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Bing,
Howard answered your comments regarding using anything other than the true t-test formula.
Regarding your question of why "as N increases, expectancy/StdDevofR would tend to decrease". This is simply a comment based upon a number of prevailing theories and axioms such as:
1. No strategy will work forever, the market is always changing.
2. Efficient market hypothesis.
3. Random Walk theory.
4. etc.
All of the above suggest that there is no such thing as an everlasting edge, that over time (i.e. after many trades) the expectancy will approach zero and the standard deviation will grow larger.
The more trades you have, the more difficult it is to sustain a non zero return. A large sqrt(N) multiplied by zero is still zero ;)
The only value to Tharp's limitation is to have a consistent measure for comparison with his writings.
Mike
--- In amibroker@xxxxxxxxxxxxxxx, "bingk66" <bing.kwok@xxx> wrote:
>
> Hi Mike,
>
> I understand what you are saying. I agree that the more data points in the calculations the more confidence you are entitle to have in the results of the system, and hence the usage of the sqrt(N) portion of the equation to reflect that. The concept of it all is fine.
>
> However, where I am not entirely comfortable with the equation is the sqrt(N) part, as sqrt(N) can have way too much weighting in the overall t-test score once N gets too large. Perhaps using the cube root of N might be better as a means of allowing N to be fully factored into the equation ( as opposed to Van Tharp's proposal of limiting N to 100) without overbearing the other parts of the equation. It boils down to a personal choice, I guess, not unlike the calculation of the objective function that Howard describes in his books whereby you wish to calculate a single number, and that single number could be derived from a number of sources, each with their own weighting and you like some form of partitioning across these different sources so that no one source overbears the others, inorder to get a balanced calculation can be obtained.
>
> Finally, the last part of your post would seem to indicate that as N increases, expectancy/StdDevofR would tend to decrease. I can't see or understand why that would be the case. I would appreciate it if you could provide a brief explanation as to why that might be the case or at least provide a link whereby I can read up a little more on this.
>
> Bing
>
>
>
>
>
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Mike" <sfclimbers@> wrote:
> >
> > Bing,
> >
> > In this example, the t-test is calculated to give us a level of confidence that the average of the sample is different than zero.
> >
> > If a trade strategy had no predictive power, then its results would be purely random, producing a net gain (over the long run) of zero with an equal number of winners and losers.
> >
> > Actually, it would be a net gain of zero *over the prevailing trend*, where the trend itself might be greater than zero, as per Aronson. But, that is another conversation.
> >
> > The more trades taken, the more likely the true average would show. For example; Flip a coin 4 times. You might get 3 heads, 1 tail for an average of 0.75 heads. Flip a coin 1000 times and the average number of heads will be much much closer to 0.5.
> >
> > Going back to your trade example, if we are getting a non zero average after thousands of trades, then we are more and more confident that in fact the average is not zero. Thus, the larger t-test score is justified, and is in fact built into the equation.
> >
> > In other words, you don't have to worry about getting a SQN score of 7 after 5000 trades, because you will likely never find a trade strategy that is capable of producing an expectancy of 0.1 after that many trades!
> >
> > Mike
> >
> > --- In amibroker@xxxxxxxxxxxxxxx, "bingk66" <bing.kwok@> wrote:
> > >
> > > Hi Howard,
> > >
> > > If there are no means to limit the number of transactions in the calcs, then one seriously runs the risk of challenging the mystical t-test score of 7 that you spoke about previously.
> > >
> > > As an example, if the OOS test was run over a 5 year period with 5000 transactions (a mere 1000 transaction/year, which is not excessive, especially for very short term trades), sqrt(5000) alone would yield in excess of 70 for the multiplier. This would leave expectancy/StdDev of R with just a target of 0.1, to reach the 7 t-tests score.
> > >
> > > Now, if you had 1,000,000 tranasctions in your OOS test....
> > >
> > > The concept of limiting the trade count does make sense to me. Maybe 100 is too low, and should be set higher. There does come a point whereby the sqrt(N) part of the equation will render the rest of the equation irrelevant once N gets too large.
> > >
> > > $0.02
> > >
> > > Bing
> > >
> > >
> > >
> > > --- In amibroker@xxxxxxxxxxxxxxx, Howard B <howardbandy@> wrote:
> > > >
> > > > Hi Zozu --
> > > >
> > > > I must disagree with Van Tharp on this.
> > > >
> > > > If the runs are truly out-of-sample, then each and every one contributes to
> > > > the computation. It makes no sense to limit the count to 100. It is poor
> > > > procedure to limit the count. It is bad science to limit the count. Do not
> > > > limit the count.
> > > >
> > > > If the runs are in-sample, then the test has no meaning anyway. Computing
> > > > the t-test statistic using any N will be misleading. Do not even do the
> > > > computation. If a decision to trade a system is made after computing the
> > > > t-test statistic on trades that came solely from in-sample results, there is
> > > > an extremely high probability that a Type I error will be committed. That
> > > > is, the trader will believe that his system is better than random, when it
> > > > is in fact not better than random. Type I errors result in loss of money.
> > > >
> > > > Thanks,
> > > > Howard
> > > >
> > > >
> > > > On Tue, Oct 13, 2009 at 10:54 AM, zozuzoza <zozuka@> wrote:
> > > >
> > > > >
> > > > >
> > > > > Hi Howard,
> > > > >
> > > > > Limiting the number of N doesn't mean that you are not using all trades for
> > > > > the calculation of SQN. Only the sqrt(N) part of the formula is limited in
> > > > > order not to distort the results if there are many trades. It makes sense.
> > > > > The other part of the formula does count on all the trades.
> > > > >
> > > > > Zozu
> > > > >
> > > > >
> > > > >
> > > >
> > >
> >
>
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