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I am using Rapidshare for file sharing.
Free downloads are available but they are slower than paid download
and limited to 1 download per time ... wait a while and you can
download again (still good value for my customers).
http://rapidshare.com/files/195190948/BinomialMaster_ABVersion.xls
A short ReadMe, to help understand the file, is at:
http://zboard.wordpress.com/
I can answer a few questions about the details in the file for a
limited time (while my memory is fresh) .... post questions, if any,
via comments at the Zboard.
--- In amibroker@xxxxxxxxxxxxxxx, "brian_z111" <brian_z111@xxx> wrote:
>
> File limits prevented me uploading the BinomialSimulation file(s)
to
> this group ... 20MB per file. I will post links to at least one
> example, at the following temporary site, sometime this week:
>
> http://zboard.wordpress.com/
>
> I will post some basic notes afterall because the task of following
> the Excel sheets would be beyond anyone without them.
>
> The site might live on for a while after that.
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "brian_z111" <brian_z111@> wrote:
> >
> > I decided to post the Binomial Simulation files a few days
ago ...
> I
> > am not going to announce the upload so this post is the
discussion
> > link for them (one or more files will appear at some stage).
> >
> > FTR They do predict the eq dist quite well, for biased and none
> > biased 'coins' but there is one thing about them that does
concern
> > me ... I referenced the same synthetic trade series to make the
> > binomial distribution and to create the synthetic eq curves ...
> that
> > seems a bit incestuous in some ways.
> >
> > On the other hand they could be full of incorrect math
assumptions
> > cos I got the math off Wikipedia!
> >
> > Guru Brian ;-)
> >
> >
> > --- In amibroker@xxxxxxxxxxxxxxx, "brian_z111" <brian_z111@>
wrote:
> > >
> > >
> > > > This is a valid model as long as stationarity holds ... I
have
> > > > simulated random trading 'systems' and predicted the outcome
by
> > > using
> > > > binomial probability, that references a frequency
distribution
> of
> > > the
> > > > randomly generated trades, and it predicted the actual equity
> > > > distributions extremely well (a lognormal dist appears at
very
> > high
> > > > N's).
> > >
> > >
> > > More precisely, I have simulated trade series, using the RNG in
> > > Excel, for random walks (50/50 systems) and biased systems,
with
> > > normally distributed trade series (I used CentralLimitThereom
to
> > > create NormDists from the uniform output of the generator.
> > >
> > > I simulated equity curves, using the synthetic trades, and at
the
> > > same time used BinomialProb to model the predicted distribution
> of
> > > the eq curves (I imagined I was tossing a coin with variable
> values
> > > for heads and tails ... of course in trading we can win lose or
> > draw
> > > whereas in my model we can only win or lose).
> > >
> > > You might like to see the files?
> > >
> > > I am bored with that topic.
> > >
> > > I am not a mathematician ... it might be a load of old rubbish
> for
> > > all I know.
> > >
> > > As our discussion shows .. we can't get any statistical
certainty
> > > anywhere in trading ... only approximations and probabilties.
> > >
> > > It is just another approximation, like MCS and involves massive
> > > number crunching.
> > >
> > > I didn't finish it because I wanted a quick and dirty method.
> > >
> > > The files are rough as old bags.
> > >
> > > I didn't make notes so even I have a hard time following the
> > > logic ... I had a look at them the other day I had to start
> tracing
> > > the formulas in the cells to see how I had done it.
> > >
> > > I'll post some of them in the file section one day (Howard
> collects
> > > trading things).
> > >
> > > I won't scrub them up though ... take them or leave them ...
> sorry
> > no
> > > questions or explanations (anyway Howard and other maths people
> > know
> > > how to do that stuff).
> > >
> > >
> > > --- In amibroker@xxxxxxxxxxxxxxx, "brian_z111" <brian_z111@>
> wrote:
> > > >
> > > > Gidday Mate,
> > > >
> > > > I wasn't planning on posting again today as I am going away
for
> a
> > > few
> > > > days ..... a good question though so I couldn't resist.
> > > >
> > > >
> > > > I did notice Fred's comment on the priority he places on
> > > sensitivity
> > > > analysis.
> > > >
> > > > He has made the comment before and I came to that view
> > > independently
> > > > a way back anyway (Howard's random noise test is another
> > > interesting
> > > > idea for single sample analysis).
> > > >
> > > > I also recall that he doesn't believe scrambling the order of
> the
> > > > trades provides any meaningful feedback.
> > > >
> > > > That isn't a reason for me not to reach my own conclusions.
> > > >
> > > > Fred has also talked about small N retesting (walk forward),
> and
> > > > adjusting his system rules, on a short term basis, so while I
> am
> > > not
> > > > keen on the idea I am keeping an open mind on the subject.
> > > >
> > > >
> > > >
> > > > > This is the second time in the >past few
> > > > > days that you seem to have equated trading/backtesting
system
> > > > >outcomes
> > > > > to a random series of coin flip outcomes (random binary
> > > occurances).
> > > > >
> > > > > Serious question... what is your point? What is the
> relevence
> > os
> > > > >the
> > > > > "Coin Flip" metaphor where trading systems is concerned?
> > > >
> > > > Well, developers are selling software specifically designed
for
> > > > performing MSC for trading analysis and at least one guy has
> > > written
> > > > a book on the subject.
> > > >
> > > > In both software packages, that I have some familiarity with,
> > their
> > > > model assumes stationarity, and independency i.e. their model
> > > treats
> > > > the data as if it is the outcome of a coin toss with variable
> > > values
> > > > on the +- side of the coin.
> > > >
> > > > This is a valid model as long as stationarity holds ... I
have
> > > > simulated random trading 'systems' and predicted the outcome
by
> > > using
> > > > binomial probability, that references a frequency
distribution
> of
> > > the
> > > > randomly generated trades, and it predicted the actual equity
> > > > distributions extremely well (a lognormal dist appears at
very
> > high
> > > > N's).
> > > >
> > > > The value, to me in that model, is that it is a training tool
> > that
> > > > conditioned me to accept variance as 'normal' and if the
market
> > is
> > > > stationary then it would have direct relevance to
trading.....
> > the
> > > > worst case outcome would be that I could incur losses, with a
> > > > probability as indicated by the Cumulative Distrubution
> Function
> > > for
> > > > the possible equity outcomes (simulation is one way for non -
> > > > mathematicians to calc this and view it in a chart).
> > > >
> > > >
> > > > Ask yourself ....
> > > >
> > > > afer you have conducted a successful OOS, and collated the
> trade
> > > > sample, when you start to trade it do you expect:
> > > >
> > > > - all trades to be the same, or similar, and occur with the
> same
> > > > frequency (TradeSim),
> > > > - all trades to be the same, or similar, and have variations
in
> > the
> > > > frequency (MSA),
> > > > - something else?
