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

[Aaron Katz]

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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