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Re: [amibroker] Re: Is the Walk forward study useful?



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Hi Mike --

CAR is compound annual rate of return.  Expectancy is the percentage (or dollar amount, but not for this discussion) gain on the average trade.  The final value of the trading account, Terminal Relative Wealth in some descriptions, is: (1 + expectancy) raised to the power of the number of trades.  When there are a few large trades included, this relationship is slightly different, but not enough to worry this discussion.  CAR is: (1 + annual gain) raised to the power of the number of years.  These are both based on geometric means.  Aren't they the same, or so close that they act the same when used as an objective function?

Van Tharp defines System Quality Number on page 28 of "Definitive Guide to Position Sizing."  SQN = (expectancy / standard deviation) times squareroot of number of trades.  SQN decreases when a median trade is replaced by either a large win or a large loss.   It is possible to redefine the metric so that large wins are not penalized, such as by using the semi-deviation instead of the standard deviation as the denominator.  But without making that change, outliers, both good and bad, do affect SQN by reducing it. 

What happens with open (or potentially open) trades at the boundaries of walk forward periods is difficult to handle in both theory and practice.  Tomasz' implementation is to close all open trades at the end of each WF period; and go into each WF period flat, not taking a new position until there is a new signal.  This creates a potentially serious distortion of results when trades are typically held a long time (a large proportion of a WF period) or when there are a few large trades that comprise the majority of a system's profit or loss.

I think this leads to a conclusion that we both agree on -- high quality trading systems that can benefit from position sizing are based on high frequency trading with very careful control over losses, and even control over gains. 

Thanks for listening,
Howard


On Wed, Oct 7, 2009 at 2:36 PM, Mike <sfclimbers@xxxxxxxxx> wrote:
 

Howard,

Assuming that SQN is the t-test for expectancy, then optimizing on the t-test of expectancy (i.e. SQN) is not the same as optimizing on CAR.

The primary reason that CAR is a poor target for optimization is that outliers can significantly improve the calculation. The exact opposite is true for SQN.

SQN rewards consistency and punishes outliers. Consistent winners with a few large wins will improve CAR but hurt SQN, resulting in different parameter combinations being selected during an optimization.

As for writing a custom method, AmiBroker's stats are calculated based on the assumption that all open trades are closed out at the backtest boundary date. Many open trades, or even just a few large open trades, can skew these values.

For high frequency strategies or strategies using heavy position sizing, creating a custom function is the only way to get reliable measurements.

Mike



--- In amibroker@xxxxxxxxxxxxxxx, Howard B <howardbandy@xxx> wrote:
>
> Greetings all --
>
> There has been a lot of activity on this thread. I'll not respond to each
> point individually, but will make a couple of general comments.
>
> I know David Aronson, speak with him regularly, and collaborate with him on
> projects. I have a copy of his book, "Evidence-Based Technical Analysis."
> His book is excellent and I highly recommend it. I think David and I are in
> pretty close agreement on most of the modeling, simulation, testing, and
> validation issues.
>
> I have spoken with Robert Pardo and have exchanged several emails and forum
> postings with him. I think his earlier book was very good, particularly at
> the time it was published. And his more recent book is not quite up to
> those standards. There are several important areas he did not cover and
> several areas where I see things considerably differently than Robert.
>
> I have spoken with and exchanged emails with Van Tharp, and I have copies of
> his books "Trade Your Way to Financial Freedom" and "Definitive Guide to
> Position Sizing." Both are excellent, and I recommend them both highly. Be
> sure to get the second edition of Trade Your Way to Financial Freedom -- it
> has some important corrections and clarifications.
>
> Permit me a short rant on my soapbox. I really dislike it when people claim
> ownership of common terms. Tom DeMark, Robert Pardo, Van Tharp, and others
> put Service Mark symbols on terms that they think are unique to them, but
> are not. I appreciate Tharp's enthusiasm over what he calls System Quality
> Number, but I wish he would not put the Service Mark symbol next to every
> occurrence of it. And trying to Service Mark the term Position Sizing is
> like a dietician service marking "calorie counting." Robert Pardo claims
> "Walk Forward." I used exactly that term describing exactly that process in
> research papers I delivered at conferences in the late 1960s. The mark has
> been registered, not by Robert, but by a company I used to work for and with
> which Robert was not associated, over my strong objection. End of rant.
>
> System quality number is equivalent to t-test. Systems with SQNs above 2
> work well for exactly the same reasons that systems with t-test scores above
> 2 work well. In fact, it is possible to create a custom objective function
> that Is the t-test and use it for optimization. Attendees at my workshops
> in Melbourne later this month will see that demonstrated. Optimizing for
> the t-test of expectancy is equivalent to optimizing for CAR, so don't
> bother creating the custom function unless you have a better candidate for
> your objective function than CAR.
>
> Back to the topic at hand -----
>
> There is No rule of thumb to determine how long the in-sample period should
> be. The Only way to determine that is by testing the model and the data
> together. And be prepared for that length to change over time. Some
> writers suggest a relationship between the number of free parameters and the
> number of data points, or some proportional division of the available data.
> Those techniques do work on industrial time-series data which is usually
> stationary, but they do not work on financial time-series data which is
> non-stationary and changes as trading systems become better at extracting
> inefficiencies from it.
>
> No matter how good the in-sample results look, no matter how high the t-test
> score is, no matter how many closed trades are represented -- in-sample
> results have no value in estimating the future performance of the system.
> None. The only information you have that gives any indication of future
> performance are the out-of-sample results from testing on data that was
> never used at all -- not even once -- during system development.
>
> Tomorrow is out-of-sample. The only way to prepare for real-money trading
> tomorrow is to be rigorous during the system testing and validation
> process. Anything less will overestimate the probability of success.
>
> Thanks for listening,
> Howard
>




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