Block Shrinkage Targets for Covariance Matrices Across Asset Classes

Summary

The document asks how to shrink a sample covariance matrix when a constant-correlation target is unsuitable for a portfolio containing different asset classes, such as stocks and bonds. Covariance shrinkage blends sample estimates with a structured target to make inputs to portfolio optimization more robust, while the target’s assumptions matter for assets with distinct relationships.

The reply points to research that develops a block-based shrinkage approach, where the target can represent groups of assets rather than imposing one common correlation across the whole universe. This provides a direction for finding a more general target, but the exchange does not describe the model’s construction, estimation details, or results. It cites a paper without summarizing its evidence, so readers would need to consult that work to assess when block structure is appropriate and how it performs in practice.

Key ideas

• Covariance shrinkage combines sample estimates with a structured target to support more robust portfolio optimization.
• A constant-correlation target may be inappropriate when a portfolio contains distinct asset classes.
• Block-based targets can represent different covariance structures among groups of assets.
• The exchange points to research but does not explain the method or report its performance.

Tags

# shrinking covariance matrix for assets coming from different asset class


# shrinking covariance matrix for assets coming from different asset class












From this paper: Ledoit, Olivier, and Michael Wolf. "Honey, I shrunk the sample covariance matrix." (2003).

I learned a way of shrinking the covariance matrix to get more robust portfolio optimization performance. Yet in the note #4, it says,

> The constant correlation model would not be appropriate if the assets came from different asset classes, such as stocks and bonds. But in such cases more general models for the shrinkage target are available.

Does anyone know any such "more general models"? Thanks.

## Answer by Hans-Peter Schrei (score 2)

https://quant.stackexchange.com/a/60924

In the meantime, Gianluca de Nard has published Oops! I Shrunk the Sample Covariance Matrix Again: Blockbuster Meets Shrinkage, which works out the idea eluded to in the comments explicitly.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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