How to optimize trading system
NOTE: This is fairly advanced topic. Please read previous AFL tutorials
first.
Introduction
AmiBroker 3.70 brings a new feature to Automatic Analysis window called "Optimization".
The idea behind an optimization is simple. First you have to have a trading
system, this may be a simple moving average crossover for example. In almost
every system there are some parameters (as averaging period) that decide how
given system behaves (i.e. is is well suited for long term or short term, how
does is react on highly volatile stocks, etc). The optimization is the process
of finding optimal values of those parameters (giving highest profit from the
system) for a given symbol (or a portfolio of symbols). AmiBroker is one of the
very few programs that allow you to optimize your system on multiple symbols
at once.
To optimize your system you have to define from one upto ten parameters to
be optimized. You decide what is a minimum and maximum allowable value of the
parameter and in what increments this value should be updated. AmiBroker then
performs multiple back tests the system using ALL possible combinations of parameters
values. When this process is finished AmiBroker displays the list of results
sorted by net profit. You are able to see the values of optimization parameters
that give the best result.
Writing AFL formula
Optimization in back tester is supported via new function called optimize.
The syntax of this function is as follows:
variable = optimize( "Description", default, min,
max, step );
where:
variable - is normal AFL variable that gets assigned the value returned by
optimize function.
With normal backtesting, scanning, exploration and comentary modes the optimize
function returns default value, so the above function call is equivalent
to: variable = default;
In optimization mode optimize function returns successive values from min
to max (inclusively) with step stepping.
"Description" is a string that is used to identify the optimization
variable and is displayed as a column name in the optimization result list.
default is a default value that optimize function returns in exploration,
indicator, commentary, scan and normal back test modes
min is a minimum value of the variable being optimized
max is a maximum value of the variable being optimized
step is an interval used for increasing the value from min to
max
Notes:
- AmiBroker supports upto 10 calls to optimize function (therefore upto 10
optimization variables)
- Each call to optimize generate (max - min)/step optimization loops
and multiple calls to optimize multiply the number of runs needed. For example
optimizing two parameters using 10 steps will require 10*10 = 100 optimization
loops.
- Call optimize function only ONCE per variable at the beginning of your formula
as each call generates a new optimization loops
- Multiple-symbol optimization is fully supported by AmiBroker
Examples
1. Single variable optimization:
sigavg = Optimize( "Signal
average", 9, 2, 20, 1 );
Buy = Cross( MACD( 12, 26 ), Signal( 12, 26,
sigavg ) );
Sell = Cross( Signal( 12, 26,
sigavg ), MACD( 12, 26 )
);
2. Two-variable optimization (suitable for 3D charting)
per = Optimize("per", 2, 5, 50, 1 );
Level = Optimize("level", 2, 2, 150, 4 );
Buy=Cross( CCI(per),
-Level );
Sell = Cross(
Level, CCI(per) );
3. Multiple (3) variable optimization:
mfast = Optimize( "MACD
Fast", 12, 8, 16, 1 );
mslow = Optimize("MACD
Slow", 26, 17, 30, 1 );
sigavg = Optimize( "Signal
average", 9, 2, 20, 1 );
Buy = Cross( MACD(
mfast, mslow ) , Signal(
mfast, mslow, sigavg ) );
Sell = Cross( Signal(
mfast, mslow, sigavg ), MACD(
mfast, mslow ) );
After entering the formula just click on Optimize button in "Automatic
Analysis" window. AmiBroker will start testing all possible combinations
of optimization variables and report the results in the list. After optimization
is done the list of result is presented sorted by the Net % profit. As you can
sort the results by any column in the result list it is easy to get the optimal
values of parameters for the lowest drawdown, lowest number of trades, largest
profit factor, lowest market exposure and highest risk adjusted annual % return.
The last columns of result list present the values of optimization variables
for given test.
When you decide which combination of parameters suits your needs the best all
you need to do is to replace the default values in optimize function calls with
the optimal values. At current stage you need to type them by hand in the formula
edit window (the second parameter of optimize function call).
Displaying 3D animated optimization charts
To display 3D optimization chart, you need to run two-variable optimization
first. Two variable optimization needs a formula that has 2 Optimize() function
calls. An example two-variable optimization formula looks like this:
per = Optimize("per", 2, 5, 50, 1 );
Level = Optimize("level", 2, 2, 150, 4 );
Buy=Cross( CCI(per),
-Level );
Sell = Cross(
Level, CCI(per) );
After
entering the formula you need to click "Optimize" button.
Once optimization is complete you should click on the drop down arrow
on Optimize button
and choose View 3D optimization graph. In a few seconds
a colorful three-dimensional surface plot will appear in a 3D chart viewer
window. An example 3D chart
generated using above formula is shown below. |
 |
By default the 3D charts display values of Net profit against
optimization variables. You can however plot 3D surface chart for any column
in the optimization result table. Just click on the column header to sort it
(blue arrow will appear indicating that optimization results are sorted by
selected column) and then choose View 3D optimization graph again.
By visualizing how your system's parameters affect trading performance, you
can more readily decide which parameter values produce "fragile" and
which produce "robust" system performance. Robust settings are regions
in the 3D graph that show gradual rather than abrupt changes in the surface
plot. 3D optimization charts are great tool to prevent curve-fitting. Curve-fitting
(or over-optimization) occurs when the system is more complex than it needs
to be, and all that complexity was focused on market conditions that may never
happen
again. Radical changes (or spikes) in the 3D optimization charts show clearly
over-optimization areas. You should choose
parameter region that produces a broad and wide plateau on 3D chart for your
real life trading.
Parameter sets producing profit
spikes will not work reliably in real trading.
3D chart viewer controls
AmiBroker's 3D chart viewer offers total viewing capabilities with full graph
rotation and animation. Now you can view your system results from every conceivable
perspective.
You can control the position and other parameters of the chart using the mouse,
toolbar and keyboard shortcuts, whatever you find easier for you. Below you
will find the list.
Mouse controls:
- to Rotate - hold down LEFT mouse button and move in X/Y directions
- to Zoom-in, zoom-out - hold down RIGHT mouse button and move in X/Y directions
- to Move (translate) - hold down LEFT mouse button and CTRL key and move in
X/Y directions
- to Animate - hold down LEFT mouse button, drag quickly and release button
while dragging
Keyboard controls:
SPACE - animate (auto-rotate)
LEFT ARROW KEY - rotate vert. left
RIGHT ARROW KEY - rotate vert. right
UP ARROW KEY - rotate horiz. up
DOWN ARROW KEY - rotate horiz. down
NUMPAD + (PLUS) - Near (zoom in)
NUMPAD - (MINUS) - Far (zoom out)
NUMPAD 4 - move left
NUMPAD 6 - move right
NUMPAD 8 - move up
NUMPAD 2 - move down
PAGE UP - water level up
PAGE DOWN - water level down