Statistics question

hhiusa

Well-known member
May 5, 2015
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#1
I have taken a sample population of a population with unknown size. The sample size is 54 trades. The sample mean is 2.1% (1.021) return per trade. The sample standard deviation is 0.01. 100% of the 54 trades were profitable i.e., X>1.00. I wish to know with a certain confidence, how close the sample mean and standard deviation are to the population mean and standard deviation. I would also like to know what is the probability of the 55th trade and subsequent trades being >1.00.



Z-score = 0.021/0.01 = 2.1

Z from the cumulative normal distribution function



The extrema should then be the greatest standard deviation with the lowest mean and the lowest standard deviation with the highest mean.



Does this mean that I am 95% confident that 91.8% of future trades will be profitable or that the 55th trade will be profitable. Does this also mean that at that exact point in time the worst case scenario is 91.8%.
 
Oct 27, 2013
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#2
This statistical question you have raised hhiusa is pure mathematical and so its real meaning in the real world is of limited use.

My question back to you would therefore be .............Why ?

You mention that 100% of the sample - ie 54 trades - were profitable.

OK - so then go on to show that the Z score is 2.1 and positive

So the probability is very high

Ok in the real world the 55th trade could still fail - and that is the most important part of what you need to know

Whether you are 95% confident that 91.8% of all future trades will be profitable or not is of NO significance in the real world to you saying you are only 86% confident of 94.2% of all future trades will be profitable.

Personally - I reckon you need a larger sample - ie >100+ or even better >1000

Otherwise stick 3 Maths Professors in a room together - and I bet one would disagree with the other 2 and would be able to explain with another formula that the assumption you have made are incorrect

Last point

What ever you do - dont ask any American Maths Professors - stick with reliable European ones - Harvard and MIT students are not the World's best - as I am sure you want to prove next ;-))

Look forward to your next thread with 99.9% enthusiasm - make sure its a good one

(y)


Regards


F
 

Splitlink

Well-known member
Nov 18, 2001
10,850
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#5
It's all Greek to me, but I should say that the chances of the 55th trade going up, or down, were 50-50.
 

hhiusa

Well-known member
May 5, 2015
2,623
130
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#6
This statistical question you have raised hhiusa is pure mathematical and so its real meaning in the real world is of limited use.

My question back to you would therefore be .............Why ?

You mention that 100% of the sample - ie 54 trades - were profitable.

OK - so then go on to show that the Z score is 2.1 and positive

So the probability is very high

Ok in the real world the 55th trade could still fail - and that is the most important part of what you need to know

Whether you are 95% confident that 91.8% of all future trades will be profitable or not is of NO significance in the real world to you saying you are only 86% confident of 94.2% of all future trades will be profitable.

Personally - I reckon you need a larger sample - ie >100+ or even better >1000

Otherwise stick 3 Maths Professors in a room together - and I bet one would disagree with the other 2 and would be able to explain with another formula that the assumption you have made are incorrect

Last point

What ever you do - dont ask any American Maths Professors - stick with reliable European ones - Harvard and MIT students are not the World's best - as I am sure you want to prove next ;-))
Did you really feel the need to post if you weren't going to answer or couldn't not answer the math question. I don't really care about your views on mathematical finance and its use in the real world. Do you have anything worthwhile to say about the math.

The Chi-squared distribution takes the sample size into account. The only need for a higher sample size is the need to increase your confidence. If you were following the math you would understand that.
 
Oct 27, 2013
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#9
Did you really feel the need to post if you weren't going to answer or couldn't not answer the math question. I don't really care about your views on mathematical finance and its use in the real world. Do you have anything worthwhile to say about the math.

The Chi-squared distribution takes the sample size into account. The only need for a higher sample size is the need to increase your confidence. If you were following the math you would understand that.
To answer the important part underlined -

Do you have anything worthwhile to say about the math ?

Yes

grammatical error - no "s" on math

Also learn from this - Trading is not a pure mathematical science

Repeat - Trading is not a pure mathematical science.

