Hierarchical Risk Parity: Clustering Assets to Allocate Portfolio Risk

Summary

This article explains Hierarchical Risk Parity (HRP) as an alternative to covariance-inversion methods such as the Critical Line Algorithm. It identifies estimation errors, unstable matrix inversion, computational burden, and the loss of meaningful asset groupings as practical drawbacks of traditional optimization. HRP instead builds an agglomerative hierarchy from return correlations, converts those relationships into distances, and uses single-linkage clustering to organize similar assets.

The resulting cluster order is used to rearrange the covariance matrix so related assets sit near one another. Recursive bisection then divides the hierarchy into subclusters and assigns weights according to their estimated variances, giving lower-risk groups more allocation. The article illustrates the procedure with stock data and compares HRP with the Critical Line Algorithm and inverse-variance portfolios under a variance shock. It reports that HRP reallocates within related clusters in that example, but this is a limited exercise; it does not establish that HRP will outperform in other markets or periods.

Key ideas

• HRP avoids directly inverting the full covariance matrix, reducing a source of allocation instability.
• Hierarchical clustering groups assets using distances derived from their return correlations.
• Matrix seriation orders assets so correlated groups appear together in the covariance matrix.
• Recursive bisection assigns weights across clusters using their estimated variances.
• The article’s shock comparison illustrates behavior in one example and does not establish general outperformance.

Tags

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