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I'm enjoying the thread -- but I think we should move it to the Amibroker-ts
group where it probably should be. And so I will post my further comments
on the Sharpe ratio there.
Thanks
chuck
----- Original Message -----
From: "brian.z123" <brian.z123@xxxxxxxxxxxx>
To: <amibroker@xxxxxxxxxxxxxxx>
Sent: Tuesday, November 07, 2006 7:21 PM
Subject: [amibroker] Re: Margin of Error
> Hello Ton,
>
> Thankyou for the compliment.
>
> In the example given it makes no difference what timeframe you are
> working, as Win/Loss is a number ratio.
>
> For other statistics that are measured in magnitude e.g. StDev, the
> weekly value will be greater than the daily value so the maths will
> take care of that for us.
>
> There is a lot more to it than the brief discussion and small
> example I attempted here.
>
> Different measures,like StDev, might be treated differently in stats
> e.g. StdErrorofStDev = = 0.71StDev/SqRt(N)
>
> Keep in mind that I am not a mathematician and not the best person
> to comment on maths specifics.
>
> I do have a very good radar system so I am mainly sharing with the
> forum my perception that a lot of us are short on skills in this
> area and that it is a very important part of trading.
>
> I would recommend that anyone who sees some relevance in the stats
> component of this project should read some of the books written for
> traders by mathematicians and/or ask some further questions of the
> mathematicians in the forum.
>
> I ahve thoroughly enjoyed every post in the topic so far; but I
> would say Fred hit the nail right on the head.
>
> BrianB2.
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Ton Sieverding"
> <ton.sieverding@xxx> wrote:
>>
>> Good work Brian. Thanks. I like what I see but just one little
> question. So the SE is based upon the number of trades N. Let's say
> N = 1.000. Any difference between N = 1.000 days or N = 1.000 weeks
> etc. ?
>>
>> Ton.
>>
>> ----- Original Message -----
>> From: brian.z123
>> To: amibroker@xxxxxxxxxxxxxxx
>> Sent: Tuesday, November 07, 2006 1:51 AM
>> Subject: [amibroker] Margin of Error
>>
>>
>> Part1 of Project Based Training No1.
>>
>> The objective of the project is to introduce new traders to the
> main
>> concepts of system design/testing and demonstrate their
> application
>> in AmiBroker.
>> At the same time it is hoped that the ideas presented will
> provoke
>> discussion and provide trading stimulation.
>>
>> All of the stages in the design process will not be demonstrated
> as
>> most have already been covered elsewhere in the AmiBroker
> support
>> material.
>>
>> A basic understanding of the application of some statistical
> methods
>> to the trading environment is a pre-requisite.
>> The opening topics address this need.
>>
>> To those who find the subject matter new *the project* will be a
>> workbook .
>> To those who have experience in the subject it will be an
>> opportunity to workshop.
>>
>> I would like to acknowledge my indebtedness to the academic
>> community .
>> I often refer to the material so generously interpreted for the
>> layperson and made available at websites by academic
> specialists,
>> particularly those associated with Universities.
>>
>>
> *******************************************************************
>> Margin of Error.
>>
>> Back-testing of historical data provides traders with a sample,
>> typical of the trade they are testing. From that sample they
> make
>> inferences about the larger group, or population, of all past
> trades
>> and future trades, of the same type, that were not included in
> their
>> test window.
>> Despite the fact that the people who teach them to back-test
> also
>> teach them that the past can not predict the future, some
> continue
>> to act as if it can.
>>
>> If the past can't predict the future. How can anyone trade with
>> confidence?
>>
>> The answer is that while the future can't be predicted, the
>> likelihood of some mathematically defined outcomes can be
> predicted
>> with a degree of confidence.
>> Statistics is the mathematical discipline that manages that very
>> well.
>>
>> The caveat is that to apply statistical methods to trading
> samples,
>> the assumption is made that they are the result of a random
> process.
