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> 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@xxx> 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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