An Empirical Evaluation of Distance Metrics in Hierarchical Risk Parity Methods for Asset Allocation

Francisco Salas-Molina (), David Pla-Santamaria (), Ana Garcia-Bernabeu () and Adolfo Hilario-Caballero ()
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Francisco Salas-Molina: Universitat Politècnica de València, Economics and Social Sciences
David Pla-Santamaria: Universitat Politècnica de València, Economics and Social Sciences
Ana Garcia-Bernabeu: Universitat Politècnica de València, Economics and Social Sciences
Adolfo Hilario-Caballero: Universitat Politècnica de València, Systems Engineering and Automation

Computational Economics, 2025, vol. 66, issue 6, No 27, 5189-5206

Abstract: Abstract Hierarchical Risk Parity methods address instability, concentration, and underperformance in asset allocation by taking advantage of machine learning techniques to build a diversified portfolio. HRP methods produce a hierarchical structure to the correlation between assets by means of tree clustering that results in a reorganization of the covariance matrix of returns. However, HRP admits multiple variations in terms of clustering algorithms and distance metrics. In this paper, we evaluate the out-of-sample performance of alternative hierarchical distance metrics for clustering purposes using real stock markets in three different market scenarios: bull market, sideways trend, and bear market. We pay special attention to the mean-variance performance of the output portfolios as an estimation of the ability of alternative methods to estimate future return and risk. Our results show that correlation-based metrics provide better performance than non-correlation metrics. In addition, HRP methods outperform quadratic optimizers in two of the three stock market scenarios.

Keywords: Portfolio selection; Machine learning; Clustering; Distance metrics; Risk management (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10614-025-10848-w

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