Central Limit Theorem & Trading

K-Pia

K-Pia

I know it's a concept describing diversification.
The more diversified the portfolio, the more probable the return of being mediocre.
Sounds not sexy at all ... Right. But we talk more about risks than returns here.

As day traders. We take trades instead of securities as inputs.
We set the Min and the Max of our range to define the sample space.
Let it be Max Loss and the Current or Expected Max Reward then populate.
According to Max Entropy principle I'll set P(Outcome)=1/n or Equiprobability.

I've set Min(-5) & Max(2)
Here is a distribution of multiple totals of 100 consecutives trades :
-5.2.jpg

I've set Min(-5) & Max(5)
Here is a distribution of multiple totals of 100 consecutives trades :
-5.5.jpg

I've set Min(-2) & Max(5)
Here is a distribution of multiple totals of 100 consecutives trades :
-2.5.jpg


Uh ... What do you think about that ?
For R:R > 0 the distribution shows NO negative sum.
So ... Why do so many traders can fail knowing this fact ?!

Actually.. Does the shape of your own distribution looks normal ?
 
Last edited:
The more your portfolio is diversified, the closer your return seems to be Normal-shape, I agree.

Although return might be NOT good enough in short-term, your return SHOULD be more secure.

Furthermore, instead of Normal-shape, it may be Log-Normal, if I heard correctly.
 
Sergio77 said:
R:R does not determine P/L. You also need sufficient hit rate.
More...

R:R (Sample Space) & Frequency.
That's true equiprobability is a blind assumption.

jk90029 said:
The more your portfolio is diversified, the closer your return seems to be Normal-shape, I agree.

Although return might be NOT good enough in short-term, your return SHOULD be more secure.

Furthermore, instead of Normal-shape, it may be Log-Normal, if I heard correctly.
More...

What do you mean in your second paragraph?

Markets are said to be Log-Normal.
PnL is a different story.

However I am not saying PnL is Gaussian.
CLT can work under different probability distribution.
It needs to be a sum of multiple random process,
With them having a finite mean & variance.



I remember having read Taleb talking about that.
He said it applies to market maker. But not to speculators.
Speculators go to Ruin at the limit whereas MM converge toward CLT.
 
K-Pia said:
R:R (Sample Space) & Frequency.
That's true equiprobability is a blind assumption.



What do you mean in your second paragraph?

Markets are said to be Log-Normal.
PnL is a different story.

However I am not saying PnL is Gaussian.
CLT can work under different probability distribution.
It needs to be a sum of multiple random process,
With them having a finite mean & variance.
More...

I agree that CLT is powerful, since "CLT can work under different probability distribution."

BTW, what do you mean by "second paragraph"?
 
jk90029 said:
I agree that CLT is powerful, since "CLT can work under different probability distribution."

BTW, what do you mean by "second paragraph"?
More...

You said :
Although return might be NOT good enough in short-term, your return SHOULD be more secure.

And I don't really get it ^^
Why did you told me that ? And what do you mean by secure ?
 
K-Pia said:
You said :
Although return might be NOT good enough in short-term, your return SHOULD be more secure.

And I don't really get it ^^
Why did you told me that ? And what do you mean by secure ?
More...


I just mean that 10 pieces of portfolio (at one time) may NOT be enough to follow population (index change), at least 30 pieces might be preferable.

Also, 3 years of return rate (profit curve) may be TOO short for any conclusion.... Prabably at least 10 years of return is meaningful(significant).
 
You must log in or register to reply here.
Back
Top