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RE: Objective functions (was RE: [amibroker] Re: Optimization -- again)



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What 
is being (mostly) ignored in this discussion is that is entirely possible to end 
up with ALL subsequent trades being different.   Let's say we are 
talking about whether or not the first five trades were taken as a result of 
starting the backtest earlier vs. later.   So the first trade in the 
run that starts later MAY have been the sixth trade in the run that starts 
earlier.   
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The 
only problem is that the system may not have any cash available to make the 
sixth trade.   So it, and maybe the next couple of trades are 
skipped due to no availability of funds.   I hope that you can see 
that the two backtests may NEVER be in sync from that point 
on.
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size=2> 
Of 
course, if the system is such that all positions are dumped every time there is 
a change in market trend (therefore a stock system), then the two backtests 
should get back in sync at the next trend change.   In these scenario, 
however, the number of shares will (probably) be different.   

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size=2> 
This 
thread all started by someone asking if it was a bug that two equity curves did 
not look alike (other than the beginning) when the backtest continued on for 
several years.   I think we have come up with dozens of instances why 
they may be different.   I tried two systems (after thinking about 
what type of systems to try).   One produced perfectly matching 
equity curves (after the start) and the other produced completely different 
trades and, therefore, equity curve.
<BLOCKQUOTE 
>
  <FONT face="Times New Roman" 
  size=2>-----Original Message-----From: John 
  [mailto:jea55129@xxxxxxxxx]Sent: Monday, October 20, 2003 8:35 
  AMTo: amibroker@xxxxxxxxxxxxxxxSubject: Objective 
  functions (was RE: [amibroker] Re: Optimization -- 
  again)Dave,Your missing something :) Pal 
  wrote that he was missing the first two trades. Here is a small example I 
  just did in excel. Two accounts both starting out with 1000. On the column 
  on the left, I made 100% profit on the first trade, 90% on the second, 
  etc...The last trade I made 10%, compounded. I only took out the 100% 
  profitable trade on the other column. Everything else the same. Quite a 
  difference in equity, corrrect?1000      
  10002000      
  19003800      
  34206840      
  581411628      
  930218605      
  1395427907      
  1953539070      
  2539650791      
  3047560949      
  3352267044      John--- In 
  amibroker@xxxxxxxxxxxxxxx, "Dave Merrill" <dmerrill@xxxx> 
  wrote:> it's counterintuitive to some degree, but whether your 
  gains or losses come> first doesn't effect the final outcome (with 
  the possible minor exception of> interest effects). multiplication 
  is commutative, so the order in which> several multiplications are 
  done doesn't matter.> > $10k x 150% x 50% is the same as $10k x 
  50% x 150%> >     because> > 
  $10k x 150% = $15k and $15k * 50% = $7.5k>     
  and> $10k x 50% = $5k and $5k * 150% = $7.5k> > > 
  or am I missing something?> > dave>   I have a 
  lot of reading to catch up so I don't know if anybody>   
  responded to your equity line question.> >   It sounds 
  to me that you are compounding your results, correct? If 
  so>   a few big wins at the start of your equity line vs 
  several losses at>   the start will greatly affect your 
  equity line. Check the first>   several trades. Here is where 
  it has the greatest effect. A way>   around this is to test 
  on a single issue or set amount.> >   
  Regards,>   John>   --- In 
  amibroker@xxxxxxxxxxxxxxx, "palsanand" <palsanand@xxxx> 
  wrote:>   > Hi,>   
  >>   > Here is an interesting observation on system 
  testing:>   >>   > Say you run a 
  system test over 10,000 bars of data, then print out>   
  a>   > chart of the system's equity line. Then repeat the 
  test, but start>   > 100 bars later. Let's say two 
  trades were included in those 100>   
  bars,>   > so they've been dropped. Now print the second 
  equity line and>   compare>   > it to the 
  first. You'd get exactly the same equity line, but 100>   
  bars>   > shorter. Right? Wrong!>   
  >>   > When I do this I get a radically different 
  equity line on the>   second>   > test, 
  i.e., they are not near-mirror images of each other. My 
  hunch>   > is that a form of the chaotician's 
  "butterfly-effect" has arisen:>   > changing any given 
  trade's market position (long, short, flat) will>   > 
  effect in a chain reaction all the subsequent trades in complex 
  and>   > unexpected ways. Here dropping the first two 
  trades could very well>   > change the system's market 
  position when the third trade is>   > calculated, and so 
  on.>   >>   > I believe this 
  observation has profound and unfortunate>   
  implications>   > for the robustness of system testing. 
  It's a second and more subtle>   > problem that lies 
  behind the mere curve-fitting/optimization>   
  problem.>   >>   > If dropping a 
  couple of early trades will always effect later>   
  trades,>   > then there's no truly "neutral" starting 
  point with any test data.>   > Where your test data 
  starts determines the final test results just>   
  as>   > much as your system does.>   
  >>   > The success or failure of many different 
  mechanical systems is>   > predicated to a surprising and 
  varying degree on the sequence of>   > events just prior 
  to the first actual trade generated by the>   
  system.>   >>   > The trade setup and 
  timing of the first trade can have a profound>   > 
  effect on the subsequent trading results. The circumstances 
  and>   > timing of entry into the first trade can 
  sometimes make a huge>   > difference in the overall 
  trading performance.>   >>   > 
  Regards,>   >>   > Pal> 
  > > >         
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