2026/04/26 by Bernd Johannes Wuebben · 2 voices
Economics, Econometrics and Finance · #q-fin.PM
Hierarchical Risk Parity (De Pardo) and the Schur-complement generalization of Cotton are among the most widely adopted regularised portfolio construction methods, yet both are signal-blind: they solve only the minimum-variance problem and cannot accommodate an arbitrary expected-return forecast. This paper introduces three methods that incorporate alpha signals into hierarchical and regularised portfolio construction. HRP-μ is a hierarchical allocator that accepts an arbitrary signal μ and nests standard HRP when γ= 0 and μ=1. It preserves the tree-based structure of HRP while extending it beyond the minimum-variance setting. HRP-Σμ strengthens this construction by replacing inverse-variance representatives with recursive local mean-variance optima, thereby using richer within-cluster covariance information at the same O(N2) asymptotic cost. CRISP (Correlation-Regularised Iterative Shrinkage Portfolios) is an iterative solver for Pγw = μ with Pγ= (1-γ)diag(Σ) + γΣ, so that γ interpolates between a diagonal portfolio rule and full Markowitz. At convergence, CRISP is Markowitz applied to a variance-preserving shrunk covariance-diagonal variances unchanged, off-diagonal correlations shrunk-with γ tuned for out-of-sample Sharpe rather than covariance-estimation loss. In Monte Carlo experiments across multiple covariance regimes and estimation ratios, HRP-μ and HRP-Σμ both outperform plain HRP with HRP-Σμ consistently improving on HRP-μ. CRISP at intermediate γ is the dominant method in both regimes, outperforming HRP, Cotton, Ledoit-Wolf shrinkage, direct Markowitz, and the signal-aware hierarchical methods.