Covariance Shrinkage in Black-Litterman Framework

Question

Good evening guys

I am looking into the effects of covariance shrinkage on the diversification of asset weights for different portfolio optimisations. Initially, I was interested to see how it affects classic mean-variance, but I now digged into risk-parity and Black-Litterman.

Long story short: where should I apply the shrinkage in the case of Black-Litterman? I would assume to shrink the covariance matrix that goes into the Black-Litterman model in order to get mu_BL and sigma_BL. Alternatively, I thought I could run BL without any shrinkage, and then shrink the resulting sigma_BL? Does anybody have a view on this?

Otherwise, I wish you a happy weekend (and happy July 4th for the American friends).

Cheers, Rsky

Answer 1

Yes all you have to do is estimate the Black Litterman covariance matrix that includes investor views using a shrinkage estimator. Covariance shrinkage like Ledoit Wolf is an old technique, however, that has been outperformed by the denoised or detoned covariance matrix estimated by random matrix theory, as well as the nested clustered optimization (NCO) portfolio which takes into account intracluster and intercluster correlations.