Applying Covariance Shrinkage to Black–Litterman Portfolios

Summary

The document asks where covariance shrinkage belongs in a Black–Litterman workflow: on the covariance input used to estimate posterior returns and risk, or on the posterior covariance after running the model. The accepted response recommends estimating the Black–Litterman covariance matrix that incorporates investor views with a shrinkage estimator.

The response names Ledoit–Wolf shrinkage and also points to random matrix theory methods, including denoising or detoning, and nested clustered optimization as alternatives. It offers a recommendation rather than comparative evidence: no portfolio data, tests, or criteria are supplied to establish when one method outperforms another. The practical takeaway is to consider covariance estimation in the view-adjusted Black–Litterman output, while treating the suggested alternatives as claims that require validation for the investor’s assets, views, and optimization objective.

Key ideas

• The question is whether to shrink Black–Litterman inputs or its posterior covariance.
• The accepted answer recommends estimating the view-adjusted Black–Litterman covariance with shrinkage.
• The response also mentions random matrix theory denoising and detoning, and nested clustered optimization.
• No empirical comparison is provided to verify the stated ranking of methods.

Tags

# Covariance Shrinkage in Black-Litterman Framework


# Covariance Shrinkage in Black-Litterman Framework












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 by develarist (score 2, accepted)

https://quant.stackexchange.com/a/55453

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.