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Re: [amibroker] Re: What is best statistic for straightness of equity curve?



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Greetings all --

With reference to Brian's comments, I have a little different take on the purpose of the objective function .

Brian wrote:

"That is a slightly different discussion to the one on deciding which
ObjectiveFunction is superior (relatively speaking) but if we don't
understand the first point what basis do we have for making a
decision on ObjectiveFunctions?

Where I am at is to dig in further on the mechanics, with the view to
checking the value of our current thinking. The eventual OF that
comes out of that research may well surprize.

brian_z"

In my opinion, the purpose of the objective function is to align the characteristics of the trading system with the psychology and personality of the trader.  Different people, and different organizations, value different characteristics.  Some want high net profit without regard to drawdown, some want high proportion of winning trades, some want low drawdowns, and so forth.  The purpose of the objective function is to incorporate those characteristics into a single-valued function that can be computed from any and every test run.  

All we can ever do as system developers is hope to find trading systems that have the characteristics we desire, worked well in the past, and will continue to work well in the near future.  In my opinion, the days of being able to identify the underlying reasons a trading system works are long gone -- outside of insider information, the market is too efficient for that.  But I do believe that we can find system that work without knowing why they work. 

Since the next trades will be made with real money in an unknown environment, the best we can hope for is increased confidence that our system is likely to be profitable in the future.  And the best way to achieve that is by practicing.  That is, develop a system using in-sample data, then test it on out-of-sample data and observe the results.  Move forward in time and do this again -- and again -- and again.  The process of walking forward, selecting the best alternative by sorting alternatives according to their objective function values, gives us as much experience as we can get in the transition from development to trading.

In my opinion, the definition of the objective function comes First.  Having said that, there may be alternative objective functions that are equally acceptable, some of which select systems that are more robust and are more likely to produce profit trades. 

But!   Once the objective function has been selected, it is used to rank alternatives.  The developer / trader Must have full confidence that the ranking made according to the objective function is the one he or she would have made with full knowledge of all of them.  If that is not the case, then the objective function must be modified until that is the case.  During the walk forward process, there is no opportunity to examine the characteristics of any of the alternatives -- the one with the highest objective function score is the one that will be used for the following out-of-sample period.  If this were not to be the case, the resulting trading system would not be a fully mechanical one, but would incorporate subjective judgment of the developer, and out-of-sample results would not be a reliable estimate of future performance.

Thanks for listening,
Howard
www.quantitativetradingsystems.com

On Thu, Mar 13, 2008 at 5:14 PM, brian_z111 <brian_z111@xxxxxxxxx> wrote:

BTW

That is a slightly different discussion to the one on deciding which
ObjectiveFunction is superior (relatively speaking) but if we don't
understand the first point what basis do we have for making a
decision on ObjectiveFunctions?

Where I am at is to dig in further on the mechanics, with the view to
checking the value of our current thinking. The eventual OF that
comes out of that research may well surprize.