> > > >
> > > > Trading, however, is not a coin toss.
> > > >
> > > > It is more like a sample generator that produces trades as a
> > result
> > > > of presenting dynamic data to the system (filter).
> > > >
> > > > To what extent could a 'real life' trading system emulate a
> coin
> > > > toss, with variable values ... how could that come about?
> > > >
> > > > (interesting that the very functional optF formula came about
> as
> > > the
> > > > variable value coin toss staking formula).
> > > >
> > > > Is it possible or not?
> > > >
> > > > A lot of people seem to think it is, judging by their books
and
> > > > software.
> > > >
> > > > Presumably, when the underlying data changes, the sample
> profile
> > > > (mean, StDev etc) can change and we end up with a better or
> worse
> > > > outcome than anticipated by the OOS.
> > > >
> > > > So, does the non-stationary behaviour of the markets
invalidate
> > the
> > > > coin toss model?
> > > >
> > > > That is the ineresting question, and I don't know the answer
to
> > it,
> > > > or even if there is a definite answer.
> > > >
> > > > I was hopeful that people would pick up on that key point and
> > shed
> > > > some light on the subject.
> > > >
> > > > I know, from my long hours of simulating random data, what
> random
> > > > behaviour looks like when I see it.
> > > >
> > > > Clearly the markets have a certain amount of random behaviour.
> > > >
> > > > Howard commented somewhere, or another, that there is a
certain
> > > > amount of randomness in the market (I can't recall the method
> he
> > > used
> > > > to measure it).
> > > >
> > > > It is quite easy to observe if data has any random qualities,
> > > > especially if we measure the core attributes (50/50 heads and
> > tails
> > > > and its persistence into 2,3,4 heads in a row etc).
> > > >
> > > > Once again I ask you to consider:
> > > >
> > > > if I measure the S&P500 index, on close, and it goes up
approx
> 50
> > > and
> > > > down approx 50 (+- variance that is typical of a random
> binomial
> > > > event) and the subsequent second head or tail follow with 0.5
> > prob
> > > > etc I am justified in considering it top be a pseudo random
> > > binomail
> > > > event?
> > > >
> > > > I have done quick and dirty measurements, and accurate
> > > measurements,
> > > > on dependency (or on its inverse, which is independency) and
> find
> > > > that there is a good deal of independency in the markets (I
> > posted
> > > > some q&d code to measure that last week).
> > > >
> > > > I have speculated before, on the point, that the rational
> market
> > is
> > > > the market that follows fundamental value, which tends to be
>=
> > the
> > > > yearly (macro) timeframe, and, everything else is the
> irrational
> > > > market.
> > > >
> > > > Consider an intraday market ... what is rational about the
> price
> > > > movement during any given part of the day?
> > > >
> > > > - Draw a trend line on the chart .. we will assume that we
know
> > > what
> > > > a trend is for this exercise, although that is a debatable
> point.
> > > >
> > > > - The trend, a straight line, is rational (it is perfectly
> > > following
> > > > fundamental value).... it is 2007 and it is up ;-)
> > > >
> > > > - All of the ups and downs that occur around it are
irrational
> > > > (bucking the trend).
> > > >
> > > > - The trend line goes under the pivot lows.
> > > >
> > > > - Your system buys at the pivot lows and sells at = = 2 StDev
> > above
> > > > the trend line.
> > > >
> > > > - Place a stop under the trend line at - 1 stDev.
> > > >
> > > > - Assume no commission and no slippage.
> > > >
> > > > - Your payoff ratio is 2/1
> > > >
> > > > - assume there is no variance in volatility so the PR is a
> > constant
> > > > value
> > > >
> > > > - the win/loss ratio is determined by the random meandering
of
> > the
> > > > irrational price movements up and down.
> > > >
> > > > Note they are irrational because people are buying and
selling
> at
> > > the
> > > > wrong time and for the wrong reasons - if they were rational
> they
> > > > would only be buying selling as fundamental values change.
> > > >
> > > > - the trade series produced would look exactly that that
> produced
> > > by
> > > > a coin tossed with +2, -1 value on it.
> > > >
> > > > Now, you have tested this system, OOS, and it is a winner.
> > > >
> > > > What chance for stationarity when you trade live?
> > > >
> > > > If the trend continues there is a very good chance that the
> > random
> > > > emualator (system meeting dynamic data) will continue to
> perform
> > > like
> > > > a biased coin +- variance i.e. the payoff ratio can't change
> but
> > > the
> > > > W/L will (it always does when I toss a coin).
> > > >
> > > > If the trend changes your winning model will be more likely
to
> > bust.
> > > >
> > > > That could be the reason Fred, and others, like to
continually
> > > retest.
> > > >
> > > > I have another approach to getting around this problem (this
is
> > > > actually the real point of my posts) ...
> > > >
> > > > ..... to accomodate non-stationarity either adjust quickly OR
> use
> > a
> > > > dimensionless model e.g. don't believe in trends and then you
> > can't
> > > > be on the wrong side of them.
> > > >
> > > >
> > > >
> > > > However, that is only speculation.
> > > >
> > > > What do you think?
> > > >
> > > >
> > > > Again ... what is the relevance of coin tosses to trading IMO:
> > > >
> > > >
> > > > - wonderful training tool
> > > > - a good OOS can not predict exactly what the outcome of live
> > > trading
> > > > will be (subject to nonstationarity) and neither can
simulation
> > > (coin
> > > > tossing) but it gives a good approximation of the
possibilities
> > > (also
> > > > subject to non-stationarity).
> > > >
> > > > As a quid pro quo .....
> > > >
> > > > ..... if you, or anyone else, can give me any explanation
> and/or
> > > > proof that the coin toss metaphor has no relevance to trading
I
> > > would
> > > > be delighted.
> > > >
> > > >
> > > > Anyway, I think Patrick already answered the question, or
told
> us
> > > > where to find it.
> > > >
> > > > Good luck with your trading.
> > > >
> > > > brian_zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
> > > >
> > > >
> > > > --- In amibroker@xxxxxxxxxxxxxxx, "Phsst" <phsst@> wrote:
> > > > >
> > > > > Hello Brian,
> > > > >
> > > > > Thanks for the mention in your New Years post. I felt
> humbled
> > to
> > > > be in
> > > > > the same honerable mention list as Fred (He is a very smart
> > Dude
> > > (no
> > > > > kidding!)) It took me a while (some years back) to figure
out
> > > what a
> > > > > smart guy Fred really is. I've since learned that when Fred
> > > speaks,
> > > > it
> > > > > pays to think and be silent for a good long while before
> > drawing
> > > any
> > > > > conclusions.
