Nested Cluster Methods for Portfolio Construction

Nested cluster optimization reduces a large allocation problem into within-cluster and between-cluster steps. The notebooks examine conditioning, denoising, exposure constraints, and the resulting allocation error.

The central relation

Covariance sensitivity is summarized by the spectral condition number

\kappa_2(\Sigma)=\frac{\lambda_{\max}(\Sigma)}{\lambda_{\min}(\Sigma)}.

$\Sigma$ is a positive-definite covariance matrix. Its largest and smallest eigenvalues are $\lambda_{\max}$ and $\lambda_{\min}$ . A large ratio indicates that inversion can magnify small input changes.

Building portfolios through nested clusters

The weight plot separates within-cluster allocations from the final portfolio. The rolling public comparison shows how NCO behaves beside benchmark methods.

Between-cluster weights and final asset weights produced by nested cluster optimization. — The final allocation combines a decision inside each cluster with a second decision across cluster portfolios.

Rolling public-data risk and allocation comparison for nested cluster optimization. — The rolling result evaluates allocations fitted on earlier returns and reports their later risk and stability on common windows.

Breaking the problem into clusters can reduce estimation error, but it also makes the clustering rule and cluster stability part of the portfolio result.

Notebooks


1. Optimizing within clusters before combining them
2. Nested Clustered Optimization under Estimation Error
3. Building a constrained hedge