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A constrained hierarchical risk parity algorithm with cluster-based capital allocation


  • Johann Pfitzinger

    (Department of Economics, Stellenbosch University)

  • Nico Katzke

    (Department of Economics, Stellenbosch University & Prescient Securities, Cape Town)


Hierarchical Risk Parity (HRP) is a risk-based portfolio optimisation algorithm, which has been shown to generate diversified portfolios with robust out-of-sample properties without the need for a positive-definite return covariance matrix (Lopez de Prado 2016). The algorithm applies machine learning techniques to identify the underlying hierarchical correlation structure of the portfolio, allowing clusters of similar assets to compete for capital. The resulting allocation is both well-diversified over risk sources and intuitively appealing. This paper proposes a method of fully exploiting the information created by the clustering process, achieving enhanced out-of-sample risk and return characteristics. In addition, a practical approach to calculating HRP weights under box and group constraints is introduced. A comprehensive set of portfolio simulations over 6 equity universes demonstrates the appeal of the algorithm for portfolios consisting of 20 - 200 assets. HRP delivers highly diversified allocations with low volatility, low portfolio turnover and competitive performance metrics.

Suggested Citation

  • Johann Pfitzinger & Nico Katzke, 2019. "A constrained hierarchical risk parity algorithm with cluster-based capital allocation," Working Papers 14/2019, Stellenbosch University, Department of Economics.
  • Handle: RePEc:sza:wpaper:wpapers328

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    References listed on IDEAS

    1. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    2. Roncalli, Thierry, 2013. "Introduction to Risk Parity and Budgeting," MPRA Paper 47679, University Library of Munich, Germany.
    3. Tola, Vincenzo & Lillo, Fabrizio & Gallegati, Mauro & Mantegna, Rosario N., 2008. "Cluster analysis for portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 235-258, January.
    4. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
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    Cited by:

    1. Illya Barziy & Marcin Chlebus, 2020. "HRP performance comparison in portfolio optimization under various codependence and distance metrics," Working Papers 2020-21, Faculty of Economic Sciences, University of Warsaw.
    2. Yukari Shirota & Basabi Chakraborty, 2022. "Amplitude-Based Time Series Data Clustering Method," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 59(2), pages 127-140.
    3. MohammadAmin Fazli & Parsa Alian & Ali Owfi & Erfan Loghmani, 2021. "RPS: Portfolio Asset Selection using Graph based Representation Learning," Papers 2111.15634,

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    More about this item


    Risk Parity; Diversification; Portfolio Optimisation; Clustering;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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    This paper has been announced in the following NEP Reports:


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