> > > > >
> > > > > To your "crystal clear" point... This is the second time in
> the
> > > > past few
> > > > > days that you seem to have equated trading/backtesting
system
> > > > outcomes
> > > > > to a random series of coin flip outcomes (random binary
> > > occurances).
> > > > >
> > > > > Serious question... what is your point? What is the
> relevence
> > os
> > > > the
> > > > > "Coin Flip" metaphor where trading systems is concerned?
> What
> > am
> > > I
> > > > > missing?
> > > > >
> > > > > Your Bud... Phsst
> > > > >
> > > > >
> > > > >
> > > > > This is the second time
> > > > > --- In amibroker@xxxxxxxxxxxxxxx, "brian_z111"
<brian_z111@>
> > > wrote:
> > > > > >
> > > > > > To be chrystal clear about my hypothesis:
> > > > > >
> > > > > >
> > > > > > We are trying to design a system that produces the same
set
> of
> > > > > > trades, in the future, as it has in the past i.e trades
and
> > not
> > > > > > combinations of trades.
> > > > > >
> > > > > > If a solid gold coin, minted by the US treasury, with a
> head
> > > and a
> > > > > > tail clearly stamped on each side, and only two values +1
> or -
> > 1
> > > > can't
> > > > > > reproduce two equity curves that look the same, after N
> > tosses,
> > > > how
> > > > > > can we expect a trading system to do that when it has a
> range
> > of
> > > > > > possible values?
> > > > > >
> > > > > > AND it doesn't get any better as N increases.
> > > > > >
> > > > > > Put your time and effort into maximising the STABILITY
> > > > > > (predictability, boundness) of the trade set 'with an
edge'
> > > THEN
> > > > use
> > > > > > MM to optimise the equity outcome the system produces
> > (optimise
> > > ==
> > > > > > your definition e.g. max return, min risk or whatever).
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > > --- In amibroker@xxxxxxxxxxxxxxx, "brian_z111"
brian_z111@
> > > wrote:
> > > > > > >
> > > > > > > Howard,
> > > > > > >
> > > > > > > Thanks for your post.
> > > > > > >
> > > > > > > A very well written article.
> > > > > > >
> > > > > > > Some contrary comment (first referencing some of your
> > points
> > > and
> > > > > > > then, later, some comments of my own):
> > > > > > >
> > > > > > >
> > > > > > > > By trying many
> > > > > > > > combinations of logic and parameter values, we will
> > > eventually
> > > > > > find
> > > > > > > >a system that is profitable for the date range
analyzed.
> > > > > > >
> > > > > > > You are assuming that all successful long term traders
> > > arrived
> > > > at
> > > > > > > their system(s) by using this approach ... perhaps
there
> > are
> > > > > > systems
> > > > > > > out there that have no optimiseable parameters and only
> one
> > > > > > > underlying logic.
> > > > > > >
> > > > > > > If so they are likely be based on primal market
behaviour
> > and
> > > > > > > therefore persistent across markets and time i.e they
> would
> > > > have to
> > > > > > > be systems based on market characteristics that are
> > relatively
> > > > > > > stationary.
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > > testing the
> > > > > > > > profitability of a trading system that was developed
> > using
> > > > recent
> > > > > > > >data
> > > > > > > > on older data is guaranteed to over-estimate the
> > > > profitability of
> > > > > > > the
> > > > > > > > trading system.
> > > > > > >
> > > > > > > You know that in science (philosophy/logic) it only
takes
> > one
> > > > > > > refutation to dethrone the current ruling hypothesis ...
> > > > > > >
> > > > > > > if a long system, developed on the last 12 months of
data
> > > (when
> > > > the
> > > > > > > market was experiencing a bear riot) is then tested OOS
> on
> > the
> > > > > > prior
> > > > > > > years data it will outperform the in sample tests (OOS
> > would
> > > be
> > > > > > > conducted on bull market data).
> > > > > > >
> > > > > > >
> > > > > > > > There is very little reason to expect that future
> > behavior
> > > and
> > > > > > > > profitability of well known trading systems will be
the
> > > same
> > > > as
> > > > > > past
> > > > > > > > behavior.
> > > > > > >
> > > > > > > Do we have any empirical evidence of this?
> > > > > > >
> > > > > > > First we would have to have an agreed definition
of 'well
> > > > known',
> > > > > > > make a list of the systems, and then perform massive
> > testing.
> > > > > > >
> > > > > > > To scrupulously prevent any bias creeping testing would
> > have
> > > to
> > > > be
> > > > > > > conducted live, and not on historical data.
> > > > > > >
> > > > > > >
> > > > > > > We only know that they were successful 'in the past' by
> IS
> > > > testing,
> > > > > > > or by claim.
> > > > > > >
> > > > > > > Do we have any, or many, certified performance records
> > > provided
> > > > by
> > > > > > > traders who claim to have had success with those 'well
> > known'
> > > > > > systems.
> > > > > > >
> > > > > > > > Statistics gathered from in-sample results have
> > > > > > > > no relationship to statistics that will be gathered
> from
> > > > trading.
> > > > > > >
> > > > > > > Not, so.
> > > > > > >
> > > > > > > They have every bearing on the stats gathered in
trading
> > > because
> > > > > > only
> > > > > > > systems with good IS performance make it to the OS, or
> live
> > > > > > trading,
> > > > > > > phase.
> > > > > > >
> > > > > > > OOS testing is only proceeded with because the analyst
> has
> > > every
> > > > > > > expectation, or hope, that the good IS stats will be
> > > reproduced
> > > > OOS.
> > > > > > >
> > > > > > > In fact it is the relative performance between the IS
and
> > OOS
> > > > stats
> > > > > > > the encourages us to proceed or abort.
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > Re trading the edge erodes the edge:
> > > > > > >
> > > > > > > It is an assumption that all players are trading
> > systems ...
> > > > many
> > > > > > are
> > > > > > > not, in fact the vast majority are not.... those who
> aren't
> > > > control
> > > > > > > vastly greater sums of money than those who do.
> > > > > > >
> > > > > > > It is an assumption that all wins erode the system ...
> they
> > > > could
> > > > > > be
> > > > > > > just lucky wins that the trader can't exploit long
term,
> or
> > > > > > > successful wins that the trader doesn't sustain e.g
they
> > > might
> > > > not
> > > > > > > have the capital, use the correct staking or maintain
> self-
> > > > > > discipline
> > > > > > > in the future.
> > > > > > >
> > > > > > > Only a very small percentage of traders are successful,
> and
> > > > hence
> > > > > > > trading a successful system ... every one else who is
> > trading
> > > is
> > > > > > just
> > > > > > > making noise.
