Clustering Assets for Cardinality-Limited Portfolio Optimization

Summary

The document describes a portfolio construction problem in which an optimizer can process at most a fixed number of assets at once, while the full investment universe is larger. The proposed workflow is to divide the assets into groups no larger than the optimizer's limit and optimize each group separately. The author asks how to form such groups and whether there is a way to optimize across the full universe despite the per-run asset limit.

Sector or geographic grouping and constrained k-means are mentioned as possible clustering approaches, but no method is developed or compared. The text provides no portfolio results, objective function, or evidence about how clustering affects diversification or optimal weights. It therefore frames a useful computational and portfolio-design challenge while leaving the choice of clustering method and the integration of group-level portfolios unresolved.

Key ideas

• The optimizer has a maximum number of assets it can handle in one portfolio.
• The proposed workaround is to partition the full asset universe into groups within that limit.
• Sector and geographic grouping, along with constrained k-means, are mentioned as candidate approaches.
• The document asks how to cluster assets or optimize the full universe but does not recommend a solution.
• Separate optimization of groups may leave the combined portfolio design question unresolved.

Tags

# Subportfolio optimisation and asset clustering with maximum cluster cardinality constraint


# Subportfolio optimisation and asset clustering with maximum cluster cardinality constraint












Assume that $N \in \mathbb{N}$ assets are given, but the portfolio optimisation algorithm can only compute portfolios with $m<N$ assets. To compute a portfolio, I would like to cluster the $N$ assets into groups containing at most $m$ assets, and apply the portfolio optimisation algorithm to each group separately.

I could only find simple sectorial or geographical clustering as well as constrained k-means algorithm as clustering methods. How could assets be clustered into groups with a maximum cardinality constrained?

Is there some other approach to compute a portfolio for the $N$ assets with the portfolio optimisation algorithm which can only deal with $m$ assets at a time?

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