RE: [amibroker] Re: What is best statistic for straightness of equity curve?, AmiBroker Email List Archive

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@xxxxxxcom.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@xxxxxxxxxps.com [mailto:amibroker@xxxxxxxxxps.com] On Behalf OfDennis Brown
Sent: Thursday, 13 March 2008 12:24 PM
To: amibroker@xxxxxxxxxps.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@xxxxxxxxxps.com, Dennis Brown <see3d@xxx> 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@xxx>
>>> 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
>>>
>>>
>>>
>>>
>>
>
>
>
>
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