> > > > > > >
> > > > > > > There are millions of system permutations, instruments,
> > > markets,
> > > > > > > staking systems etc ..... how many successful traders
> would
> > > it
> > > > take
> > > > > > > to exahaust all of the successful permutations?
> > > > > > >
> > > > > > > > The follow-on point, which relates to Monte Carlo
> > analysis,
> > > is
> > > > > > that
> > > > > > > > rearranging the in-sample trades gives no insight
into
> > the
> > > > future
> > > > > > > > characteristics of the system. Yes, you can see the
> > effect
> > > of
> > > > > > taking
> > > > > > > > the trades in different orders. But why bother? They
> are
> > > still
> > > > > > > > in-sample results and still have no value.
> > > > > > >
> > > > > > > If you are engineering an F1 racing car there is only
> track
> > > > > > > testing/simulation (99.9 of the time) and racing
> > performance
> > > > (1% of
> > > > > > > the time).
> > > > > > >
> > > > > > > The more information you gather off the track the more
> > likely
> > > > you
> > > > > > are
> > > > > > > to perform on the track OR know what to adjust and when
> to
> > > > adjust
> > > > > > it
> > > > > > > if performance doesn't meet expectations.
> > > > > > >
> > > > > > > Do you know of any F1 teams that don't test/simulate?
> > > > > > >
> > > > > > > Do you know of any F1 teams that only test/simulate
one,
> or
> > > > > > limited,
> > > > > > > metrics?
> > > > > > >
> > > > > > > What is testing if not 'massive examination of what-if
> > > > scenarios'?
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > Re MonteCarlo and stationarity
> > > > > > >
> > > > > > > I haven't studied the subject in depth.
> > > > > > >
> > > > > > > Mainly it is has been used outside of trading and in
> > > different
> > > > ways
> > > > > > > to the ways that traders use it .... possibly it would
> be
> > > best
> > > > to
> > > > > > > limit trading discussion to 'trading simulation' and
drop
> > the
> > > MC
> > > > > > part
> > > > > > > of the name.
> > > > > > >
> > > > > > > I have only found one book devoted to the subject and I
> > regret
> > > > > > buying
> > > > > > > it .... 'MCS and System Trading' by Volker Butzlaff.
> > > > > > >
> > > > > > > I have also test driven TradeSim and MSA.
> > > > > > >
> > > > > > > Referencing their trading apps.
> > > > > > >
> > > > > > > TS arranges the trades, as a time series, and randomly
> > walks
> > > > > > through
> > > > > > > all permutations to simulate 'live trading'..... it is
an
> > MM
> > > > test,
> > > > > > of
> > > > > > > some kind, because equity is allocated prior to the
walk
> > > > through.
> > > > > > >
> > > > > > > AB's backtester, in default mode, does this once.
> > > > > > >
> > > > > > > I assume other methods could be used ... as per my
> pervious
> > > XYZ
> > > > > > > example:
> > > > > > >
> > > > > > > - abcXdefghi with simultaneous trades on day 4,
> > > > > > > - we can only achieve a finite set of permutations,
> > > > > > > - the outcome of massive sampling will tend to the mean
+-
>
> > > > variance,
> > > > > > > - we can simulate the eq outcomes using random sampling
> of
> > > > uniform
> > > > > > > size, ave the result per random series and then freq
dist
> > the
> > > > means
> > > > > > > (Central Limit Theoreom predicts a pseudo norm dist).
> > > > > > > > 30 selections per series * ? series will achieve an
> > approx
> > > of
> > > > > > > possible eq outcomes (I'm not sure if distrubtions obey
> the
> > > > laws of
> > > > > > > sample error ... I don't think they do).
> > > > > > >
> > > > > > > TradeSims real life simulation assumes stationarity
(the
> > > balls
> > > > in
> > > > > > the
> > > > > > > bin, and their values will remain constant into the
> future).
> > > > > > >
> > > > > > > It also assumes that they will be selected from the bin
> in
> > > the
> > > > same
> > > > > > > order, or frequency to be absolutely correct (the order
> > > doesn't
> > > > > > > change anything only the frequency).... to be precise
> about
> > > it,
> > > > > > their
> > > > > > > model assumes that if you have picked the worst
> historical
> > > loss
> > > > out
> > > > > > > of the bin 2/1000 trades that you will not only
> experience
> > > the
> > > > same
> > > > > > %
> > > > > > > as the worst loss in the future but that it will also
> only
> > > occur
> > > > > > > 2/1000 times.
> > > > > > >
> > > > > > > MSA puts all of the balls in the bin and selects them
in
> a
> > > way
> > > > that
> > > > > > > allows new combinations (frequencies) until all possible
> > > > > > frequencies
> > > > > > > are exhausted i.e. they assume stationarity only in
> values
> > > but
> > > > not
> > > > > > > frequency of dist (they assume dist is a probability
> > > statement
> > > > and
> > > > > > > not a constant or series of constants).... to be
precise
> > > about
> > > > it
> > > > > > > they assume that if it can happen it will.
> > > > > > >
> > > > > > > So, stationarity is the issue.
> > > > > > >
> > > > > > > So many people are confusing variance with non-
> > > stationarity ....
> > > > > > they
> > > > > > > are being fooled by randomness e.g.
> > > > > > >
> > > > > > > we know that the trial records of fair coin tosses are
> > > > stationary
> > > > > > AND
> > > > > > > they have a surprising range of outcomes (variance) ...
> > this
> > > is
> > > > > > very
> > > > > > > easy to see if simulated and expressed as equity
outcomes.
> > > > > > >
> > > > > > > Therefore, in trading, we can, at the least expect a
> > > tremendous
> > > > > > > amount of variance ... no less than what can be
expected
> > from
> > > a
> > > > > > coin
> > > > > > > toss experiment ... this variance can be estimated
using
> > > several
> > > > > > > methods, simulation being one easy, push the computer
> > button
> > > and
> > > > > > look
> > > > > > > at the graph method.
> > > > > > >
> > > > > > > So, the value of the simulation is in training the mind
> to
> > > > accept
> > > > > > > variance and mentally prepare for the worst case losses.
> > > > > > >
> > > > > > > However, it doesn't matter how we design our systems we
> can
> > > not
> > > > do
> > > > > > > anything about stopping non-stationarity.
> > > > > > >
> > > > > > > Our system will get wiped out in OOS if it is not
robust
> OR
> > > if
> > > > the
> > > > > > > market changes.
> > > > > > >
> > > > > > > If our system is robust it will still get wiped out if
> the
> > > > market
> > > > > > > changes.
> > > > > > >
> > > > > > > However, IMO, non-stationarity is not, or need not be,
as
> > > > pervasive
> > > > > > > in trading as we think.
