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27
votes
5answers
3k views

Random matrix theory (RMT) in finance

The new kid on the block in finance seems to be random matrix theory. Although RMT as a theory is not so new (about 50 years) and was first used in quantum mechanics it being used in finance is a ...
15
votes
2answers
2k views

Cleansing covariance matrices via Random matrix theory

I am exploring de-noising and cleansing of covariance matrices via Random Matrix Theory. RMT is a competitor to shrinkage methods of covariance estimation. There are various methods expressed usually ...
12
votes
3answers
768 views

What are some research articles on using principle components to generate alpha?

Here's an example by Marco Avellenada from NYU titled "Statistical Arbitrage in the U.S. Equities Market". The idea of this paper involves capturing mean reversion in the residual returns of a ...
9
votes
1answer
728 views

One dimensional analog of cleansing a correlation matrix via random matrix theory

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. These are then ...
8
votes
3answers
851 views

Does random matrix theory (RMT) for returns' correlation matrices apply if there are high correlations?

Steps to replicate: Take the correlation matrix of a sample of stocks in the SP500, or a set of ETF's that are include some that are highly correlated (0.7 and above). Problem observed: I observe ...
8
votes
4answers
592 views

How to treat large (5K-10K) non-positive-definite (particularly near-singular) covariance matrices for Cholesky decomposition?

I have a very large covariance matrix (around 10000x10000) of returns, which is constructed using a sample size of 1000 for 10000 variables. My goal is to perform a (good-looking) Cholesky ...
5
votes
1answer
292 views

RMT (Random Matrix Theory) issue with callibrating MP distribution -

I am seeing an issue when callibrating an MP distribution. Assume a log return series for the SP500 with the following dimensions dim(xts.sp500.ret.stocksonly) ==> [1] 1133 478 ...
1
vote
1answer
50 views

What does each bar in the empirical average eigenvalues spectrum of the correlation matrix of log-returns of stocks represent?

An example diagram, taken from this paper, looks like follows: What is its physical interpretation? The highest eigenvalue, the paper says, represents market mode. So, what does the difference in ...
1
vote
0answers
49 views

Marchenko–Pastur, Student distribution and returns

I have a question regarding random matrix theory. I've been studying various papers and I found some confusing definitions of Marchenko-Pastur law. The most clear was the one on wiki: wiki-Pastur-...
0
votes
0answers
52 views

Physical interpretation of variance in returns in a portfolio design

I have a downloaded the log-returns at successive times of 98 stocks from S&P index over 753 days. I calculated the total daily return according to the formula 1 below, where ...
0
votes
0answers
37 views

Exponentially weighted random matrix - which variance should I use?

I am currently playing around with exponentially weighted correlation matrices and filtering based on Random Matrix Theory. However, there is one thing I am not really sure about: In the equation ...