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Thomas,
The ninjatrader thread that you point to is incomplete. In the definitive guide, Tharp explicitly says that when there are a large number of trades, SQN can become grossly overstated. To counteract this he suggests using a maximum of 100 for 'N' in the formula that you quoted. Since the formula takes the square root of N, and the square root of 100 is 10, the multiplier becomes
max(10, square root of N)
or expressed differently,
square root of max(100, N).
Yes, Tharp does make a distinction in his calculation of expectancy that differs from other sources.
For the purposes of calculating SQN, Tharp expresses expectancy per unit of risk. This would be roughly equivalent to AmiBroker's average profit/loss divided by the average loss. Unfortunately, due to open trades being included in those calculations, the values produced by AmiBroker can sometimes skew the results and custom backtest code becomes necessary.
Yes, the example 3 that you point to is exactly the right approach. In it you will see that Tomasz is calculating multiples based on per trade initial risk, then summing those multiples to give the expectancy. This is the most precise calculation of Tharp's version of expectancy.
What remains to be done is to divide that expectancy by the standard deviation of those multiples and multiply it by the square root of max(100, number of trades).
Tomasz's example can be generalized by calculating the average loss of the closed trades and using that as the initial risk for all trades (instead of 10% stoploss per trade) when calculating the multiples. This allows the calculation to still work for strategies that do not use a stop loss, though at reduced precision.
Mike
--- In amibroker@xxxxxxxxxxxxxxx, Thomas Ludwig <Thomas.Ludwig@xxx> wrote:
>
> Mike,
>
> thanks for your answer!
>
> On 06.10.2009, 08:47:28 Mike wrote:
> > Thomas,
> >
> > When I was reading "Van Tharp's Definitive Guide To Position Sizing", I put
> > togeather a web page hosting a position sizing simulator for the examples
> > in the book. I wrote the simulator for usage against my own strategy. Then
> > hosted it for anyone else to compare against the book.
> >
> > You can play with it to get a feel for how different SQN values affect
> > position sizing:
> >
> > http://www.afltools.com/positionsize.html
> >
> > If you do play with the simulator, and have any questions, please send them
> > to the email address provided on that page, as opposed to on this forum.
>
> Very interesting - I will have a close look inti it!
> >
> > To answer your question;
> >
> > SQN = (Expectancy / Standard deviation of R) x max(10, square root of
> > number of trades)
>
> Since I don't have the book I found a different formula on
> http://www.ninjatrader-support2.com/vb/showthread.php?t=4320 which may not be
> correct.
> >
> > The most precise calculation of Expectancy (according to Tharp) is the summ
> > of all closed trade R multiples.
> >
> > Ideally you would have a precise R for each trade from which to calculate
> > the closing R multiple. Otherwise, you can use the average loss as R (e.g.
> > like when using a moving average crossover for exit there is no
> > predetermined R like there would be when using a stoploss).
> >
> > If you are unable to sum the R multiples, you can use
> >
> > Expectancy = ((Avg. Profit x Prob. of win) - (Avg. Loss x Prob. of loss)) /
> > Avg. Risk
>
> There might be different definitions of expectancy. According to Howard's book
> QTS (p. 319) Expectancy is equivalent with Average Profit/Loss already reported
> in Amibroker.
> >
> > Unfortunately, for this usage, the summary statistics produced by AmiBroker
> > are based on the assumption that open trades are closed out at the current
> > price. This skews the values. So, you must write custom backtest code to
> > only work with *closed* trades to figure avg. win, avg. loss, etc.
> >
> > Also, your usage of StDev is not correct. You must calculate the R
> > multiple for each closed trade, then calculate the standard deviation of
> > those values yourself.
>
> I will investigate how to do this. Example 3 on
> http://www.amibroker.net/guide/a_custommetrics.html should be a good place to
> start.
>
> >
> > Hope that helps
> >
> > Mike
>
> Thanks again.
>
> Thomas
> >
> > --- In amibroker@xxxxxxxxxxxxxxx, Thomas Ludwig <Thomas.Ludwig@> wrote:
> > > Mike,
> > >
> > > how do calculate SQN? I've tried this:
> > >
> > > SQN=sqrt(st.GetValue("AllQty"))*st.GetValue("AllAvgProfitLoss")/StDev(st.
> > >GetValue("NetProfit")); bo.AddCustomMetric("SQN",SQN);
> > >
> > > but I'm not sure if this is correct.
> > >
> > > What do you think?