> > > > > > >
> > > > > > > As I have said in the past, and already in this
post ...
> > many
> > > > > > traders
> > > > > > > are slayed by the innocuous looking Black Swan, because
of
> > > > > > ignorance
> > > > > > > about its behaviours.
> > > > > > >
> > > > > > > Also, we are very lucky, in trading, to be able to have
> some
> > > > > > control
> > > > > > > over our dataset i.e. our sample space is bounded by
our
> > > stops
> > > > and
> > > > > > > other inherent factors in the design.
> > > > > > >
> > > > > > > Example:
> > > > > > >
> > > > > > > If we have a stop in place then we are reasonably
> unlikely
> > to
> > > > > > > experience losses beyond the stop + commission +
> > > slippage ....
> > > > when
> > > > > > a
> > > > > > > stop failure does occur it is very infrequent and not
> > > > necessarily
> > > > > > > career destroying.
> > > > > > >
> > > > > > > When we have a profit stop in place we can expect to at
> > least
> > > > get
> > > > > > the
> > > > > > > stop OR BETTER.
> > > > > > >
> > > > > > > We can also, in some circumstances, buy a guaranteed
stop
> > > loss.
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > In summary:
> > > > > > >
> > > > > > > Because, as traders, we are statistically lucky, we can
> > > choose,
> > > > to
> > > > > > > some extent, which marbles to put in the bin.
> > > > > > >
> > > > > > > We can absolutely limit the worst case, ensure we get
at
> > > least
> > > > the
> > > > > > > best case and then take everything in between that
comes
> > > along.
> > > > > > >
> > > > > > > Since the boundaries are limited, the range of possible
> > > values
> > > > on
> > > > > > the
> > > > > > > balls is finite and will always be normally
distributed,
> > when
> > > > > > > expressed as possible mean P & L (central limit
> > > theoreom).....
> > > > the
> > > > > > > staging post on the trail towards possible equity
> outcomes.
> > > > > > >
> > > > > > > I think under those circumstances that the balls in the
> > > bucket,
> > > > > > > collected over a long sample, are a pretty fair
> > > representation
> > > > of
> > > > > > > what we can expect in the future.
> > > > > > >
> > > > > > > If they are not then we only have ourselves to blame
for
> > our
> > > > poor
> > > > > > > system design.
> > > > > > >
> > > > > > > Nothing anyone can do, can put an end to stockmarket
non-
> > > > > > stationarity
> > > > > > > but the challenge for the trader is to find ways to
> either
> > > > absorb
> > > > > > it
> > > > > > > or anticipate it.
> > > > > > >
> > > > > > >
> > > > > > > One important point was absent from your post.
> > > > > > >
> > > > > > > Kelly and Vince et al have proved conclusively that
> staking
> > > > > > directly
> > > > > > > and remarkably affects outcomes.
> > > > > > >
> > > > > > > Based on that fact I can't understand why you, and many
> > other
> > > > > > > commentators, continue to draw inferences from
backtests
> > that
> > > > > > include
> > > > > > > a limited range of portfolio allocations ... either
don't
> > > > involve
> > > > > > eq
> > > > > > > at all OR test across all possible eq allocations.
> > > > > > >
> > > > > > > (if you do opt for the latter choice wouldn't it be
> smarter
> > > to
> > > > do
> > > > > > > that using the short mathematical solution rather than
> the
> > > long
> > > > > > > massive optimisation approach?).
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > The babblers epilogue:
> > > > > > >
> > > > > > > I guess it is appropriate that an informal book should
> have
> > an
> > > > > > > informal ending!
> > > > > > >
> > > > > > > "Always look on the bright side of life" ...
> > > > > > >
> > > > > > > ... from the life of Brian :-)
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > --- In amibroker@xxxxxxxxxxxxxxx, "Howard Bandy"
> > > <howardbandy@>
> > > > > > > wrote:
> > > > > > > >
> > > > > > > > Greetings all --
> > > > > > > >
> > > > > > > > The posting was originally made by me to Aussie Stock
> > > Forums
> > > > on
> > > > > > > > February 2, 2009. But in light of recent
discussions,
> > I'll
> > > > cross
> > > > > > > post
> > > > > > > > it here.
> > > > > > > >
> > > > > > > > Some of my thoughts on using Monte Carlo techniques
> with
> > > > trading
> > > > > > > systems.
> > > > > > > >
> > > > > > > > First, some background.
> > > > > > > >
> > > > > > > > Monte Carlo analysis is the application of repeated
> random
> > > > > > sampling
> > > > > > > > done in order to learn the characteristics of the
> process
> > > > being
> > > > > > > studied.
> > > > > > > >
> > > > > > > > Monte Carlo analysis is particularly useful when
closed
> > form
> > > > > > > solutions
> > > > > > > > to the process are not available, or are too
expensive
> to
> > > > carry
> > > > > > out.
> > > > > > > > Even in cases when a formula or algorithm can supply
the
> > > > > > information
> > > > > > > > desired, using Monte Carlo analysis can often be used.
> > > > > > > >
> > > > > > > > Here is an example of Monte Carlo analysis. Assume
that
> a
> > > > student
> > > > > > is
> > > > > > > > unaware of the formula that relates the area of a
> circle
> > to
> > > > its
> > > > > > > > diameter. A Monte Carlo solution is to conceptually
> draw
> > a
> > > > square
> > > > > > > with
> > > > > > > > sides each one unit in length on a graph, with the
> origin
> > > at
> > > > the
> > > > > > > lower
> > > > > > > > left corner. The horizontal side goes from 0.0 to 1.0
> > along
> > > > the x-
> > > > > > > axis
> > > > > > > > and the vertical side goes from 0.0 to 1.0 along the
y-
> > > axis.
> > > > Draw
> > > > > > a
> > > > > > > > circle with a diameter of one unit inside the square.
> The
> > > > center
> > > > > > of
> > > > > > > > the circle will be at coordinates 0.5, 0.5. The Monte
> > Carlo
> > > > > > process
> > > > > > > to
> > > > > > > > compute the area of the circle is to generate many
> random
> > > > points
> > > > > > > > inside the square (each point a pair of number with
the
> > > > values of
> > > > > > > the
> > > > > > > > x-coordinate and y-coordinate being drawn from a
uniform
> > > > > > > distribution
> > > > > > > > between 0.0 and 0.999999), then count the number of
> those
> > > > points
> > > > > > > that
> > > > > > > > are also inside the circle. The ratio between the
> number
> > of
> > > > points
> > > > > > > > inside the circle to the number of points drawn gives
> an
> > > > estimate
> > > > > > of
> > > > > > > > the constant pi. Running this experiment several
times,
> > > each
> > > > using
> > > > > > > > many random points, allows application of statistical
> > > analysis
> > > > > > > > techniques to estimate the value of pi to within some
> > > probable
> > > > > > > > uncertainty. The process being studied in that
example
> is
> > > > > > > stationary.
