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Hi Horward,
I would like comment on your last statement about entropy and trading.
Shannon,the founder of information theory, was the master of Thorp and
Kelly (the one of the criterion) and he gave a definition of entropy
in information theory which is very similar to the one used in physics.
In the end physics is about information or viceversa .. so iit is not
surprising.
I know hedge funds approach trading from a purely information theory
point of view, applying statistical pattern recognition tools borrowed
from physics and automatic translation.
In the end there is some information (previous history price) and we
try to extract some valuable information from it, and if the entropy
is maximum there is not information, (market efficiency hypothesys).
I recently read a paper about this:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1104957
which applies Shannon entropy to finance showing how emerging markets
tend to be more inefficient.
Regards
Ly
--- In amibroker@xxxxxxxxxxxxxxx, Howard B <howardbandy@xxx> wrote:
>
> Greetings all --
>
> I was just rereading my posting about whether trading the edge
removes the
> edge. I could have saved a lot of words if I had just reminded
myself that
> CTAs, brokerages, mutual funds get into trouble when they front-run, not
> when they back-run.
>
> Thanks,
> Howard
>
>
>
>
> On Wed, Feb 4, 2009 at 10:48 AM, Howard B <howardbandy@xxx> wrote:
>
> > Greetings all --
> >
> > Wheeee -- there were Way Too Many questions postulated in the previous
> > posts for me to even try to answer in an organized manner.
> >
> > May I suggest --- One question per post. Or a posting making the
case for
> > some argument, followed by one or two well clearly stated, well
identified
> > questions at the end?
> >
> > But one question stood out. Brian asks whether trading the edge
reduces
> > the edge, and suggests that may not be true. Correct me if I
misunderstood,
> > Brian.
> >
> > The premise is that of technical analysis. That all information
is Not
> > reflected in the current price of the issue being traded. That
the price
> > does not always move instantly from the old "correct" and
"efficient" price
> > to the new correct and efficient price when the fundamental
characteristics
> > of the issue change. That there often remains some inefficiency
in the
> > price, and that mechanical trading systems can be developed that
recognize
> > that inefficiency and make a profit by buying and selling at
appropriate
> > times and prices.
> >
> > My position is that any system that recognizes an inefficiency,
and trades
> > it profitably, removes some of that inefficiency.
> >
> > Following -- with a lower remaining inefficiency, other systems
trading the
> > same inefficiency will be less profitable. With a sufficiently
large number
> > of systems trading that same inefficiency, the total profit for
all of the
> > systems trading that inefficiency will not be large enough to
cover the
> > total frictional costs of bid-ask spreads and brokerage
commissions, and
> > none of the trading systems will make a profit, on average.
> >
> > A thought experiment ---
> >
> > Assume I have a crystal ball trading system and no one else has it. A
> > certain stock has been trading at an average price of $10 per
share with an
> > average daily range of $0.10 for a relatively long time. On
occasion, it
> > rises in price. After reaching $12 in a rather orderly fashion,
it goes no
> > higher. It eventually drops back to $10, where it stays for a
time, then
> > the cycle repeats. The order book always shows 100 shares to buy
and 100
> > shares to sell at every $0.05 increment. There is a bid-asked
spread of a
> > few cents per share. My system knows with very high probability
that the
> > price of that stock will rise from $10 per share to $12 per share
whenever
> > the daily range expands so that the high price reaches the average
plus
> > $0.25. My system gives me a signal whenever the price rises to
$10.25 (Buy
> > to open at $10.25, stop order) and I take a long position of 100
shares. I
> > exit on a profit target of $12.00 (Sell to close at $12.00,
> > market-if-touched). I make $175 with each trade, less the
bid-asked spread
> > on the stop order to enter and the market order to exit, less
commission,
> > and potentially less slippage from being unable to execute at my
price on
> > the stop order to enter and the market order to exit. All other
trades in
> > this stock are unrelated and can be treated collectively as
random. That
> > is, they may take away one of the bids or offers that my system
would have
> > used, but some of the time my entry will be better and some of the
time
> > worse. On average, I enter at $10.25 and exit at $12.00.