> > >
> > > Regards,
> > >
> > > Thomas
> > >
> > > On 05.10.2009, 09:29:41 Mike wrote:
> > > > Ton,
> > > >
> > > > Are you saying that you have not found an IS/OOS pair that works well?
> > > > What measure are you using to judge "stability" of the walk forward
> > > > process (i.e. what measure are you using to judge the process as
> > > > random)?
> > > >
> > > > After testing with multiple IS periods, and with multiple OOS periods,
> > > > I was able to identify "fixed" window lengths that proved more
> > > > consistent than the others tested.
> > > >
> > > > I reached this conclusion by charting a distribution curve of CAR for
> > > > the OOS results. My fitness function is currently based on UPI, and
> > > > thus my walk forward is driven by that value. However, ultimately my
> > > > interest is in how consistent CAR would be which is why I used that for
> > > > evaluating the goodness of fit for the IS/OOS period lengths.
> > > >
> > > > In my case, over a 13 year period, a 2 year IS and 6 month OOS (for a
> > > > total of 26 OOS data points) produced the most normal looking
> > > > distribution of CAR results (i.e. central peak, smallest standard
> > > > deviation). Excluding the results from all of 1999 and the first half
> > > > of 2000 (during which results were abnormally strong), the distribution
> > > > curve looks even better.
> > > >
> > > > Also, have you tried working with different fitness functions? Perhaps
> > > > your fitness function doesn't adequately identify the "signal" and thus
> > > > misguides the walk forward, regardless of IS/OOS window lengths.
> > > >
> > > > I am in the process of running a new walk forward over the last 7.5
> > > > years using Van Tharp's System Quality Number (SQN) as my fitness
> > > > function. I have kept the same 2 year IS/6 months OOS for a total of 15
> > > > OOS data points. My system strives to generate a minimum average of 2
> > > > trades per day, so each IS period generally has 1000 or more trades
> > > > from which to calculate the fitness.
> > > >
> > > > It has not run to completion yet. But, for the periods that have
> > > > produced results, the results look promising (at least with respect to
> > > > the SQN of the OOS relative to the SQN of the IS, I have not yet
> > > > created the distribution of CAR for OOS).
> > > >
> > > > Assuming that the remainder of the results are equally strong, I will
> > > > walk forward further back in history to get the full 26 data points to
> > > > compare against the results produced using my UPI fitness. If the CAR
> > > > distribution is more normal using SQN as fitness, then I will
> > > > officially start using SQN for generating optimal values for my next
> > > > live OOS.
> > > >
> > > > If you are willing to share, I would be curious to hear if SQN as a
> > > > fitness function was able to produce a more stable walk forward for
> > > > you, and what measure you are using to judge "stable".
> > > >
> > > > Mike
> > > >
> > > > --- In amibroker@xxxxxxxxxxxxxxx, "Ton Sieverding" <ton.sieverding@>
> > >
> > > wrote:
> > > > > Hi Howard,
> > > > >
> > > > > I still am struggling with the following sentence from David
> > > > > Aronson
> > > > >
> > > > > : "The decision about how to apportion the data between the IS and
> > > > > : OOS
> > > > >
> > > > > subsets is arbitrary. There is no theory that suggests what fraction
> > > > > of the data should be assigned to training ( IS ) and testing ( OOS
> > > > > ). Results can be very sensitive to these choices ... ". Because this
> > > > > is exactly what I am seeing. WalkFoward results are more then
> > > > > sensitive to the IS/OOS relation and in many cases a pure random
> > > > > story. I am getting more and more the feeling that WalkForward is not
> > > > > the correct or better objective way to test trading systems. With all
> > > > > respect to Robert Pardo's idea's about this topic and what you are
> > > > > writing in QTS ...
> > > > >
> > > > > Regards, Ton.
> > > > >
> > > > >
> > > > > ----- Original Message -----
> > > > > From: Howard B
> > > > > To: amibroker@xxxxxxxxxxxxxxx
> > > > > Sent: Monday, October 05, 2009 12:48 AM
> > > > > Subject: Re: [amibroker] Re: Is the Walk forward study useful?
> > > > >
> > > > >
> > > > > Greetings all --
> > > > >
> > > > > My point of view on the length of the in-sample and out-of-sample
> > > > > may be a little different.
> > > > >
> > > > > The logic of the code has been designed to recognize some pattern
> > > > > or characteristic of the data. The length of the in-sample period is
> > > > > however long it takes to keep the model (the logic) in
> > > > > synchronization with the data. There is no one answer to what that
> > > > > length is. When the pattern changes, the model fits it less well.