> > > > > > > > The relationship between the area of the circle and
the
> > > area
> > > > of
> > > > > > the
> > > > > > > > square is always the same.
> > > > > > > >
> > > > > > > > When we are developing trading systems, the ultimate
> > > question
> > > > we
> > > > > > are
> > > > > > > > most often asking is "What is the future performance
of
> > this
> > > > > > trading
> > > > > > > > system?" Recall that the measure of goodness of a
> trading
> > > > system
> > > > > > is
> > > > > > > > your own personal (or corporate) choice. Some people
> want
> > > > highest
> > > > > > > > compounded annual return with little regard for
> drawdown.
> > > > Others
> > > > > > > value
> > > > > > > > systems that have low drawdown, or infrequent
trading,
> or
> > > > whatever
> > > > > > > > else may be important. But, in all cases, the goal is
> to
> > > have
> > > > the
> > > > > > > > trading system be profitable. Assume that many of us
> are
> > > > trading a
> > > > > > > > single issue over a period of several years, and that
> the
> > > > price
> > > > > > per
> > > > > > > > share at the end of that period is the same as it was
> at
> > the
> > > > > > > beginning
> > > > > > > > of the period, with significant price variations in
> > > between.
> > > > If we
> > > > > > > > ignore frictional costs -- the bid - ask spread of
the
> > > market
> > > > > > maker
> > > > > > > > and the commission of the broker -- we are playing a
> zero-
> > > sum
> > > > > > game.
> > > > > > > > Those of us who make money are taking it from those
who
> > lose
> > > > > > money.
> > > > > > > > If, instead of the final price being the same as the
> > > beginning
> > > > > > > price,
> > > > > > > > the final price is higher, then the price has an
upward
> > > bias
> > > > and
> > > > > > > more
> > > > > > > > money is made than lost. This is when we all get to
> claim
> > > it
> > > > was
> > > > > > our
> > > > > > > > cleverness that made us money. If the final price is
> > lower,
> > > > the
> > > > > > > price
> > > > > > > > has a downward bias and more money is lost than made.
> > > > > > > >
> > > > > > > > The price data for the period we are trading has two
> > > > components.
> > > > > > One
> > > > > > > > is the information contained in the data that
> represents
> > the
> > > > > > reason
> > > > > > > > the price changes -- the signal component. The other
is
> > > > > > everything
> > > > > > > we
> > > > > > > > cannot identify profitably -- the noise component.
Note
> > that
> > > > > > there
> > > > > > > may
> > > > > > > > be two (or more) signal components. Say one is a long
> > term
> > > > trend
> > > > > > in
> > > > > > > > profitability of the company, and the price follows
> > > > > > profitability.
> > > > > > > Say
> > > > > > > > the other is cyclic price behavior that goes through
> two
> > > > complete
> > > > > > > > cycles every month for some unknown but persistent
> > reason.
> > > In
> > > > > > every
> > > > > > > > financial price series, there is always the random
> price
> > > > variation
> > > > > > > > that is noise. The historical price data that we see
> > > > consists, in
> > > > > > > this
> > > > > > > > case, of trend plus cycle plus noise. Each component
> has a
> > > > > > strength
> > > > > > > > that can be measured. If the signal is strong enough,
> > > > relative to
> > > > > > > the
> > > > > > > > noise, our trading system can identify the signal and
> > issue
> > > > buy
> > > > > > and
> > > > > > > > sell signals to us. If our trading system has coded
> into
> > it
> > > > logic
> > > > > > > that
> > > > > > > > only recognizes changes in trend, the cycle component
> is
> > > > noise as
> > > > > > > seen
> > > > > > > > by that system. That is -- anything that a trading
> system
> > > > does not
> > > > > > > > identify itself, even though it may have strong signal
> > > > > > > characteristics
> > > > > > > > when analyzed in other ways, is noise.
> > > > > > > >
> > > > > > > > Over the recent decades, analysis of financial data
has
> > > > progressed
> > > > > > > > from simple techniques applied by a few people in a
few
> > > > markets
> > > > > > > using
> > > > > > > > proprietary tools to sophisticated techniques applied
> by
> > > many
> > > > > > people
> > > > > > > > in many markets using tools that are widely available
> at
> > low
> > > > > > cost.
> > > > > > > The
> > > > > > > > techniques used successfully by Richard Donchian from
> the
> > > > 1930s,
> > > > > > and
> > > > > > > > Richard Dennis and William Eckhart in the 1980s, were
> > > simple.
> > > > To
> > > > > > the
> > > > > > > > extent that the markets they traded did not have
strong
> > > > trends,
> > > > > > > every
> > > > > > > > profitable trade they made was at the expense of
> another
> > > > trader.
> > > > > > > > Today, every person hoping to have a profitable
career
> in
> > > > trading
> > > > > > > > learns about techniques that did work at one time.
They
> > are
> > > > well
> > > > > > > > documented and are often included in the trading
system
> > > > examples
> > > > > > > when
> > > > > > > > a trading system development platform is installed.
> > > > > > > >
> > > > > > > > Assume that a data series is studied over a given
date
> > > range.
> > > > > > Using
> > > > > > > > hindsight, we can determine the beginning price and
the
> > > ending
> > > > > > > price.
> > > > > > > > Continuing with hindsight, we can develop a trading
> > system
> > > > that
> > > > > > > > recognizes the signal component -- some
characteristic
> > > about
> > > > the
> > > > > > > data
> > > > > > > > series that anticipates and signals profitable
trades.
> By
> > > > trying
> > > > > > > many
> > > > > > > > combinations of logic and parameter values, we will
> > > eventually
> > > > > > find
> > > > > > > a
> > > > > > > > system that is profitable for the date range
analyzed.
> If
> > > we
> > > > are
> > > > > > > lucky
> > > > > > > > or clever, the system recognizes the signal portion
of
> > the
> > > > data.
> > > > > > Or,
> > > > > > > > the system may have simply been fit to the noise. The
> > data
> > > > that
> > > > > > was
> > > > > > > > used to develop the system is called the in-sample
> data.
> > If
> > > > the
> > > > > > > system
> > > > > > > > does recognize the signal and a few of us trade that
> > system,
> > > > > > while
> > > > > > > all
> > > > > > > > the rest of the traders make random trades, those of
us
> > who
> > > > trade
> > > > > > > the
> > > > > > > > system will make a profit. On average, the rest lose.