> >
> > Someone else discovers this pattern and gets the same signals.
Their code
> > may or may not be exactly the same as mine, but it trades the same
pattern
> > and the same price movement. That is, it recognizes the same
inefficiency
> > and is attempting to trade it profitably. Next time the price breaks
> > $10.25, there are twice as many orders to buy. One of us gets
filled at
> > $10.25, the other cannot. The other stop order is filled at
$10.30. One of
> > us gets our market-if-touched order filled at $12.00, the other
cannot. We
> > cannot both make $175 on this trade. One entered at $10.25 and
exited at
> > $12.00 and made $175; the other entered at $10.30 and exited at
$11.95 and
> > made $165. A third trader would get an entry at $10.35 and exit
at $11.90
> > and make $155. It makes no difference which trader gets which
fill -- the
> > average is the same -- add up all exit prices, subtract all entry
prices,
> > subtract all the commissions and bid-asked spreads, divide by the
number of
> > trades.
> >
> > The more traders who try to trade this pattern, the less profit
there is
> > for each. Attempts are made to enter earlier. Some are
profitable, some
> > are false breakouts. Attempts are made to exit earlier, resulting
in less
> > profit per trade and making the fill of other exits worse because
the shares
> > bid at those prices are no longer available. The more orders that
try to
> > enter long positions at $10.25, the more quickly the price moves
up once it
> > breaks $10.25, making it more difficult to efficiently enter the
trade. The
> > more orders try to exit at $12.00, the more the price falls back from
> > $12.00, making it more difficult to exit with a profit.
> >
> > Certainly this is an over-simplified example. My point is that
the more
> > orders there are to buy at a given price, the less likely they
will all be
> > filled at the best price; and the more orders there are to sell at
a given
> > price, the less likely they are to be filled at the best price.
No matter
> > which system -- mechanical or discretionary -- is trying to profit
from
> > buying at the same time my crystal ball system buys and selling at
the same
> > time my crystal ball system sells, the trades that other system
makes reduce
> > my profit -- on average.
> >
> > Think about what the counter-example would have to be. Whenever
my crystal
> > ball system gets a signal to buy and I get filled, if the price
did not
> > rise, then the price would have to drop so that the next trader
would get a
> > better price. And the third trader would get a still better
(lower) price.
> > And so on until my maximum loss stop is hit and I exit at a
serious loss.
> >
> > I think that there is an analogy between trading systems and price
> > inefficiency in the financial markets, and energy and entropy in
physical
> > systems. Removing profit from an inefficiently priced financial
market
> > reduces the amount of remaining inefficiency. In the analogous way as
> > removing energy from a closed physical system reduces order --
increases
> > disorder and increases entropy.
> >
> > Thanks for listening,
> > Howard
> >
> >
> >
> > On Wed, Feb 4, 2009 at 5:32 AM, brian_z111 <brian_z111@xxx> wrote:
> >
> >> I decided to post the Binomial Simulation files a few days ago
... I
> >> am not going to announce the upload so this post is the discussion
> >> link for them (one or more files will appear at some stage).
> >>
> >> FTR They do predict the eq dist quite well, for biased and none
> >> biased 'coins' but there is one thing about them that does concern
> >> me ... I referenced the same synthetic trade series to make the
> >> binomial distribution and to create the synthetic eq curves ... that
> >> seems a bit incestuous in some ways.
> >>
> >> On the other hand they could be full of incorrect math assumptions
> >> cos I got the math off Wikipedia!
> >>
> >> Guru Brian ;-)
> >>
> >>
> >> --- In amibroker@xxxxxxxxxxxxxxx <amibroker%40yahoogroups.com>,
> >> "brian_z111" <brian_z111@> wrote:
> >> >
> >> >
> >> > > This is a valid model as long as stationarity holds ... I have
> >> > > simulated random trading 'systems' and predicted the outcome by
> >> > using
> >> > > binomial probability, that references a frequency distribution of
> >> > the
> >> > > randomly generated trades, and it predicted the actual equity
> >> > > distributions extremely well (a lognormal dist appears at very
> >> high
> >> > > N's).
