Anyone interested in random matrix theory?

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...).

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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