> As
> > > more
> > > > and
> > > > > > > more
> > > > > > > > people join us trading the system, each of us earns a
> > lower
> > > > > > profit.
> > > > > > > In
> > > > > > > > order to continue trading profitably, we must be
> earlier
> > to
> > > > > > > recognize
> > > > > > > > the signal, or develop better signal recognition
logic
> > and
> > > > trade
> > > > > > > > different signals or lower strength signals. By the
> time
> > > the
> > > > date
> > > > > > > > range we have studied has passed, most of the profit
> that
> > > > could
> > > > > > have
> > > > > > > > been taken out of that price series using that system
> has
> > > been
> > > > > > > taken.
> > > > > > > > Perhaps the future data will continue to carry the
same
> > > > signal in
> > > > > > > the
> > > > > > > > same strength and some traders will make profitable
> > trades
> > > > using
> > > > > > > their
> > > > > > > > techniques, or perhaps that signal changes, or
perhaps
> so
> > > many
> > > > > > > traders
> > > > > > > > are watching that system that the per-trade profit
does
> > not
> > > > cover
> > > > > > > > frictional costs.
> > > > > > > >
> > > > > > > > Data that was not used during the development of the
> > system
> > > is
> > > > > > > called
> > > > > > > > out-of-sample data. But -- important point -- testing
> the
> > > > > > > > profitability of a trading system that was developed
> > using
> > > > recent
> > > > > > > data
> > > > > > > > on older data is guaranteed to over-estimate the
> > > > profitability of
> > > > > > > the
> > > > > > > > trading system.
> > > > > > > >
> > > > > > > > Financial data is not only time-series data, but it
is
> > also
> > > > > > > > non-stationary. There are many reasons related to
> > > > profitability of
> > > > > > > > companies and cyclic behavior of economies to explain
> why
> > > the
> > > > > > data
> > > > > > > is
> > > > > > > > non-stationary. But -- another important point --
every
> > > > profitable
> > > > > > > > trade made increases the degree to which the data is
> non-
> > > > > > stationary.
> > > > > > > > There is very little reason to expect that future
> > behavior
> > > and
> > > > > > > > profitability of well known trading systems will be
the
> > > same
> > > > as
> > > > > > past
> > > > > > > > behavior.
> > > > > > > >
> > > > > > > > Which brings me to several key points in trading
systems
> > > > > > > development.
> > > > > > > >
> > > > > > > > 1. Use whatever data you want to to develop your
> systems.
> > > All
> > > > of
> > > > > > the
> > > > > > > > data that is used to make decisions about the logic
and
> > > > operation
> > > > > > of
> > > > > > > > the system is in-sample data. When the system
> developer --
> >
> > > > that
> > > > > > is
> > > > > > > you
> > > > > > > > and me -- is satisfied that the system might be
> > profitable,
> > > > that
> > > > > > > > conclusion was reached after thorough and extensive
> > > > manipulation
> > > > > > of
> > > > > > > > the trading logic until it fits the data. The in-
sample
> > > > results
> > > > > > are
> > > > > > > > good -- they are Always good -- we do not stop
fooling
> > with
> > > > the
> > > > > > > system
> > > > > > > > until they are good. In-sample results have no value
in
> > > > > > predicting
> > > > > > > the
> > > > > > > > future performance of a trading system. None! It does
> not
> > > > matter
> > > > > > > > whether the in-sample run results in three trades, or
> 30,
> > or
> > > > > > 30,000.
> > > > > > > > In-sample results have no value in predicting the
future
> > > > > > performance
> > > > > > > > of a trading system. Statistics gathered from in-
sample
> > > > results
> > > > > > have
> > > > > > > > no relationship to statistics that will be gathered
> from
> > > > trading.
> > > > > > > None!
> > > > > > > >
> > > > > > > > The follow-on point, which relates to Monte Carlo
> > analysis,
> > > is
> > > > > > that
> > > > > > > > rearranging the in-sample trades gives no insight
into
> > the
> > > > future
> > > > > > > > characteristics of the system. Yes, you can see the
> > effect
> > > of
> > > > > > taking
> > > > > > > > the trades in different orders. But why bother? They
> are
> > > still
> > > > > > > > in-sample results and still have no value.
> > > > > > > >
> > > > > > > > The Only way to determine the future performance of a
> > > trading
> > > > > > system
> > > > > > > > is to use it on data that it has never seen before.
> Data
> > > that
> > > > has
> > > > > > > not
> > > > > > > > been used to develop the system is out-of-sample data.
> > > > > > > >
> > > > > > > > 2. As a corollary to my comments above, that out-of-
> > sample
> > > > data
> > > > > > Must
> > > > > > > > be more recent that the in-sample data. The results
of
> > using
> > > > > > earlier
> > > > > > > > out-of-sample data are almost guaranteed to be better
> > than
> > > the
> > > > > > > results
> > > > > > > > of using more recent out-of-sample data.
Consequently,
> > > > techniques
> > > > > > > > known as boot-strap or jack-knife out-of-sample
testing
> > are
> > > > > > > > inappropriate for testing financial trading systems.
> > > > > > > >
> > > > > > > > So, when is Monte Carlo analysis useful in trading
> system
> > > > > > > development?
> > > > > > > >
> > > > > > > > 1. During trading system development. It may be
> possible
> > to
> > > > test
> > > > > > the
> > > > > > > > robustness of the system by making small changes in
the
> > > > values of
> > > > > > > > parameters. This can be done by making a series of in-
> > > sample
> > > > test
> > > > > > > > runs, each run using the central value of the
parameter
> > > (such
> > > > as
> > > > > > the
> > > > > > > > length of a moving average) adjusted by a random
> amount.
> > The
> > > > > > values
> > > > > > > of
> > > > > > > > the parameters can be chosen using Monte Carlo
methods.
> > > Note
> > > > that
> > > > > > > this
> > > > > > > > does not guarantee that the system that works with a
> wide
> > > > range of
> > > > > > > > values over the in-sample period will be profitable
out-
> > of-
> > > > > > sample,
> > > > > > > but
> > > > > > > > it does help discard candidate systems that are
> unstable
> > > due
> > > > to
> > > > > > > > selection of specific parameter values.
> > > > > > > >
> > > > > > > > Note that this technique is not appropriate for all
> > > > parameters.
> > > > > > For
> > > > > > > > example, a parameter may take on a limited set of
> values,
> > > > each of
> > > > > > > > which selects a specific logic. Such parameters,
> > associated
> > > > with
> > > > > > > what
> > > > > > > > are sometimes called state variables, are only
> meaningful
> > > for
> > > > a
> > > > > > > > limited set of values.