> > > > > When the pattern changes significantly, the model must be
> > > > > re-synchronized. The only person who can say whether the length is
> > > > > correct or should be longer or shorter is the person running the
> > > > > tests.
> > > > >
> > > > > The length of the out-of-sample period is however long the model
> > > > > and the data remain in sync. That must be some length of time beyond
> > > > > the in-sample period in order to make profitable trades. It could
> > > > > be a long time, in which case there is no need to modify the model at
> > > > > all during that period. There is no general relationship between the
> > > > > length of the in-sample period and the length of the out-of-sample
> > > > > period -- none. There is no general relationship between the
> > > > > performance in-sample and the performance out-of-sample. The greater
> > > > > the difference between the two, the better the system has been fit to
> > > > > the data over the in-sample period. But that does not necessarily
> > > > > mean that the out-of-sample results are less meaningful.
> > > > >
> > > > > You can perform some experiments to see what the best in-sample
> > > > > length is. And then to see what the typical out-of-sample length is.
> > > > > Knowing these two, set up a walk forward run using those lengths.
> > > > > After the run is over, ignore the in-sample results. They have no
> > > > > value in estimating the future performance of the system. It is the
> > > > > out-of-sample results that can give you some idea of how the system
> > > > > might act when traded with real money.
> > > > >
> > > > > It is nice to have a lot of closed traded in the out-of-sample
> > > > > period, but you can run statistics on as few as 5 or 6. Having fewer
> > > > > trades means that it will be more difficult to achieve statistical
> > > > > significance. The number 30 is not magic -- it is just conventional.
> > > > >
> > > > > I think it helps to distinguish between the in-sample and
> > > > > out-of-sample periods this way -- in-sample is seeing how well the
> > > > > model can be made to fit the older data, out-of-sample is seeing how
> > > > > well it might fit future data.
> > > > >
> > > > > Ignore the television ads where person after person exclaims
> > > > > "backtesting!" as though that is the key to system development. It
> > > > > is not. Backtesting by itself, without going on to walk forward
> > > > > testing, will give the trading system developer the impression that
> > > > > the system is good. In-sample results are always good. We do not
> > > > > stop fooling with the system until they are good. But in-sample
> > > > > results have no value in predicting future performance -- none.
> > > > >
> > > > > There are some general characteristics of trading systems that make
> > > > > them easier to validate. Those begin with having a positive
> > > > > expectancy -- no system can be profitable in the long term unless it
> > > > > has a positive expectancy. Then going on to include trade
> > > > > frequently, hold a short time, minimize losses. Of course, there
> > > > > have been profitable systems that trade infrequently, hold a long
> > > > > time, and suffer deep drawdowns. It is much harder to show that
> > > > > those were profitable because they were good rather than lucky.
> > > > >
> > > > > There is more information about in-sample, out-of-sample, walk
> > > > > forward testing, statistical validation, objective functions, and so
> > > > > forth in my book, "Quantitative Trading Systems."
> > > > > http://www.quantitativetradingsystems.com/
> > > > >
> > > > > Thanks for listening,
> > > > > Howard
> > > > >
> > > > >
> > > > >
> > > > > On Sun, Oct 4, 2009 at 10:56 AM, Bisto <bistoman73@> wrote:
> > > > >
> > > > >
> > > > > Yes, I believe that you should increase the IS period
> > > > >
> > > > > as general rule is not true "the shortest the best" trying to
> > > > > catch every market change because it's possible that a too short IS
> > > > > period produces a too low number of trades with no statistical
> > > > > robustness --> you will find parameters that are more likely
> > > > > candidated to fail in OS
> > > > >
> > > > > try a longer IS period and let's see what will happen
> > > > >
> > > > > I read an interesting book on this issue: "The evaluation and
> > > > > optimization of trading strategies" by Pardo. Maybe he repeated too
> > > > > much times the same concepts nevertheless I liked it
> > > > >
> > > > > if anyone could suggest a better book about this issue it would
> > > > > be very appreciated
> > > > >
> > > > >
> > > > >
> > > > > Bisto
> > > > >
> > > > > --- In amibroker@xxxxxxxxxxxxxxx, "Gonzaga" <gonzagags@> wrote:
> > > > > > Oh, sorry, I am lost in translation ... ;-)
> > > > > > Yes I meant trades of my IS period.
> > > > > > I've got about 70 trades in my IS period, three months.