> >> >
> >> >
> >> > More precisely, I have simulated trade series, using the RNG in
> >> > Excel, for random walks (50/50 systems) and biased systems, with
> >> > normally distributed trade series (I used CentralLimitThereom to
> >> > create NormDists from the uniform output of the generator.
> >> >
> >> > I simulated equity curves, using the synthetic trades, and at the
> >> > same time used BinomialProb to model the predicted distribution of
> >> > the eq curves (I imagined I was tossing a coin with variable values
> >> > for heads and tails ... of course in trading we can win lose or
> >> draw
> >> > whereas in my model we can only win or lose).
> >> >
> >> > You might like to see the files?
> >> >
> >> > I am bored with that topic.
> >> >
> >> > I am not a mathematician ... it might be a load of old rubbish for
> >> > all I know.
> >> >
> >> > As our discussion shows .. we can't get any statistical certainty
> >> > anywhere in trading ... only approximations and probabilties.
> >> >
> >> > It is just another approximation, like MCS and involves massive
> >> > number crunching.
> >> >
> >> > I didn't finish it because I wanted a quick and dirty method.
> >> >
> >> > The files are rough as old bags.
> >> >
> >> > I didn't make notes so even I have a hard time following the
> >> > logic ... I had a look at them the other day I had to start tracing
> >> > the formulas in the cells to see how I had done it.
> >> >
> >> > I'll post some of them in the file section one day (Howard collects
> >> > trading things).
> >> >
> >> > I won't scrub them up though ... take them or leave them ... sorry
> >> no
> >> > questions or explanations (anyway Howard and other maths people
> >> know
> >> > how to do that stuff).
> >> >
> >> >
> >> > --- In amibroker@xxxxxxxxxxxxxxx <amibroker%40yahoogroups.com>,
> >> "brian_z111" <brian_z111@> wrote:
> >> > >
> >> > > Gidday Mate,
> >> > >
> >> > > I wasn't planning on posting again today as I am going away for a
> >> > few
> >> > > days ..... a good question though so I couldn't resist.
> >> > >
> >> > >
> >> > > I did notice Fred's comment on the priority he places on
> >> > sensitivity
> >> > > analysis.
> >> > >
> >> > > He has made the comment before and I came to that view
> >> > independently
> >> > > a way back anyway (Howard's random noise test is another
> >> > interesting
> >> > > idea for single sample analysis).
> >> > >
> >> > > I also recall that he doesn't believe scrambling the order of the
> >> > > trades provides any meaningful feedback.
> >> > >
> >> > > That isn't a reason for me not to reach my own conclusions.
> >> > >
> >> > > Fred has also talked about small N retesting (walk forward), and
> >> > > adjusting his system rules, on a short term basis, so while I am
> >> > not
> >> > > keen on the idea I am keeping an open mind on the subject.
> >> > >
> >> > >
> >> > >
> >> > > > This is the second time in the >past few
> >> > > > days that you seem to have equated trading/backtesting system
> >> > > >outcomes
> >> > > > to a random series of coin flip outcomes (random binary
> >> > occurances).
> >> > > >
> >> > > > Serious question... what is your point? What is the relevence
> >> os
> >> > > >the
> >> > > > "Coin Flip" metaphor where trading systems is concerned?
> >> > >
> >> > > Well, developers are selling software specifically designed for
> >> > > performing MSC for trading analysis and at least one guy has
> >> > written
> >> > > a book on the subject.
> >> > >
> >> > > In both software packages, that I have some familiarity with,
> >> their
> >> > > model assumes stationarity, and independency i.e. their model
> >> > treats
> >> > > the data as if it is the outcome of a coin toss with variable
> >> > values
> >> > > on the +- side of the coin.