> > > > > > > >
> > > > > > > > 2. During trading system development. It may be
> possible
> > to
> > > > test
> > > > > > the
> > > > > > > > robustness of the system by making small changes in
the
> > > data.
> > > > > > > Adding a
> > > > > > > > known amount of noise may help quantify the signal to
> > noise
> > > > ratio.
> > > > > > > > When done over many runs, it may reduce (smooth out)
the
> > > > > > individual
> > > > > > > > noise components and help isolate the signal
components.
> > > > > > > >
> > > > > > > > 3. During trading system development. It may be
> possible
> > to
> > > > > > > > investigate the effect of having more opportunities
to
> > > trade
> > > > than
> > > > > > > > resources to trade. If the trading system has all of
> the
> > > > following
> > > > > > > > conditions:
> > > > > > > > A. A large number of signals are generated at exactly
> the
> > > same
> > > > > > time.
> > > > > > > > For example, using end-of-day data, 15 issues appear
on
> > the
> > > > Buy
> > > > > > > list.
> > > > > > > > B. The entry conditions are identical. For example,
all
> > the
> > > > > > issues
> > > > > > > are
> > > > > > > > to be purchased at the market on the open. If,
instead,
> > the
> > > > > > entries
> > > > > > > > are made off limit or stop orders, these can and
should
> be
> > > > > > resolved
> > > > > > > > using intra-day data -- as they would be in real time
> > > trading.
> > > > > > > > C. The number of Buys is greater than can be taken
with
> > the
> > > > > > > available
> > > > > > > > funds. For example, you only have enough money to buy
5
> > of
> > > > the 15.
> > > > > > > >
> > > > > > > > If your trading system development platform provides
a
> > > method
> > > > for
> > > > > > > > breaking ties, use it. For example, you may be able
to
> > > > calculate a
> > > > > > > > reward-to-risk value for each of the potential
trades.
> > Take
> > > > those
> > > > > > > > trades that offer the best ratio. AmiBroker, for
> example,
> > > > allows
> > > > > > the
> > > > > > > > developer to include logic to compute what is known as
> > > > > > > PositionScore.
> > > > > > > > Trades that are otherwise tied will be taken in order
of
> > > > > > > PositionScore
> > > > > > > > for as long as there are sufficient funds.
> > > > > > > >
> > > > > > > > Alternatively, Monte Carlo methods allow you to test
> > random
> > > > > > > selection
> > > > > > > > of issues to trade. My feeling is that very few
traders
> > > will
> > > > make
> > > > > > a
> > > > > > > > truly random selection of which issue to buy from the
> > long
> > > > list. I
> > > > > > > > recommend quantifying the selection process and
> > > incorporating
> > > > it
> > > > > > > into
> > > > > > > > the trading system logic.
> > > > > > > >
> > > > > > > > 4. During trading system validation. After the
trading
> > > system
> > > > has
> > > > > > > been
> > > > > > > > developed using the in-sample data, it is tested on
out-
> > of-
> > > > sample
> > > > > > > > data. Preferably there is exactly one test, followed
by
> a
> > > > > > decision
> > > > > > > to
> > > > > > > > either trade the system or start over. Every time the
> out-
> > > of-
> > > > > > sample
> > > > > > > > results are examined and any modification is made to
> the
> > > > trading
> > > > > > > > system based on those results, that previously out-of-
> > > sample
> > > > data
> > > > > > > has
> > > > > > > > become in-sample data. It takes very few (often just
> one
> > > will
> > > > do
> > > > > > it)
> > > > > > > > peeks at the out-of-sample results followed by
trading
> > > system
> > > > > > > > modification to contaminate the out-of-sampleness and
> > > destroy
> > > > the
> > > > > > > > predictive value of the out-of-sample analysis.
> > > > > > > >
> > > > > > > > One possibly valuable technique that will help you
> decide
> > > > whether
> > > > > > to
> > > > > > > > trade a system or start over is a Monte Carlo
analysis
> of
> > > the
> > > > > > > > Out-of-sample results. The technique is a reordering
of
> > > > trades,
> > > > > > > > followed by generation of trade statistics and equity
> > > curves
> > > > that
> > > > > > > > would have resulted from each trade sequence. What
this
> > > > provides
> > > > > > is
> > > > > > > a
> > > > > > > > range of results that might have been achieved. Note
> that
> > > this
> > > > > > > > technique cannot be applied to all trading systems
> without
> > > > > > knowledge
> > > > > > > > of how the system works. If the logic of the system
> makes
> > > use
> > > > of
> > > > > > > > earlier results, such as equity curve analysis or
> > sequence
> > > of
> > > > > > > winning
> > > > > > > > or losing trades, then rearranging the trades will
> result
> > > in
> > > > trade
> > > > > > > > sequences that could never have happened and the
> analysis
> > is
> > > > > > > > misleading and not useful. Also note that most of the
> > > results
> > > > > > > produced
> > > > > > > > by the Monte Carol analysis could also be developed
from
> > > > > > techniques
> > > > > > > of
> > > > > > > > probability and statistics without using Monte Carlo
> > > > techniques --
> > > > > > > > runs of wins and losses, distribution of drawdown,
and
> so
> > > > forth.
> > > > > > > >
> > > > > > > > In summary --
> > > > > > > >
> > > > > > > > Monte Carlo analysis can be useful in trading system
> > > > development.
> > > > > > > But
> > > > > > > > only in those cases described in items 1, 2, 3, and 4
> > above.
> > > > > > > >
> > > > > > > > Rearranging in-sample trades has no value.
> > > > > > > >
> > > > > > > > Obtaining meaningful results from Monte Carlo
> techniques
> > > > requires
> > > > > > > > large numbers -- thousands -- of additional test runs.
> > > > > > > >
> > > > > > > > If you decide to apply Monte Carlo techniques, I
> > recommend
> > > > that
> > > > > > they
> > > > > > > > be applied sparingly, primarily to test robustness of
a
> > > likely
> > > > > > > trading
> > > > > > > > system as in numbers 1 and 2 above, not in the early
> > > > development
> > > > > > > stages.
> > > > > > > >
> > > > > > > > On the other hand -----
> > > > > > > >
> > > > > > > > What is tremendously useful in trading system
> development
> > is
> > > > > > > automated
> > > > > > > > walk-forward testing. I believe that is the Only way
to
> > > > answer the
> > > > > > > > question "How can I gain confidence that my trading
> > system
> > > > will be
> > > > > > > > profitable when traded?" But that is the subject of
> > another
> > > > > > posting.
> > > > > > > >
> > > > > > > > Thanks for listening,
> > > > > > > > Howard
> > > > > > > >
> > > > > > >
> > > > > >
> > > > >
> > > >
> > >
> >
>
------------------------------------
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