[R-SIG-Finance] Anyone interested in random matrix theory?

[Brian Lee Yung Rowe]

Hi All,

There has been more interest in this than I was expecting, so I will
indeed be packaging this up and sharing with the community. Hopefully
the initial release will meet the high expectations of the community! I
will send out more when it is available.

Brian


On Wed, 2008-12-10 at 13:29 -0500, Aaron Katz wrote:
> Sounds fascinating, actually.  I can't speak for the maintainers of Rmetrics, etc. but it seems to me that having more quality code out there is available.  Especially stuff that gets at real-world problems and improves on the stylized models of classical finance ("Modern" Portfolio theory if you will...).
> 
> ---
> Aaron Katz
> Bendheim Center for Finance
> Princeton University
> 
> 
> On Tue 09/12/08  9:58 PM , Brian Lee Yung Rowe <brian at muxspace.com> wrote:
> 
> > Hi,
> > Is anyone interested in portfolio optimization based on random
> > matrix
> > theory? I am considering packaging some code I wrote that filters
> > portfolio correlation matrices based on random matrix theory. The
> > basic
> > idea is that there is a predictable eigenvalue distribution for a
> > random
> > matrix and based on that you can take a custom returns correlation
> > matrix, fit the eigenvalue distribution to the theoretical
> > distribution
> > (based on Marcenko-Pastur) and then filter out those eigenvalues.
> > You
> > can then reconstruct the correlation matrix, which in theory has
> > more
> > signal to noise than you would get otherwise. 
> > >From my initial tests, when optimizing a portfolio using the
> > cleaned
> > correlation matrix, you do get lower risk (and better Sharpe ratio)
> > than
> > you would with an equal weighted portfolio or a portfolio optimized
> > using a multi-factor model. 
> > What is really interesting about random matrix theory is that the
> > fit to
> > the Marcenko-Pastur theoretical distribution is quite resilient and
> > can
> > handle small portfolios with a short window. This addresses one of
> > my
> > biggest gripes I have regarding the Barra approach, that you need to
> > have so much data and the response is somewhat slow due to the long
> > windows in the regressions.
> > Anyway, I am considering packaging this code, but prior to doing so
> > wanted to get a sense if anybody has done this (cheap searches say
> > no)
> > and if anyone is interested in RMT to make it worthwhile.
> > Regards,
> > Brian
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