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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@xxx> 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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