brian_z



--- In amibroker@xxxxxxxxxxxxxxx, "brian_z111" <brian_z111@xxx> wrote:
>
> I agree with Howard's (past) comments that the best metric is the
OOS
> metric (that is for those who have used optimization to design the
> system) or better still, several OOS metrics (if we have the data).
>
> The speculative (at this stage) point that I am introducing into
the
> discussion is that foward looking performance can be estimated from
> the root causes (mechanics of the trading system).
>
> By continually focussing on the unknown future we are chasing
> phantasms. While we try to catch one others are popping up
everywhere
> (just like a horror movie).
>
> Better off to find the mother ship, and understand the spawning
> process, if we are to have any hope of dealing with the offspring.
>
> brian_z
>
>
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Paul Ho" <paultsho@> wrote:
> >
> > This particular shortcoming of Sharpe ratio as mentioned by
Howard
> has been
> > well flaged by many books. and It make sense when one is
comparing
> PAST
> > performance from one fund manger to another, or from one system
to
> another.
> > However, when one is comparing forward looking performance, such
as
> when one
> > is developing new systems or evaulating new variations of an
> existing
> > system. Then IMHO this criticism is a little unjustified. Reason:
> If there
> > are an equity curve in front of me, one that is with a occasional
> surge of
> > profit (positive deviation) followed by a relatively flat patch.
I
> wouldn't
> > know with a lot of confidence I'm go to experience a flat patch or
> > continuing surge if I trade this system in the future. I have
seen
> a number
> > of systems that have a very quick rise in patches during backtest
> and
> > optimisation, but basically flat during forward testing. If I
have
> a choice,
> > I would prefer a lower return but with less deviation (both
> positive and
> > negative) when I'm developing new system because I'm more
confident
> that it
> > will generate a regular profit for me. I must confess I am a
short
> term
> > trader, my trades last for hours to days. I can apprecriate that
> long term
> > traders, those with trades lasting weeks to years, might have a
> different
> > psychology and can withstand large period of flat patches to wait
> for the
> > big one. Of course, once I have started using a system, I'm all
for
> positive
> > surprises.
> > I personally think the biggest drawback of Sharpe ratio lies with
> the fact
> > that the straightness of an equity curve cannot be adequately
> described by a
> > single Sharpe Ratio, because vastly different equity curves
shares
> similar
> > ratio numbers. A series of Sharpe Ratios measured periodically is
a
> better
> > guide. Tuschar Chande even went as far as suggesting measuring
> a "Sharpe
> > Ratio" over the series of Sharpe Ratio, I think this has merit.
> >
> >
> > _____
> >
> > From: amibroker@xxxxxxxxxxxxxxx
[mailto:amibroker@xxxxxxxxxxxxxxx]
> On Behalf
> > Of Dennis Brown
> > Sent: Friday, 14 March 2008 4:46 AM
> > To: amibroker@xxxxxxxxxxxxxxx
> > Subject: Re: [amibroker] Re: What is best statistic for
> straightness of
> > equity curve?
> >
> >
> >
> > Howard,
> >
> >
> > You make an excellent point. The metrics used to evaluate a
system
> needs to
> > take into consideration the normal "character" of the trading
> systems basic
> > methodology.
> >
> > For instance my system takes small profits and losses many times
a
> day. It
> > is not biased for long or short. It does not hold overnight, It
> only trades
> > broad market futures. It does not compound equity. It is
goodness
> be able
> > to take a consistent draw from a fixed account size.
> >
> > This means that my system will be subject to very different
market
> forces
> > than a system that swing trades stocks for a week or two, and is
> subject to
> > overnight gaps, company earnings announcements, dividends,
interest
> rates
> > (on margin accounts), and other unpredictable events.
> >
> > My system will perform with a much smoother equity curve just
> because of the
> > way it is defined. Commissions and Bid/Ask spreads are the main
> hurdles to
> > profitability, but they are constants.
> >
> > I have a much easier time telling if my system is robust.
> >
> > Best regards,
> > Dennis
> >
> >
> > On Mar 13, 2008, at 1:01 PM, Howard B wrote:
> >
> >
> >
> > Greetings all --
> >
> > Professional money managers are sometimes evaluated based on the
> Sharpe
> > Ratio of their performance, so it has some value. But, in my
> research, I
> > have not found Sharpe Ratio to be a very good metric for use when
> developing
> > systems. Yes, higher Sharpe Ratios will have smaller standard
> deviations
> > than lower Sharpe Ratios, but the standard deviation includes
both
> positive
