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Hi Brian:
I'm not an expert, but it seems that your analysis is correct. The Sharpe
Ratio basically does the same thing -- how variable are the trades compared
to their standard deviation within a sample, or to the standard error of
their samples? Of course this all assumes that the effectiveness of the
system does not change over time...
chuck
----- Original Message -----
From: "brian.z123" <brian.z123@xxxxxxxxxxxx>
To: <amibroker@xxxxxxxxxxxxxxx>
Sent: Tuesday, November 07, 2006 2:21 AM
Subject: [amibroker] Re: Margin of Error
OT:margin of error example.
As the trader is more interested in the general population of future
trades than the test sample, what can be learnt from the sample?
One answer is to trade the system for a decade or two and find out.
Another option is to simulate decades or even centuries of trading
by applying Monte Carlo analysis.
In laymans terms MCS is a computer generated, random walk through
*all*, of the possible trading outcomes based on the trading sample
provided.
The result is a report or system profile that provides statistics on
which to base our levels of trading confidence for the future.
There are other ways of sneaking a peak into a trading systems
future but MCS is the most commonly used.
I have developed my own system, that I don¡¦t want to headline here
for various reasons, not the lest of which is that I can¡¦t provide a
mathematical proof if called on to do so.
Assuming that an MCS has been conducted on a sample of 50 trades
produced by a back-tested system and the report indicates that the
meanW/meanL for the system over a large number of trading
simulations is 53/47. The StDev is 40% for both Wins and Losses.
How confident can we be in that result?
>From David Lanes statistical website:
http://davidmlane.com/hyperstat/A103397.html
The standard error of a statistic is the standard deviation of the
sampling distribution of that statistic.
The formula for the standard error of the mean is:
StErrorOfMeanPopulation = StDevPopulation/SqRt(N)Sample
For any statistic:
StErrorOfMeanPopulation(statistic) = StDevPopulation(statistic)/SqRt
(N)Sample
Applying the StdErrorMean equation to the example:
Back-test sample size N = = 50,
MCS meanWin/meanLoss = = 53/47,
MCS Win StDev% = = 40%,
MCS Win StDev$ = = 40% x 53 = = 21.2,
MCS Loss StDev% = = 40%,
MCS Loss StDev$ = = 40% x 47 = = 18.8,
StdError%Wins = = 40/SqRt(50) = = multiply mean by +/- 5.6 %,
Trading Win range = = 50 ¡V 56,
(min = = 53 x 0.943 = = 50, max = = 53 X 1.056 = = 56).
The same result can be obtained using StDev as a number ($) rather
than as a percentage.
StdError$Wins = = 21.2/SqRt(50) = = +/- 3 = = Win range = = 47 +/-3
= = 50 -56 .
Repeating the calculations for Losses shows the the mean Losses
range between 44 ¡V 50.
I chose this extreme example to demonstrate the outcome for a small
back-test sample with high volatility trades and a small win/loss
margin.
If the same trading pattern were generated from a back-test sample
of 2500 trades and the simulated meanWins and mean Losses each had a
StDev of 10% the range for the margin of error would be:
Wins 52.9 ¡V 53.1,
Losses 46.9 ¡V 47.1.
This means that the we can be 95% confident the real mean values are
somewhere within those ranges.
For a higher level of confidence the range will be greater.
Resorting to the age-old teaching trick of asking the students for
the answer while pretending to already know it yourself; can anyone
in the forum tell me if this is the correct way to use StdError when
applied to trading?
BrianB2 fº
--- In amibroker@xxxxxxxxxxxxxxx, "brian.z123" <brian.z123@xxx>
wrote:
>
> 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¡K¡K.the running example with 1,013 random samples¡K¡Kwould
> yield essentially the same margin of error (4% with a 99% level of
> confidence) regardless of whether the population¡K¡K¡K.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.
>
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