% with
> a
>>   99%
>>   > > level
>>   > > > of
>>   > > > > > > confidence) regardless of whether the
>>   > > > population..........consisted of
>>   > > > > > > 100,000 or 100,000,000.*
>>   > > > > > >
>>   > > > > > > In short the tail of the trading system sample is
>>   swinging
>>   > > the
>>   > > > > > > trading system cat.
>>   > > > > > >
>>   > > > > > > BrianB2
>>   > > > > > >
>>   > > > > > > The material contained in this topic is for
> educational
>>   and
>>   > > > > > > discussion use only.
>>   > > > > > > It is not intended as financial advice and should
> not be
>>   > > > construed
>>   > > > > > > as such.
>>   > > > > > > The author is not an accredited academic or
> financial
>>   > > advisor.
>>   > > > > > >
>>   > > > > >
>>   > > > > >
>>   > > > >
>>   > > >
>>   > >
>>   >
>>
>
>
>
>
>
> Please note that this group is for discussion between users only.
>
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>
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>
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>
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>
>
>
> 


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