>> Where the trading system chosen is biased to non-random
> behaviour it
>> will be prone to failure if the market acts contrary to that
> bias.
>>
>> For that reason system traders are faced with a choice between
>> attempting to define market behaviour e.g. a trend, and pick a
>> system to suit that, or search for a universal signal that is
>> consistent irrespective of any assumed market bias.
>>
>> If statistics can predict the likelihood of future trading
> outcomes,
>> how accurate will it be?
>>
>> *Standard error* or *margin of error* offers traders a solution
> but
>> they are not subjects that are often discussed.
>>
>> In his book ,*Design, Testing, and Optimisation of Trading
> Systems*
>> (John Wiley & Sons, 1992), Robert Pardo raises the issue of the
>> accuracy of trading *predictions* based on the size of the
> sample
>> used:
>>
>> * The sample size must be large enough to allow the trading
> system
>> to generate a statistically significant sample of trades.
>> A sample of one trade is certainly insignificant, whereas a
> sample
>> of 50 trades or more is generally adequate.*
>>
>> He uses Standard Error as a measure of significance:
>>
>> StdError = = 1/SquareRoot(sample size),
>>
>> 1/SqRt(50) = = 14.1%.
>>
>> There is little by way of further explanation provided.
>>
>> Applying the formula to a greater number of samples:
>>
>> Where N = = the number of trades in the sample
>>
>> StdError factor = = 1/SqRt(N)
>> StdError% = 1/SqRt(N) * 100
>>
>> If N = = 2500 the StdError% = = 1/SqRt(2500) * 100 = = +/- 2%
>> If N = = 10000 the StdError% = = 1/SqRt(10000) * 100 = = +/- 1%
>>
>> A trade sample of 10000 to provide statistical accuracy of 1% is
> not
>> easily achievable for traders, although a lot easier than
> accurately
>> surveying the eye colour of Polar Bears.
>>
>> Pardos equation is in fact, a rounding of the StdError equation
> for
>> a 95% level of confidence:
>>
>> Margin of error at 99% confidence = = 1.29/SqRt(N)
>> Margin of error at 95% confidence = = 0.98/SqRt(N)
>> Margin of error at 90% confidence = = 0.82/SqRt(N)
>>
>> Later in the project I will use a basic random number generator,
>> within Xcel, to provide a visual aid that traders can use to
>> understand the *sample* concept and decide for themselves what
>> constitutes an adequate sample.
>>
>> Wikipedia provides some additional clarity on the subject:
>>
>> http://en.wikipedia.org/wiki/Margin_of_error
>>
>> *The margin of error expresses the amount of the random
> variation
>> underlying a survey's results. This can be thought of as a
> measure
>> of the variation one would see in reported percentages if the
> same
>> poll were taken multiple times. The larger the margin of error,
> the
>> less confidence one has that the poll's reported percentages are
>> close to the "true" percentages, that is the percentages in the
>> whole population.*
>>
>> *An interesting mathematical fact is that the margin of error
>> depends only on the sample size and not on the population size,
>> provided that the population is significantly larger than the
> sample
>> size, and provided a simple random sample is used. Thus for
>> instance...the running example with 1,013 random samples..would
>> yield essentially the same margin of error (4% with a 99% level
> of
>> confidence) regardless of whether the population....consisted of
>> 100,000 or 100,000,000.*
>>
>> In short the tail of the trading system sample is swinging the
>> trading system cat.
>>
>> BrianB2
>>
>> The material contained in this topic is for educational and
>> discussion use only.
>> It is not intended as financial advice and should not be
> construed
>> as such.
>> The author is not an accredited academic or financial advisor.
>>
>
>
>
>
>
> Please note that this group is for discussion between users only.
>
> To get support from AmiBroker please send an e-mail directly to
> SUPPORT {at} amibroker.com
>
> For NEW RELEASE ANNOUNCEMENTS and other news always check DEVLOG:
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>
> For other support material please check also:
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>
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>
>
>
>
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