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 that if there are clusters of high correlations the distributions of eigenvalues I see do not seem to follow the "MP marchenko pastur" distribution that RMT talks about. Essentially the first few eigenvalues are incredibly "high" and dwarf all the others, if I exclude these first few then it starts to look somewhat like an MP distribution.
Questions: 1) Is RMT valid if high correlations are present, or does it presume "independnet" return series.
2) Is it necessary to remove the "market" component or drop the first few eigenvalues before performing the "cleaning" procedure?
3) In general is there any guidance on using covariance shrinkage vs RMT - which works best and when for the purposes of minimum variance optimization?
Thanks very much, this is a fantastic forum.