> > and negative deviations. That is, it penalizes both positive and
> negative
> > performance. If you are designing trend following systems with
> long holding
> > periods, and looking for the infrequent large gains associated
with
> this
> > type of system, Sharpe Ratio penalizes these. When Sharpe Ratio
is
> used as
> > the objective function in an automated walk forward process,
systems
> > selected as the best in-sample often perform much less well out-
of-
> sample
> > than systems selected using K-Ratio, RRR, CAR/MDD, or UPI.
> >
> > Thanks for listening,
> > Howard
> >
> >
> >
> > On Wed, Mar 12, 2008 at 10:33 PM, Paul Ho <paultsho@xxxxxx
> > <mailto:paultsho@> com.au> wrote:
> >
> >
> >
> >
> > Time doesnt permit me to write a long post. But I think Jack
> Schwager in one
> > of his books povides a very good description of what You want.
> Tuschar
> > Chande also has insights.
> > One such parameter is the Sharpe ratio, but you need use it
slightly
> > differently. Firstly, take risk free return as zero, and you are
> obtaining
> > the ratio of mean return to std deviation. Secondly, calculated
> yearly
> > sharpe ratios and compare them from year to year.
> >
> >
> > _____
> >
> > From: amibroker@xxxxxxxxx <mailto:amibroker@xxxxxxxxxxxxxxx>
ps.com
> > [mailto:amibroker@xxxxxxxxx <mailto:amibroker@xxxxxxxxxxxxxxx>
> ps.com] On
> > Behalf OfDennis Brown
> > Sent: Thursday, 13 March 2008 12:24 PM
> > To: amibroker@xxxxxxxxx <mailto:amibroker@xxxxxxxxxxxxxxx> ps.com
> > Subject: Re: [amibroker] Re: What is best statistic for
> straightness of
> > equity curve?
> >
> >
> >
> > Brian,
> >
> > Thanks for your reply.
> >
> > My thinking is that the Std Error will work. I do not need to use
a
> > Log function on my equity curve, because I do not compound my
> results,
> > so they are linear. I also base my work on constant range bars,
so
> > that linearizes the curves even more. Profit potential can only
> come
> > from price movement. The smoothest and straightest equity curves
> come
> > from the most robust systems. Period. You can look at the curve
and
> > judge it, or find a number that is associated with this property.
> >
> > However, step functions get introduced into your nice trading
> system
> > from big news events that change the character of the markets
> > overnight, or in a minute during the day. I consider these things
> > that produce large quick drawdowns will be captured by a Maximum
> > Drawdown metric. The test period needs to have some of these big
> > events in it. The event may be too quick to affect a large
> > statistical function much, giving a false sense of goodness to
the
> > system. Or the perturbation might show up in a way that takes a
> great
> > system and makes the smoothness number look bad due to a one time
> > event. That is the challenge with a single number, so I will have
> to
> > experiment with the right weightings.
> >
> > That is why I say that the absolute judgement comes from
> examination
> > of the equity curve. The goodness numbers are just for ease of
> > relative comparisons of automated parameter optimization for
> candidate
> > systems. It is also nice to have a number or two as a future
point
> of
> > reference rather than going back over equity curves for every
> > comparison.
> >
> > Perhaps an FFT over the equity curve would generate an
interesting
> > signature in the period of the dominant frequency and I also need
> the
> > amplitude. I would have to look into this more, since I have not
> > tried this before.
> >
> > I will start out simple and see how better numbers compare to the
> > curves, then decide where to go from there.
> >
> > > (Why don't you just start posting some of your bits and pieces,
> like
> > > your new PlotShapes PDF, to the UKB - it is a live site - we
don't
> > > have to wait for the big bang moment to become an author - a
lot
> of
> > > my stuff is mundane and/or half finished, but it still has its
> uses).
> >
> > I am buried in work right now, so I wanted to gauge the value to
> > others of some of the things I could post on the UKB. I would
have
> to
> > fight for the time to figure out how to post and fiddle with with
> > formatting issues etc. If it were as easy as sending a PDF email
> > attachment here, I would have done it a month ago. It is the up
> front
> > time investment that is holding me back right now.
> >
> > When I get little feedback or interest from a post, I can't
> prioritize
> > the time to share more of what I am doing. If I were not so busy,
I
> > would do it anyway, but for now I need powerful justification to
> delay
> > some other important work to make time for it. This is not a
spare
> > time hobby for me, because I have no spare time right now. :-(
> >
> > I could use a teammate to get me through the initial stages.
> However,
