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Covariance, Correlation, and RMT

June 5, 2011

As previously exemplified by basket prediction, Quantivity is finding increasingly frequent use of random matrix theory (RMT), particularly in context of portfolio / basket covariance and correlation analysis across all trading frequencies. Although undoubtedly an exaggeration, RMT is beginning to feel like PCA did in the 1990s.

Below is a survey of RMT literature to whet readers’ appetite. Readers are requested to suggest additional relevant literature in comments. Subsequent posts may delve into more details on practical use of RMT, pending reader interest.

To begin, the following are modern book-length treatments of RMT:

The following are extended survey articles (focused on theory and numerical analysis, respectively), available online:

The following are applied RMT articles, in published chronological order:

These articles nicely illustrate the evolution in application of RMT, both in breadth and sophistication, over the past decade.

2 Comments leave one →
  1. John Hall permalink
    June 6, 2011 9:56 am

    I currently learning about RMT and finding it very useful. I had read a few of these before, but this is a great resource to help direct some of my future research.

    I have not yet seen a practical guide to RMT written, so I will be interested in your take on it.

    In most things I have looked at, they are looking at a bunch of stocks and cleaning all the eigenvalues below some maximum. I had been working with a sample that had one very low-volatility asset and when I tried to do the same procedure I got forecasts for this one asset that made no sense (I ultimately just estimated this one separately). When I actually read more about RMT, it turns about that there are bounds where between them you can call them noise, not just some maximum. In practice, it would make sense for a bunch of stocks to only take the larger eigenvalues as factors and clean the rest, but in a diverse set of assets, one should be more careful.

  2. June 9, 2011 3:43 pm

    I wonder how did the PCA feel in the 90’s ???

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