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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@xxx> 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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