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FAU GRADUATE SEMINAR ARCHIVE
July 2023·Friedrich-Alexander-Universität Erlangen-Nürnberg

Hierarchical Clustering & Risk Diversification in Portfolio Optimization

Machine Learning in Finance (MLFin), FAU Germany

SupervisorFAU Department of Data Science
RoleCo-Presenter & Developer
InstitutionFAU Erlangen-Nuremberg

Seminar Overview

Traditional Markowitz mean-variance portfolio optimization relies on full covariance matrix inversion, which is notorious for numerical instability and severe out-of-sample error magnification. This seminar investigated Hierarchical Risk Parity and agglomerative clustering techniques to structure multi-asset portfolios according to their underlying correlation topologies.

Clustering Formulations & Algorithmic Process

  • Hierarchical Agglomeration (AGNES): Iteratively merging asset clusters using pairwise distance metrics derived from empirical return correlation matrices.
  • Linkage Criteria Comparison: Benchmarked Single, Complete, and Ward linkage criteria for stability across historical market regimes.
  • Dendrogram Tree Partitioning: Visualizing hierarchical asset groupings and tree re-ordering to group co-dependent financial instruments without imposing rigid sector boundaries.
  • Risk Allocation: Recursively allocating portfolio weights across sub-tree clusters based on inverse variance weighting to achieve robust risk-adjusted Sharpe ratios.

Key Insights & Practical Outcomes

Hierarchical clustering structures portfolios without requiring matrix inversion, significantly improving stability against noisy covariance estimates. The risk-return profiles demonstrated superior drawdown characteristics compared to standard unconstrained quadratic optimization baselines.

Theoretical References

  • López de Prado, M. (2016). Building Diversified Portfolios that Outperform Out-of-Sample. The Journal of Portfolio Management, 42(4), 59-69.
  • Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.

Technologies & Research Topics

PythonJupyterHierarchical ClusteringAGNES / DIANAPortfolio OptimizationSharpe Ratio AnalysisDendrograms