> > > > > > BUT, I buy stocks in a multiposition way.This means, that my
> > > > > > hole capital divides among several stocks purchased
> > > > > > simultaneously. So, in my statistics, I use to average my
> > > > > > trades. When I use maxopenpositions=7, I use to average my
> > > > > > results every 7 trades. Considering that, my trades in three
> > > > > > months are not 70, but less ( not exactly 70/7, but less than
> > > > > > 70)
> > > > > >
> > > > > > If I use maxopenposition=1, which is, invest all my capital
> > > > > > every trade, in three months I would have about 29 trades. So I
> > > > > > suppose I have to increase the IS period.. isn`t it?
> > > > > >
> > > > > > --- In amibroker@xxxxxxxxxxxxxxx, "Bisto" <bistoman73@> wrote:
> > > > > > > What do you mean with "I don't have many buyings and
> > > > > > > sellings"?
> > > > > > >
> > > > > > > If you have less than 30 trades in an IS period, IMHO, you
> > > > > > > are using a too short period due to not statistical
> > > > > > > robustness --> WFA is misleading, try a longer IS period
> > > > > > >
> > > > > > > Bisto
> > > > > > >
> > > > > > > --- In amibroker@xxxxxxxxxxxxxxx, "Gonzaga" <gonzagags@>
> wrote:
> > > > > > > > Thanks for the answers
> > > > > > > > To Keith McCombs :
> > > > > > > >
> > > > > > > > I use 3 months IS test and 1 month step, this is, 1 month
> > > > > > > > OS test. My system is an end-of day-system, so I don't have
> > > > > > > > many buyings and sellings.. Perhaps I should make bigger
> > > > > > > > the IS period?
> > > > > > > >
> > > > > > > > anyway, my parameter behaves well in any period. Of course
> > > > > > > > it is an optimized variable, but it doesn't fail in ten
> > > > > > > > years, in none of those ten years, over 500 stocks.. a very
> > > > > > > > long period.. So, couldn't it be better, on the long run,
> > > > > > > > than the parameters optimized with the WF study? (In fact,
> > > > > > > > I am using it now, the optimized variable)
> > > > > > > > That's my real question..
> > > > > > > >
> > > > > > > > To dloyer123:
> > > > > > > > I haven't understood the meaning of the Walk Forward
> > > > > > > > Efficency, and seems interesting. can you explain it
> > > > > > > > better, please..?
> > > > > > > >
> > > > > > > > --- In amibroker@xxxxxxxxxxxxxxx, "dloyer123" <dloyer123@>
> > >
> > > wrote:
> > > > > > > > > I have had similar experiences. I like to use WFT to
> > > > > > > > > estimate what Pardo call's his "Walk Forward Efficency",
> > > > > > > > > or the ratio of the out of sample WF profits to just
> > > > > > > > > optimizing over the entire time period.
> > > > > > > > >
> > > > > > > > > A good system should have as high a WFE as posible.
> > > > > > > > > Systems with a poor WFE tend to do poorly in live
> > > > > > > > > trading.
> > > > > > > > >
> > > > > > > > > If you have a parm set that works well over a long period
> > > > > > > > > of live trading, then you are doing well!
> > > >
> > > > ------------------------------------
> > > >
> > > > **** IMPORTANT PLEASE READ ****
> > > > This group is for the discussion between users only.
> > > > This is *NOT* technical support channel.
> > > >
> > > > TO GET TECHNICAL SUPPORT send an e-mail directly to
> > > > SUPPORT {at} amibroker.com
> > > >
> > > > TO SUBMIT SUGGESTIONS please use FEEDBACK CENTER at
> > > > http://www.amibroker.com/feedback/
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> > > >
> > > > For NEW RELEASE ANNOUNCEMENTS and other news always check DEVLOG:
> > > > http://www.amibroker.com/devlog/
> > > >
> > > > Yahoo! Groups Links
> >
> > ------------------------------------
> >
> > **** IMPORTANT PLEASE READ ****
> > This group is for the discussion between users only.
> > This is *NOT* technical support channel.
> >
> > TO GET TECHNICAL SUPPORT send an e-mail directly to
> > SUPPORT {at} amibroker.com
> >
> > TO SUBMIT SUGGESTIONS please use FEEDBACK CENTER at
> > http://www.amibroker.com/feedback/
> > (submissions sent via other channels won't be considered)
> >
> > For NEW RELEASE ANNOUNCEMENTS and other news always check DEVLOG:
> > http://www.amibroker.com/devlog/
> >
> > Yahoo! Groups Links
> >
> >
> >
>
------------------------------------
**** IMPORTANT PLEASE READ ****
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This is *NOT* technical support channel.
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