> >> > >
> >> > > This is a valid model as long as stationarity holds ... I have
> >> > > simulated random trading 'systems' and predicted the outcome by
> >> > using
> >> > > binomial probability, that references a frequency distribution of
> >> > the
> >> > > randomly generated trades, and it predicted the actual equity
> >> > > distributions extremely well (a lognormal dist appears at very
> >> high
> >> > > N's).
> >> > >
> >> > > The value, to me in that model, is that it is a training tool
> >> that
> >> > > conditioned me to accept variance as 'normal' and if the market
> >> is
> >> > > stationary then it would have direct relevance to trading.....
> >> the
> >> > > worst case outcome would be that I could incur losses, with a
> >> > > probability as indicated by the Cumulative Distrubution Function
> >> > for
> >> > > the possible equity outcomes (simulation is one way for non -
> >> > > mathematicians to calc this and view it in a chart).
> >> > >
> >> > >
> >> > > Ask yourself ....
> >> > >
> >> > > afer you have conducted a successful OOS, and collated the trade
> >> > > sample, when you start to trade it do you expect:
> >> > >
> >> > > - all trades to be the same, or similar, and occur with the same
> >> > > frequency (TradeSim),
> >> > > - all trades to be the same, or similar, and have variations in
> >> the
> >> > > frequency (MSA),
> >> > > - something else?
> >> > >
> >> > > Trading, however, is not a coin toss.
> >> > >
> >> > > It is more like a sample generator that produces trades as a
> >> result
> >> > > of presenting dynamic data to the system (filter).
> >> > >
> >> > > To what extent could a 'real life' trading system emulate a coin
> >> > > toss, with variable values ... how could that come about?
> >> > >
> >> > > (interesting that the very functional optF formula came about as
> >> > the
> >> > > variable value coin toss staking formula).
> >> > >
> >> > > Is it possible or not?
> >> > >
> >> > > A lot of people seem to think it is, judging by their books and
> >> > > software.
> >> > >
> >> > > Presumably, when the underlying data changes, the sample profile
> >> > > (mean, StDev etc) can change and we end up with a better or worse
> >> > > outcome than anticipated by the OOS.
> >> > >
> >> > > So, does the non-stationary behaviour of the markets invalidate
> >> the
> >> > > coin toss model?
> >> > >
> >> > > That is the ineresting question, and I don't know the answer to
> >> it,
> >> > > or even if there is a definite answer.
> >> > >
> >> > > I was hopeful that people would pick up on that key point and
> >> shed
> >> > > some light on the subject.
> >> > >
> >> > > I know, from my long hours of simulating random data, what random
> >> > > behaviour looks like when I see it.
> >> > >
> >> > > Clearly the markets have a certain amount of random behaviour.
> >> > >
> >> > > Howard commented somewhere, or another, that there is a certain
> >> > > amount of randomness in the market (I can't recall the method he
> >> > used
> >> > > to measure it).
> >> > >
> >> > > It is quite easy to observe if data has any random qualities,
> >> > > especially if we measure the core attributes (50/50 heads and
> >> tails
> >> > > and its persistence into 2,3,4 heads in a row etc).
> >> > >
> >> > > Once again I ask you to consider:
> >> > >
> >> > > if I measure the S&P500 index, on close, and it goes up approx 50
> >> > and
> >> > > down approx 50 (+- variance that is typical of a random binomial
> >> > > event) and the subsequent second head or tail follow with 0.5
> >> prob
> >> > > etc I am justified in considering it top be a pseudo random
> >> > binomail
> >> > > event?
> >> > >
> >> > > I have done quick and dirty measurements, and accurate
> >> > measurements,
> >> > > on dependency (or on its inverse, which is independency) and find
> >> > > that there is a good deal of independency in the markets (I
> >> posted
> >> > > some q&d code to measure that last week).
> >> > >
> >> > > I have speculated before, on the point, that the rational market
> >> is
> >> > > the market that follows fundamental value, which tends to be >=
> >> the
> >> > > yearly (macro) timeframe, and, everything else is the irrational
> >> > > market.
