This is more of a theoretical question.
I have been working on some mean-variance / Black-Litterman models and played around with Ledoit/Wolf's covariance shrinkage method (sklearn function in Python). If I shrink the covariance matrix for mean variance portfolios, I get really nice portfolios along the efficient frontier (except for corner solutions), and the same goes for Black-Litterman.
Since I am comparing mean-variance and Black-Litterman portfolios to 1/N and Risk Parity allocations, I thought let's just feed the shrunk covariance matrix into the risk-parity optimizer. What happens is that I now get equal weights for all assets (in Risk Parity). I guess that is because the covariance matrix was shrunk to the extent that the differences in covariances are now too insignificant, and hence I get equal weights?
Did anybody run into this issue, or can anybody confirm my simple assumption is the reason for this? I am just playing a bit around but found this quite interesting. Made me question a bit whether it makes much sense to apply shrinkage to mean-variance and Black-Litterman in the first place.
Cheers, have a good week guys. RSK