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Hierarchical Risk Parity (HRP) is an advanced portfolio optimization framework developed in 2016 to compete with the prevailing mean-variance optimization (MVO) framework developed by Harry Markowitz in 1952, and for which he received the Nobel Prize in economic sciences.[1] HRP algorithms apply machine learning techniques to create diversified and robust investment portfolios that outperform MVO methods out-of-sample.[2] HRP aims to address the limitations of traditional portfolio construction methods, particularly when dealing with highly correlated assets.[3] Following its publication, HRP has been implemented in numerous open-source libraries, and received multiple extensions.[4][5][6][7][8]
Key Features of HRP
[edit]Algorithms within the HRP framework are characterized by the following features:
- Machine Learning Approach: HRP employs hierarchical clustering, a machine learning technique, to group similar assets based on their correlations.[2][9] This allows the algorithm to identify the underlying hierarchical structure of the portfolio, and avoid that errors spread through the entire network.
- Risk-Based Allocation: The algorithm allocates capital based on risk, ensuring that assets only compete with similar assets for representation in the portfolio.[4] This approach leads to better diversification across different risk sources, while avoiding the instability associated with noisy returns estimates.
- Covariance Matrix Handling: Unlike traditional methods like Mean-Variance Optimization, HRP does not require inverting the covariance matrix.[3] This makes it more stable and applicable to portfolios with a large number of assets, particularly when the covariance matrix's condition number is high.
HRP Algorithm Steps
[edit]The HRP algorithm typically consists of three main steps:[10]
- Hierarchical Clustering: Assets are grouped into clusters based on their correlations, forming a hierarchical tree structure.
- Quasi-Diagonalization: The correlation matrix is reordered based on the clustering results, revealing a block diagonal structure.
- Recursive Bisection: Weights are assigned to assets through a top-down approach, splitting the portfolio into smaller sub-portfolios and allocating capital based on inverse variance.
Advantages of HRP
[edit]HRP algorithms offer several advantages over the (at the time) MVO state-of-the-art methods:
- Improved diversification: HRP creates portfolios that are well-diversified across different risk sources.[1]
- Robustness: The algorithm has shown to generate portfolios with robust out-of-sample properties.[3][11]
- Flexibility: HRP can handle singular covariance matrices and incorporate various constraints.[2]
- Intuitive approach: The clustering-based method provides an intuitive understanding of the portfolio structure.[2]
By combining elements of machine learning, risk parity, and traditional portfolio theory, HRP offers a sophisticated approach to portfolio construction that aims to overcome the limitations of conventional methods.
References
[edit]- ^ López de Prado, Marcos (2016-05-31). "Building Diversified Portfolios that Outperform Out of Sample". The Journal of Portfolio Management. 42 (4): 59–69. doi:10.3905/jpm.2016.42.4.059. ISSN 0095-4918.
- ^ a b c R, Roman (2021-09-07). "Hierarchical Risk Parity: Introducing Graph Theory and Machine Learning in Portfolio Optimizer". Portfolio Optimizer. Retrieved 2024-12-22.
- ^ a b c Palit, Debjani; Prybutok, Victor R. (2024-09-15). "A Study of Hierarchical Risk Parity in Portfolio Construction". Journal of Economic Analysis. 3 (3): 106–125. doi:10.58567/jea03030006. ISSN 2811-0943.
- ^ a b "Hierarchical Risk Parity on RAPIDS: An ML Approach to Portfolio Allocation". NVIDIA Technical Blog. 2022-04-20. Retrieved 2024-12-22.
- ^ "Create Hierarchical Risk Parity Portfolio - MATLAB & Simulink Example". www.mathworks.com. Archived from the original on 2023-05-22. Retrieved 2024-12-22.
{{cite web}}: line feed character in|title=at position 42 (help) - ^ Vyas, Aditya (2020-01-13). "The Hierarchical Risk Parity Algorithm: An Introduction". Hudson & Thames. Retrieved 2024-12-22.
- ^ Vyas, Aditya (2020-06-22). "Portfolio Optimisation with PortfolioLab: Hierarchical Risk Parity". Hudson & Thames. Retrieved 2024-12-22.
- ^ Microprediction (2022-11-22). "Schur Complementary Portfolios — A Unification of Machine Learning and Optimization-Based…". Medium. Archived from the original on 2024-07-25. Retrieved 2024-12-22.
- ^ "Create a Portfolio with Hierarchical Risk Parity | Quantra Classroom". www.linkedin.com. Retrieved 2024-12-22.
- ^ López de Prado, Marcos (2016-05-31). "Building Diversified Portfolios that Outperform Out of Sample". The Journal of Portfolio Management. 42 (4): 59–69. doi:10.3905/jpm.2016.42.4.059. ISSN 0095-4918.
- ^ Antonov, Alexandre; Lipton, Alex; López de Prado, Marcos (2024). "Overcoming Markowitz's Instability with the Help of the Hierarchical Risk Parity (HRP): Theoretical Evidence". SSRN Electronic Journal. doi:10.2139/ssrn.4748151. ISSN 1556-5068.