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## Re: New Markowitz / Matlab

 From: Vic Norton Subject: Re: New Markowitz / Matlab Date: Mon, 12 Jan 2015 13:52:19 -0500

On Jan 12, 2015, at 12:08 PM, Julien Bect <address@hidden> wrote:

> Le 12/01/2015 15:57, Vic Norton a écrit :
>> On Jan 12, 2015, at 8:00 AM, Vic Norton<address@hidden>  wrote:
>>> >We do not have access to Matlab, but we would be very much interested in
>>> >how it performs on our data. Our package (with data) is available for
>>> >testing at
>>> >  http://vic.norton.name/finance-math/newmarkowitz-tests.tar.gz
>>> >Any information on Matlab performance would be greatly appreciated.
>
> Hello Vic,
>
> Which script would you like me to run in Matlab ? meanvariance_tests.m ?
>
> @++
> Julien

Hi Julien,

Both scripts are to be run in Octave--after the New Markowitz package has been
installed. They are for illustration.

However, the computation
[E, F, f0] = rtndecomp(R0,0, pput);  # pput = 252 market days per year
in "meanvariance_tests.m" should produce an
AssetMean: E
and
AssetCovar: V = f0 ^2 + F' * F
that can be used in some Matlab function to produce efficient portfolios.

I don't own Matlab. I don't know what the appropriate Matlab function is.
However MathWorks help at

http://www.mathworks.com/help/finance/mean-variance-portfolio-optimization.html
implies that such a function exists.

Such a Matlab function, call it
P = matlabEVtoP(E, V),
would have to produce a matrix of portfolios P (from our E and V) comparable to
our
P = minnormy(F).
With Matlab's P you could compute an efficient 15% return portfolio. How does
this portfolio compare with our efficient 15% return portfolio pX0? That's an
interesting question. I expect Matlabs portfolio to be close, but it might be
somewhat off due to the use of the poorly conditioned covariance matrix V in P
= matlabEVtoP(E, V).

I'm also interested in computation times. How does Matlab's
P = matlabEVtoP(E, V)
compare in speed with our combination
[E, F, f0] = rtndecomp(R0, 0, pput),
P = minnormy(F).
I expect our two functions will be significantly faster than Matlab's one, but
that's just a guess.

I appreciate your help, Julien, but don't waste a lot of time on this. I'm
quite sure that what I am doing compares favorably with anything Matlab has
got. In any case I hope to have my work completely written up before long.

Regards,

Vic