Reducing Asset Covariance to Cluster-Level Returns

Summary

The document asks how to reduce a covariance matrix for 100 stocks to a five-by-five matrix after grouping the stocks into five clusters. The intended use is a two-stage asset allocation process: first allocate across clustered returns, then perform a quadratic optimization to minimize portfolio variance using the reduced covariance matrix.

The question specifically concerns the covariance of weighted cluster means, but it does not provide an answer, formula, weights, or details about how the clusters are formed. Consequently, it identifies the portfolio-construction problem without specifying a reduction method. Any practical calculation would depend on how each cluster return is defined, including its constituent asset weights, and on the covariance estimates for the underlying returns. The text offers no data or comparison of possible choices, so it serves as a prompt for deriving the cluster-level risk representation rather than evidence for a particular allocation technique.

Key ideas

• The author wants to map a 100-asset covariance matrix to a five-cluster covariance matrix.
• The proposed workflow allocates across clusters before running a variance-minimizing quadratic optimization.
• The target matrix is intended to represent weighted cluster returns.
• The document does not specify cluster weights or provide a covariance-reduction formula.
• The appropriate calculation depends on how each cluster return is constructed.

Tags

# How to reduce a covariance matrix after clustering?


# How to reduce a covariance matrix after clustering?












I have an `N = 100` covariance matrix. I am clustering the covariance matrix say into `5 clusters`.

How can I compute the reduced covariance matrix of weighted cluster means which has `dimension = 5x5`?

In particular, I am working on an algorithm for financial asset allocation. This algorithm first performs an allocation on clustered returns. Initially, I have 100 stocks to allocate, but after this step, I am left with only 5 clusters. In the second and last step of the allocation, I would like to run a quadratic optimization that minimizes the portfolio variance. Nevertheless, for doing so, I would need to reduce the covariance matrix to a dimension equal to the number of clusters.

Any hint on how to achieve this?

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