> > >
40yahoogroups.com>,
> > > > > "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<amibroker%
40yahoogroups.com>
> > <amibroker%
> > >
40yahoogroups.com>,
> > > > > "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