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" <[EMAIL PROTECTED]> To: <[email protected]> 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 [email protected], "Ton Sieverding" > <[EMAIL PROTECTED]> 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: [email protected] >> 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: > http://www.amibroker.com/devlog/ > > For other support material please check also: > http://www.amibroker.com/support.html > > Yahoo! Groups Links > > > > 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: http://www.amibroker.com/devlog/ For other support material please check also: http://www.amibroker.com/support.html Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/amibroker/ <*> Your email settings: Individual Email | Traditional <*> To change settings online go to: http://groups.yahoo.com/group/amibroker/join (Yahoo! ID required) <*> To change settings via email: mailto:[EMAIL PROTECTED] mailto:[EMAIL PROTECTED] <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
