Hierarchical Risk Parity (López de Prado)
Portfolio construction that uses a hierarchical clustering of assets to allocate risk more evenly and robustly.
Definition
Hierarchical Risk Parity (HRP), introduced by Marcos López de Prado, builds a portfolio by (1) clustering assets based on correlation/distance, (2) building a hierarchical tree (dendrogram), and (3) recursively allocating risk so that clusters at each level receive equal risk contribution. The result is diversification that respects the correlation structure without inverting the full covariance matrix.
Why it matters
- Robustness: Does not require inverting the covariance matrix; more stable when the matrix is singular or noisy.
- Structure-aware: Uses the hierarchy of correlations (e.g. sectors, sub-sectors) to diversify across and within clusters.
- Risk balance: Aims for more even risk contribution across assets than naive equal weight or mean–variance.
Key steps (simplified)
- Compute distance matrix from correlations (e.g. 1 − |ρ| or similar).
- Cluster assets (e.g. hierarchical clustering); form dendrogram.
- Bisect the tree recursively; at each split, assign inverse-variance weights within each cluster so that risk is balanced.
- Combine cluster weights to get final portfolio weights.
Limitations
- Depends on the clustering method and distance definition.
- Does not explicitly incorporate expected returns; purely risk-based.
- Backtest and live results depend on the stability of the correlation structure.
Linked concepts
Risk parity, MPT, correlation clustering, position sizing.