# Tag Info

18

Google for this paper "Financial applications of random matrix theory: Old laces and new piece" from Marc Potters, Jean-Philippe Bouchaud, and Laurent Laloux. You can also check Prof. Gatheral presentation about Random Matrix Theory http://www.math.nyu.edu/fellows_fin_math/gatheral/RandomMatrixCovariance2008.pdf In R, the package "tawny" has an ...

13

Check out page 55 in "Quantitative Equity Investing: Techniques and Strategies," Fabozzi et al. Section is titled "Random Matrix Theory" - very intro. The context pertains to the estimation of a large covariance matrix. Also, see work at Capital Fund Management, filed under: Random Matrix and Finance : correlations and portfolio optimisation

8

This is a misunderstanding of how to apply RMT theory. The point of the MP distribution is to describe the expected distribution of eigenvalues assuming a symmetric matrix whose elements are drawn from a normal distribution of mean zero and some sigma. So if you observe eigenvalues beyond the level predicted by MP this means you have found factors that are ...

8

This is correct: "The general idea of cleansing a correlation matrix via random matrix theory is to compare its eigenvalues to that of a random one to see which parts of it are beyond normal randomness." This is not correct: "These are then filtered out and one is left with the non-random parts." The term "filtering", although used extensively in the ...

7

Attilio Meucci does some very interesting things with PCA. See e.g. his paper on managing diversification which makes heavy use of it (and explains it very intuitively along the way): Managing Diversification by Attilio Meucci

7

Regarding the optimization question: I haven't compared random matrix estimates to shrinkage estimates, but shrinkage seems to beat (statistical) factor models -- see a series of blog posts at http://www.portfolioprobe.com/tag/ledoit-wolf-shrinkage/ However, my guess is that random matrix estimates behave a lot like factor models, and hence that shrinkage ...

4

I tested both procedures. The results are virtually indistinguishable - the decision is not consequential. I opted for approach #1.

4

I'll throw this in as an "application of RMT" ... EDHEC and FTSE use RMT to decide the optimal number of principal components in their covariance estimation procedure for which they use PCA (Principal Component Analysis). For details look here or here in Appendix C section 4 for details.

3

If you know R; here is a very good tutorial with practical examples: http://zoonek2.free.fr/UNIX/48_R/05.html

3

Beware that the assumptions usually made are not consistent with the practical applications, especially when heavy tails are considered. For the extension to a more realistic setting see this nice paper.

2

Look at randommatrixportfolios.com

2

The plot function is smoothing the plot. You should show the distribution of eigenvalues via a bar chart. Because a bar chart is discrete you can better discern the separation of the top-most eigenvaules. The top-most eigenvalue (representing the market factor) should be substantially greater than bulk of the eigenvalue distribution. I assume by "...

2

Let $t$ be the number of days (time periods), and let $p$ be the number of assets. You have $t=1000$ and $p=10000$. For any given dataset, it is assumed that the sample covariance matrix $\mathbf{C}$ accurately represents the population covariance matrix $\boldsymbol{\Sigma}$, however, as $p \rightarrow t$ or if $p > t$ (as in your case), the ...

2

I think that your problem can be solves by using another estimator for your covariance matrix. A so called shrinkage estimator leads to covariance matrix that is non-singular. Then a Cholesky decomposition should work (maybe there is even a short-cut in the shrinkage world, I will check alter on). The R package corpcor contains functions to perform ...

1

Your issue demonstrated in R with interesting solution Equity Risk Model Using PCA. Another useful link in Matlab by Nick Higham himself NCM implementation by Nick Higham written for Matlab. Another good discussion on shrinkage and other aspects of Correlation Adjustment

1

From LEP's answer: there will be p−t zero eigenvalues whenever p>t and one zero eigenvalue whenever p=t. This is the main reason, your true covariance matrix will have p-t eigenvalues exactly 0. With computer arithmetic you'll have lots of eigenvalues around machine precision, usually about 10^-15. So there should not only be around 5K-6K zero ...

1

The Systematic Investor has a series of articles on using PCA and clustering to improve on traditional Risk Parity approaches. The series of posts start here: http://systematicinvestor.wordpress.com/2012/12/22/visualizing-principal-components/

1

There seem to be natural clusters like different sectors/industries, so maybe you could make clusterization of the correlation matrix. This is a very interesting paper about sector rotation and clusterization of stock market time-series.

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