> > I see that only a few have ventured as far as posting yet, so the
> > field is limited. I do all my content creation on a Mac, and keep
> my
> > virtual PC free of everything but AmiBroker and related support
> > programs. That is why I prefer to generate PDF content as it
works
> > everywhere. And I have exceptionally easy to use and powerful
tools
> > for generating them already.
> >
> > Best regards,
> > Dennis Brown
> >
> > On Mar 12, 2008, at 7:19 PM, brian_z111 wrote:
> >
> > > Dennis,
> > >
> > > So where is your thinking on this now?
> > >
> > >
> > > (I have been following and I am building to some possible input
> but
> > > since I don't understand logs and barely understand standard
> error I
> > > have had to go back to school - it takes quite a while for me
to
> get
> > > my head around that stuff and interpret it into trade talk).
> > >
> > > I have taken a different approach to evaluation (which is still
a
> > > work in progress) and based on that I am inclined to the view
that
> > > evaluations on one equity curve are on rather weak ground - IMO
> > > simulation is required for analysis of 'what counts most'.
> > >
> > > Also I am zeroing in on the root causes of equity curve
profiles
> and
> > > measuring smoothness of a curve is measuring the effect.
> > >
> > > BTW - your pane based analysis is very interesting but I think
> > > ultimately it might prove to have some limitations for good
> > > evaluation (but not if we correctly identify root causes - we
can
> > > just pick them out, add some mathematical antecedents and then
we
> > > will now the answers that simulation will give us and not need
to
> > > bother the processor - I have convinced myself that this is in
my
> > > grasps and later I hope the maths people will connect my
> conceptual
> > > does and bingo, we are there).
> > >
> > > However, I love your question and approach, so over to your
> immediate
> > > problem (I had it in mind to go to town on an equity curve
> smoothness
> > > metric anyway).
> > >
> > > K-ratio is actually a risk reward metric (is that what you
want)?
> > >
> > > It also (to me) gets a little mysterious in its workings
(Klestner
> > > doesn't fully explain one part of it - not from my, lay, point
of
> > > view anyway).
> > >
> > > I am still thinking about it.
> > >
> > > So far I would say StDev is out.
> > > StandardError will do exactly what you say you want to do (as
far
> as
> > > I can tell - once again the stats teachers seem to find it hard
to
> > > put it into trade talk - I see it explained in different ways in
> > > different books).
> > >
> > > I haven't reached a final conclusion but it seems most likely
> that if
> > > you use Standard Error on a compounded equity curve with the
LogN
> > > approach taken by Klestner you are there - no need to go past
> that -
> > > my reservation is based on the fact that I am not sure how to
> handle
> > > standardisation - I only work in relative % change - Klestner
> > > attempts to standardise the K-ratio - he had some trouble with
it
> to
> > > start out and had to add a standardising factor.
> > >
> > >> Everything I do is in indicator mode in realtime. I build all
my
> > >> metrics into my AFL. My charts and numbers always match and all
> > >> my
> > >> settings are stored in my Flexible Parameters scheme for
> different
> > >> test systems. It is a little different approach, but that is
one
> > >> of
> > >> the beauties of AB --that it allows a lot of flexibility of
doing
> > >> your
> > >> own thing if you don't want to use the built-in ways.
> > >
> > > Yes, all of my evaluation methods are home made, or adaptions of
> > > popular methods - works for me.
> > >
> > > As I said - if you want all of your evaluation in one window you
> > > might need a math formula to sum up the transition from root
> cause to
> > > simulation (I naively believe I have the beginning and end in
the
> bag
> > > and conceptually the middle formula seems attainable).
> > >
> > > (Why don't you just start posting some of your bits and pieces,
> like
> > > your new PlotShapes PDF, to the UKB - it is a live site - we
don't
> > > have to wait for the big bang moment to become an author - a
lot
> of
> > > my stuff is mundane and/or half finished, but it still has its
> uses).
> > >
> > > brian_z
> > >
> > >
> > > --- In amibroker@xxxxxxxxx <mailto:amibroker%40yahoogroups.com>
> ps.com,
> > Dennis Brown <see3d@> wrote:
> > >>
> > >> Howard,
> > >>
> > >> Thanks for the input. I will investigate these some more.
> > >>
> > >> However, I do not use the built-in equity functions, or any of
> the
> > >> built-in trading functions. Tomasz has done a wonderful job
with
> > >> these, but they do not fit well with what I am doing with my
> > > trading.
> > >> I find it easier to understand what I am getting if I write
> > > everything
