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

[Lezmi Edmond]

Hi Brian
I think that it is a very good idea, you can take a look at 

http://www.qgroup.org.au/SFMW/RaisePartner_Qgroup.pdf which gives an interesting application of RMT and why it is powerful

Regards
Edmond

Edmond Lezmi
Credit Agricole Asset Management Alternative Investments
tel: 33 (1) 43 23 02 86
mail:edmond.lezmi at caam-ai.com


-----Message d'origine-----
De : r-sig-finance-bounces at stat.math.ethz.ch [mailto:r-sig-finance-bounces at stat.math.ethz.ch] De la part de Brian Lee Yung Rowe
Envoyé : mercredi 10 décembre 2008 03:59
À : r-sig-finance
Objet : [R-SIG-Finance] Anyone interested in random matrix theory?

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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