Anyone interested in random matrix theory?
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...).
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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
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