> > >> myself just for my situation and not the general case.
> > >>
> > >> Everything I do is in indicator mode in realtime. I build all
my
> > >> metrics into my AFL. My charts and numbers always match and all
> > > my
> > >> settings are stored in my Flexible Parameters scheme for
> different
> > >> test systems. It is a little different approach, but that is
one
> > > of
> > >> the beauties of AB --that it allows a lot of flexibility of
doing
> > > your
> > >> own thing if you don't want to use the built-in ways.
> > >>
> > >> Sometimes, you have to march to the beat of a different
drummer
> to
> > >> make money in these markets.
> > >>
> > >> Thanks again,
> > >> Dennis Brown
> > >>
> > >>
> > >> On Mar 12, 2008, at 1:38 PM, Howard B wrote:
> > >>
> > >>> Hi Dennis --
> > >>>
> > >>> There are several metrics already built in to AmiBroker that
> > > measure
> > >>> both the steepness and smoothness of the equity curve. Try
> > >>> generating a few test runs, plot their equity curves, note the
> > >>> values of these metrics, and see which ones best fit your
> > > trading
> > >>> personality. A nice advantage to using these is that they
> > > usually
> > >>> tend to select trading systems that test well out-of-sample,
so
> > > are
> > >>> appropriate for use with the Walk-Forward technique now also
> > > built
> > >>> in to AmiBroker.
> > >>>
> > >>> KRatio
> > >>> CAR/MDD
> > >>> RAR/MDD
> > >>> RRR
> > >>> RecoveryFactor
> > >>> UlcerPerformanceIndex
> > >>>
> > >>> Thanks,
> > >>> Howard
> > >>>
> > >>> On Tue, Mar 11, 2008 at 6:06 PM, Dennis Brown <see3d@>
> > >>> wrote:
> > >>> Hello,
> > >>>
> > >>> I have my system for intraday trading complete enough that I
> need
> > > to
> > >>> start selecting goodness criteria for comparing variations. I
> have
> > >>> selected a number of metrics to display in realtime for an n
day
> > >>> backtest like:
> > >>>
> > >>> total trade count
> > >>> average bars per trade
> > >>> winning trade %
> > >>> trade bars % in green
> > >>> best trade $
> > >>> worst trade $
> > >>> average win $
> > >>> average loss $
> > >>> *total profit $
> > >>> *max draw down $
> > >>> *EDGE (average $ per trade)
> > >>> *I have a graph of the cumulative profit over time and an
> overlaid
> > >>> straight line plot. This is the most powerful tool, because it
> > > lets
> > >>> me see the real character of the system. The straighter the
> line,
> > > the
> > >>> less likely it is over fit to the data and represents a robust
> > > system.
> > >>>
> > >>> I also have a graph of the trade equity on a trade by trade
> > > basis, so
> > >>> I can see how good the entry timing is and how a trade
> progresses
> > > on
> > >>> average or in outlier conditions.
> > >>>
> > >>> The * items are my key metrics for system comparison. This
> simple
> > >>> system runs completely in indicator mode. I test about 1000-
2000
> > >>> trades over a 10 week test period.
> > >>>
> > >>> Because of the type and manner of my trades (1 futures
contract
> > > only
> > >>> traded during market hours), the data is easy to judge for
> > > goodness.
> > >>> Since every day is an island, I could even use interesting
> random
> > > day
> > >>> strategies for in and out of sample data, but so far I just
use
> > >>> various sequential segments.
> > >>>
> > >>> However, when I am spinning my scroll wheel on parameters
while
> > >>> looking at my charts, it would be nice to have a number that
> > >>> represents how straight the equity curve is as a first pass --
> > >>> especially for when I partially automate the optimization
> > > process
> > >>> later.
> > >>>
> > >>> I thought I would just take the standard deviation of the
whole
> > > curve
> > >>> to the straight line. This is easy. But I think some of you
have
> > >>> given this problem a lot of thought and I figured one of you
may
> > > have
> > >>> some additional insights into the best method for getting a
> > > meaningful
> > >>> number for straightness/smoothness of the equity curve. So
here
> I
> > > put
> > >>> the question to you now with an open mind, before I become
set
> in
> > > my
> > >>> ways ;-)
> > >>>
> > >>> Best regards,
> > >>> Dennis Brown
> > >>>
> > >>>
> > >>>
> > >>>
> > >>
> > >
> > >
> > >
> > >
> > > Please note that this group is for discussion between users
only.
> > >
> > > To get support from AmiBroker please send an e-mail directly to
> > > SUPPORT {at} amibroker.com
> > >
> > > For NEW RELEASE ANNOUNCEMENTS and other news always check
DEVLOG:
> > > http://www.amibroke <http://www.amibroker.com/devlog/>
> r.com/devlog/
> > >
> > > For other support material please check also:
> > > http://www.amibroke <http://www.amibroker.com/support.html>
> > r.com/support.html
> > >
> > > Yahoo! Groups Links
> > >
> > >
> > >
> >
>


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