You can mention chi squared distribution - non central beta distribution - pareto's distribution - non central t distribution etc etc - in fact all the theories you can come u with - BUT - its of no real use in the real trading environment


So - stick that in your pipe - and smoke it :D

Regards


F
 

hhiusa

Well-known member
May 5, 2015
2,623
130
73
#11
To answer the important part underlined -

Do you have anything worthwhile to say about the math ?

Yes

grammatical error - no "s" on math

Also learn from this - Trading is not a pure mathematical science

Repeat - Trading is not a pure mathematical science.

You can mention chi squared distribution - non central beta distribution - pareto's distribution - non central t distribution etc etc - in fact all the theories you can come u with - BUT - its of no real use in the real trading environment


So - stick that in your pipe - and smoke it :D

Regards


F
Whatever dude! It works great for me as those 54 trades are real for 1 equity over 7 years. Look up the Black Scholes asset pricing model which uses stochastic partial differential equations. You use stochastic optimization to optimize the equations. Some EMAs are partial differential equations which use a smoothing variable μ. Ds = μΔS_t + σS_tW_t. σ is volatility and W_t is a Wiener process. Math definitely has a place in finance. Investment firms spend billions on mathetical research and hire matheticians with little or no finance experience over those who are basically glorified salesmen (stock brokers). Obviously you have absolutely no research and nominal mathematical prowess.
 

hhiusa

Well-known member
May 5, 2015
2,623
130
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#12
we are not worthy then HH......you know your math dude :cool:

but do you know how to kick butt trading ?.........that's what the T2win forum is all about ......;)

N
Thank you NVP! I have more good days than bad.
 
Oct 27, 2013
39,928
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#13
Whatever dude! It works great for me as those 54 trades are real for 1 equity over 7 years. Look up the Black Scholes asset pricing model which uses stochastic partial differential equations. You use stochastic optimization to optimize the equations. Some EMAs are partial differential equations which use a smoothing variable μ. Ds = μΔS_t + σS_tW_t. σ is volatility and W_t is a Wiener process. Math definitely has a place in finance. Investment firms spend billions on mathetical research and hire matheticians with little or no finance experience over those who are basically glorified salesmen (stock brokers). Obviously you have absolutely no research and nominal mathematical prowess.

Investment firms spend billions on mathematical ( spelling mistake again - that rules you out of being a previous multi nic ) research and hire mathematicians ( another spelling mistake - proving beyond doubt your attention to detail - no good for any wannabee maths Pro )


Yes you are so correct

Do you mean these investment and finance companies -

https://en.wikipedia.org/wiki/List_...es_during_the_2007–12_global_financial_crisis

Keep providing me with jokes - I can hold the mirror up for you :D

Regards

F
 

hhiusa

Well-known member
May 5, 2015
2,623
130
73
#14
Investment firms spend billions on mathematical ( spelling mistake again - that rules you out of being a previous multi nic ) research and hire mathematicians ( another spelling mistake - proving beyond doubt your attention to detail - no good for any wannabee maths Pro )


Yes you are so correct

Do you mean these investment and finance companies -

https://en.wikipedia.org/wiki/List_...es_during_the_2007–12_global_financial_crisis

Keep providing me with jokes - I can hold the mirror up for you :D

Regards

F
Your anger seriously amuses me. If the only argument you can find is that I made some typos, then I'll be just fine. Since math isn't your strength, I honestly don't know what you use to trade. I don't use math by itself and I never stated that I did. I magine you could watch the news and fly by the seat of your pants.
 
Last edited:
Oct 27, 2013
39,928
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#15
Your anger seriously amuses me. If the only argument you can find is that I made some typos, then I'll be just fine. Since math isn't your strength, I honestly don't know you use to trade. I don't use math by itself and I never stated that I did. I magine you could watch the news and fly by the seat of your pants.

Apologies

You have confirmed you are not who I thought you were ?

I had been thinking you were another wind up merchant using another nic - and I am wrong

You did it again in your last comment - ie said math instead of maths - proving you are probably from the US and you also confirmed in another comment to ffsears that you are studying biochemistry in California.

Good Trading to you and I am pleased you don't just use maths formulations and theory in isolation

Regards

F