Hierarchical Equal Risk Contribution for Portfolio Allocation

Summary

This tutorial explains Hierarchical Equal Risk Contribution (HERC), a portfolio allocation method that combines hierarchical clustering with risk-based weighting. It motivates the approach by describing how conventional mean-variance optimization can be sensitive to estimated returns and covariance matrix changes. HERC first clusters assets using a chosen linkage method, then estimates the number of clusters with the Gap statistic. It applies recursive bisection to allocate risk across the hierarchy and uses naive risk parity within clusters to derive final asset weights. Risk can be measured in several ways, including variance, expected shortfall, or drawdown risk.

The article walks through an implementation using a 17-asset historical price dataset also used in the original HERC paper, and says the resulting allocation matches when supplied prices are replaced by returns and a covariance matrix with the same setup. This example checks implementation consistency; it does not establish out-of-sample performance or superiority in live markets. Results depend on the input data, clustering linkage, selected cluster count, and chosen risk measure. The method organizes allocation by observed similarity and risk contribution, but still relies on historical estimates and does not eliminate portfolio risk.

Key ideas

• HERC combines hierarchical clustering with risk-based allocation across and within clusters.
• The Gap statistic can guide the choice of cluster count, while linkage rules affect the resulting hierarchy.
• Recursive bisection assigns cluster weights according to risk contribution rather than asset counts.
• Naive risk parity within each cluster can use risk measures such as variance or expected shortfall.
• The tutorial’s matching allocation example checks implementation consistency, not future investment performance.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.