What Is Hierarchical Risk Parity?
In quantitative finance and portfolio construction, Hierarchical Risk Parity (HRP) is a portfolio optimization that aims to allocate risk more effectively across assets compared to traditional methods like mean-variance optimisation.
Developed by Marcos López de Prado, HRP leverages the hierarchical structure of asset correlations to create diversified portfolios that are less sensitive to estimation errors in expected returns and covariance matrices.
Key Concept
HRP focuses on risk allocation rather than capital allocation alone. It uses the correlation structure of assets to group them into clusters and then allocates risk (typically measured as variance or volatility) across these clusters in a balanced way. Unlike traditional methods that rely heavily on precise estimates of expected returns (which are notoriously hard to predict), HRP primarily depends on the covariance matrix, which is relatively more stable.
Steps in HRP
- Hierarchical Clustering:
Start with the correlation matrix of asset returns.
Use a clustering algorithm (often based on a distance metric derived from correlations) to group assets into a hierarchical tree (dendrogram). Assets with similar behavior (high correlation) are clustered together, while dissimilar assets are separated.
This process doesn’t require predefined clusters—it dynamically identifies relationships based on the data.
- Recursive Bisection:
The hierarchical tree is split recursively into smaller sub-clusters.
At each split, the algorithm calculates the total risk (variance) of the portfolio and allocates it inversely proportional to the risk contribution of each sub-cluster. This ensures that riskier clusters receive less weight.
- Weight Allocation:
Portfolio weights are assigned at the asset level by propagating the risk allocations back through the hierarchy.
The result is a set of weights where risk is distributed more evenly across the portfolio, avoiding over-concentration in any single asset or group of assets.
Advantages of HRP
Robustness: It reduces reliance on fragile inputs like expected returns, focusing instead on the covariance structure, which is easier to estimate accurately.
Diversification: By balancing risk across clusters, HRP avoids the extreme concentration often seen in mean-variance optimisation (e.g., putting all weight in a few assets).
No Matrix Inversion: Unlike Markowitz’s mean-variance optimization, HRP doesn’t require inverting the covariance matrix, which can be unstable when assets are highly correlated or the matrix is ill-conditioned.
Intuitive: The hierarchical structure reflects natural groupings in the market (e.g., sectors, asset classes), making it easier to interpret.
Limitations
Correlation Focus: HRP assumes the correlation matrix is a good representation of risk relationships, but this may not always hold (e.g., during market crises when correlations spike).
No Return Optimization: It doesn’t explicitly maximize expected returns, which might be a drawback for investors with strong views on future performance.
Complexity: The clustering and recursive process can be computationally intensive for very large portfolios.
Example
Imagine a portfolio with stocks from tech (highly correlated within the sector) and bonds (less correlated with stocks). HRP would:
Cluster tech stocks together and bonds separately based on their correlation patterns.
Allocate risk between the tech cluster and bond cluster, ensuring neither dominates the portfolio’s risk profile.
Assign weights to individual assets within each cluster, balancing their contributions.
In practice, if tech stocks are volatile, HRP might give them a lower total weight compared to a naive equal-weight approach, but it would still diversify within the tech cluster to avoid over-reliance on a single stock.
Comparison to Other Methods
Equal Weighting: Simpler but ignores risk and correlation.
Mean-Variance Optimisation: Optimises for return and risk but is sensitive to input errors.
Risk Parity: Allocates risk equally across assets but doesn’t account for hierarchical relationships like HRP does.
HRP strikes a balance—it’s more sophisticated than basic risk parity and more practical than mean-variance optimization, making it popular in modern portfolio management, especially for large, complex portfolios.
See also