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Old Feb 21st, 2012, 10:03 AM   #19
LivingInVol
 
 
Join Date: Mar 2010
Posts: 16
Quote:
Quote from intradaybill:

Yep, it is clear you have no clue what allocation means, that Vince did not answer your question and that you did not make your question clear but you think Vince was closer anyway.

Bye
I apologize for the initial incorrect wording of the problem and wasting your precious time. English is not my native tongue. Here is another problem for you. Who is most likely correct:

1. A poster that has over 2500 posts on ET and spends his time getting immediately annoyed and pissed at trivial things

2. A poster that obviously doesn't waste his time on message boards and has published work on the topic of discussion
    Quote
Old Feb 21st, 2012, 12:17 PM   #20
intradaybill
 
 
Join Date: Feb 2008
Posts: 2,962
Quote:
Quote from LivingInVol:

I apologize for the initial incorrect wording of the problem and wasting your precious time. English is not my native tongue. Here is another problem for you. Who is most likely correct:

1. A poster that has over 2500 posts on ET and spends his time getting immediately annoyed and pissed at trivial things

2. A poster that obviously doesn't waste his time on message boards and has published work on the topic of discussion
There is no hope for you.

Plonk
    Quote
Old Feb 26th, 2012, 02:39 PM   #21
bustermu
 
 
Join Date: Sep 2010
Posts: 6
How do we compare the performance of trading strategies each using the Kelly Investment System?

Please consider the paper by Q. J. Zhu:

http://homepages.wmich.edu/~ledyaev/eir.pdf

In the last paragraph of Section 2, Zhu proposes using the annualized return for the systems.

The above is the only paper I know of which addresses the question.

I will appreciate any references or comments.

Thanks,
Jim Murphy
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Old Feb 26th, 2012, 07:28 PM   #22
rvince99
 
 
Join Date: May 2009
Posts: 48
Hi Jim,

A couple of problems here. Equation 2.1 here is correct for determining an optimal fraction, but on the top of page 3, he tries to express it in terms of the sum of natural logs -- the two are NOT equivalent except in what I call the "special case" which is frequently seen in gambling and rarely in trading (for example, a short position is never a candidate for the special case. Similarly, any forex transaction can never be a candidate for the special case, nor can any spread transaction. By extension, those which are members of the special case, actually are themselves members of the non-special case by virtue of the fact that every transaction is, in effect, a spread transaction). Thus, for the second form of this to yield and optimal "fraction" is virtually impossible, and it is the second form of this that is the expression of the Kelly Criterion. So once again there is the false presumption that the Kelly Criterion solution results in the expected geometric growth optimal fraction of ones capital to bet asymptotically. It simply is not true.

That aside, his conclusion is interesting and very interestingly developed. I would say though, that it, as with everything looking at optimal growth fractions, misses the mark in that it assumes one's criterion is to maximize asymptotic expected geometric growth. Knowing where the peak of the curve is, as well as the nature of the curve itself -- it's important geometrical nuances, and the acceptance of the inescapable fact that we are somewhere on this curve, and likely moving about it from holding period to holding period, allows us the luxury of now seeking out algorithmic paths along this curve to satisfy other criteria. -Ralph Vince
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Old Mar 1st, 2012, 11:53 AM   #23
bustermu
 
 
Join Date: Sep 2010
Posts: 6
Ralph,

Thanks for your response. I would also like to express my appreciation to you for your work in generalizing the Kelly Criterion concept.

Quote:
Quote from rvince99:

Equation 2.1 here is correct for determining an optimal fraction, but on the top of page 4, he tries to express it in terms of the sum of natural logs -- the two are NOT equivalent except in what I call the "special case"... .
Please consider the paper by Ralph Vince, page 21, at:

http://ifta.org/public/files/journal...journal_11.pdf

The rhs of Vince Equation (1) is identical in form to the rhs of Zhu equation top of page 4. This form will be referred to as the sum of logs form.

The rhs of Vince Equation (1a) is identical in form to the rhs of Zhu Equation (2.1). This form will be referred to as the product form.

I paraphrase the statement by Vince regarding his Equation (1) and his Equation (1a):

"Rather than taking the sum of the logs of the returns, we can take the product of those returns. Thus, the value for f that maximizes (1) will also maximize (1a)."

Please notice that:

ln(product form) = sum of logs form

and:

exp(sum of logs form) = product form

Because of the strictly increasing and continuity properties of the ln and exp functions, a maximum is attained at a value of f for one of the forms if and only if a maximum is attained at that same value of f for the other form.

In light of this, it can be said that the two forms are equivalent for the purpose of finding values of f which maximize either form. I do not understand what the phrase, “the two are NOT equivalent”, was intended to convey. Any enlightenment would be appreciated.

Thanks,
Jim Murphy
    Quote
Old Mar 1st, 2012, 03:24 PM   #24
rvince99
 
 
Join Date: May 2009
Posts: 48
Jim,

You're absolutely right! Where you say:

<< The rhs of Vince Equation (1a) is identical in form to the rhs of Zhu Equation (2.1). This form will be referred to as the product form. >>

I had mistakenly took Zhu's equation (2.1) to be my equation (2) from my paper, when in fact it is (1a) from my paper.

I apologize for the confusion, and appreciate your pointing this out. I'm at the age where I shouldn't do anything after about 3 p.m. that requires any thinking! -Ralph Vince
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