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.