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Stock returns correlation matrices are notoriously hard to estimate, especially when the number of assets $N$ is large with respect to the size of the readily available historical returns $T$. Many methods exist to ease the estimation (and work-around the problem's ill-posedness).

I wondered if anyone tried to implement the unbiased version of the Rotational Invariant correlation matrix Estimator (RIE) described in this paper.

I've written some python code to test it and it does not seem to offer a significant advantage over the standard sample estimator of the correlation matrix.

I've already checked my code several time so I'd be interested to know if someone managed to implement it adequately (I don't need the code, just to know whether there is a typo in the paper for instance).

Thanks a lot already.

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  • $\begingroup$ I am seeing similar results, and am wondering if perhaps I am misinterpreting something or if there is a typo in the paper etc. Do you have python code that you would like to share to compare notes. I'm happy to provide R code. $\endgroup$
    – user30925
    Commented Dec 9, 2017 at 21:06
  • $\begingroup$ @user30925, could you please provide your R code? $\endgroup$
    – Nick
    Commented Dec 13, 2017 at 0:17
  • $\begingroup$ Are you using it to estimate the covariance matrix or for Markovitz allocation? For estimating the covariance matrix, the naive estimator is better as it is unbiased. $\endgroup$
    – Borun Chowdhury
    Commented Jan 9, 2018 at 17:18
  • $\begingroup$ I reach the same results. @user30925, could you please provide your R code? Thanks in advance $\endgroup$
    – Nathan Raffy
    Commented Jan 16, 2018 at 8:55
  • $\begingroup$ I implemented and am testing it. Does the "cleaned" matrix have 1's in the diagonal for you? Looking at the paper it looks to me like there's no reason to think it should (and reasons to think it shouldn't, but I want to confirm). The estimator doesn't preserve the sum of the eigenvalues. Hard to check that from eq 7 in the paper, but in eq 10 you multiply by max(1, ...), so either one or both won't preserve the trace. So it begs the question: if this produces a cleaned correlation matrix that is no longer a correlation matrix, how do you use it? $\endgroup$
    – Marses
    Commented Mar 8, 2023 at 10:03

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