Copula-based hierarchical risk parity: modelling nonlinear dependence structures for portfolio allocation

This paper proposes a Hierarchical Archimedean Copula Risk Parity (HAC-RP) framework that extends the conventional Hierarchical Risk Parity (HRP) approach by incorporating nonlinear and asymmetric dependence through hierarchical Archimedean copulas. Three copula specifications – Gumbel, Clayton, and a multi-generator HAC – are considered within the HRP allocation framework. The proposed method is evaluated using monthly U.S. sector ETF data and compared with conventional HRP, a Ledoit – Wolf global minimum-variance portfolio, and an equal-weight benchmark. Empirical results show that the proposed HAC portfolios provide competitive risk-adjusted performance while maintaining favourable diversification and turnover characteristics. Among the proposed specifications, the multi-generator HAC exhibits the strongest overall performance. These findings suggest that hierarchical copulas provide a practical extension of the conventional HRP framework for portfolio construction.