> >> > >
> >> > > Consider an intraday market ... what is rational about the price
> >> > > movement during any given part of the day?
> >> > >
> >> > > - Draw a trend line on the chart .. we will assume that we know
> >> > what
> >> > > a trend is for this exercise, although that is a debatable point.
> >> > >
> >> > > - The trend, a straight line, is rational (it is perfectly
> >> > following
> >> > > fundamental value).... it is 2007 and it is up ;-)
> >> > >
> >> > > - All of the ups and downs that occur around it are irrational
> >> > > (bucking the trend).
> >> > >
> >> > > - The trend line goes under the pivot lows.
> >> > >
> >> > > - Your system buys at the pivot lows and sells at = = 2 StDev
> >> above
> >> > > the trend line.
> >> > >
> >> > > - Place a stop under the trend line at - 1 stDev.
> >> > >
> >> > > - Assume no commission and no slippage.
> >> > >
> >> > > - Your payoff ratio is 2/1
> >> > >
> >> > > - assume there is no variance in volatility so the PR is a
> >> constant
> >> > > value
> >> > >
> >> > > - the win/loss ratio is determined by the random meandering of
> >> the
> >> > > irrational price movements up and down.
> >> > >
> >> > > Note they are irrational because people are buying and selling at
> >> > the
> >> > > wrong time and for the wrong reasons - if they were rational they
> >> > > would only be buying selling as fundamental values change.
> >> > >
> >> > > - the trade series produced would look exactly that that produced
> >> > by
> >> > > a coin tossed with +2, -1 value on it.
> >> > >
> >> > > Now, you have tested this system, OOS, and it is a winner.
> >> > >
> >> > > What chance for stationarity when you trade live?
> >> > >
> >> > > If the trend continues there is a very good chance that the
> >> random
> >> > > emualator (system meeting dynamic data) will continue to perform
> >> > like
> >> > > a biased coin +- variance i.e. the payoff ratio can't change but
> >> > the
> >> > > W/L will (it always does when I toss a coin).
> >> > >
> >> > > If the trend changes your winning model will be more likely to
> >> bust.
> >> > >
> >> > > That could be the reason Fred, and others, like to continually
> >> > retest.
> >> > >
> >> > > I have another approach to getting around this problem (this is
> >> > > actually the real point of my posts) ...
> >> > >
> >> > > ..... to accomodate non-stationarity either adjust quickly OR use
> >> a
> >> > > dimensionless model e.g. don't believe in trends and then you
> >> can't
> >> > > be on the wrong side of them.
> >> > >
> >> > >
> >> > >
> >> > > However, that is only speculation.
> >> > >
> >> > > What do you think?
> >> > >
> >> > >
> >> > > Again ... what is the relevance of coin tosses to trading IMO:
> >> > >
> >> > >
> >> > > - wonderful training tool
> >> > > - a good OOS can not predict exactly what the outcome of live
> >> > trading
> >> > > will be (subject to nonstationarity) and neither can simulation
> >> > (coin
> >> > > tossing) but it gives a good approximation of the possibilities
> >> > (also
> >> > > subject to non-stationarity).
> >> > >
> >> > > As a quid pro quo .....
> >> > >
> >> > > ..... if you, or anyone else, can give me any explanation and/or
> >> > > proof that the coin toss metaphor has no relevance to trading I
> >> > would
> >> > > be delighted.
> >> > >
> >> > >
> >> > > Anyway, I think Patrick already answered the question, or told us
> >> > > where to find it.
> >> > >
> >> > > Good luck with your trading.
> >> > >
> >> > > brian_zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
> >> > >
> >> > >
> >> > > --- In amibroker@xxxxxxxxxxxxxxx <amibroker%40yahoogroups.com>,
> >> "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 <amibroker%40yahoogroups.com>,
> >> "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
<amibroker%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>,
> >> "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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