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Perhaps it is helpful to distinguish (i.e. I believe some of the
confusion comes from) the following:
- assumptions on samples versus population;
- assumptions on algorithmic model/series versus random model/series;
- using parametric (i.e. Monte Carlo) versus non-parametric (i.e.
bootstrap) simulation
- etc.
For example,
1) In 1983 Richard Meese (UC Berkeley at the time) and Kenneth Rogoff
(Harvard at the time) published their seminal paper in which they
described the results of testing popular structural macro models on
currencies versus a naive random walk model. The latter has since
become the benchmark for testing currency models (at least in
academia).
2) The manual accompanying the RMath plug-in refers to the book by
Scherer and Martin. In it (albeit for portfolio optimization) they
discuss in detail applications of parametric and non-parametric
simulations. best thing: most of this is freely available via all
kinds of simulation packages for R.
FWIW, what this means in practise is that
1) if you truly want to analyze (the effects of) "what-if"
scenario's, you are better of simulating the underlying series which
trigger one's trades, rather than re-sampling the trades themselves;
2) if you have any doubt your selection of history is representative
of the possible population, mix-and-match parametric with non-
parametric series
3) etc.
PS
--- In amibroker@xxxxxxxxxxxxxxx, "Phsst" <phsst@xxx> 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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