I came across this passage in a book about PCA and denoising of Markowitz:
But eigenvalues that are important from risk perspective are least important ones from portfolio optimization perspective. Information matrix mixes the returns and has Reciprocal values 1/λ k of the eigenvalues of the covariance matrix λ . This is one reason why portfolio managers often do not use portfolio optimization methods.
What I understand is that the eigenvalues of the covariance matrix contribute the most to the risk in the portfolio (i.e. large eigenvalues correspond to asset with high variances and covariances). But why is that problematic in the information matrix, which mixes the returns in the Markowitz solution?
I mean why would we not consider it a good thing, if the largest eigenvalues of the covariance matrix become the smallest eigenvalue in the information matrix? From my understanding, this would mean that we don't give them too much weight and we therefore avoid heavy correlations? But it's obviously the other way round.