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Hierarchical Risk Parity


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The article “Hierarchical Risk Parity” ranked #2 on Quantpedia’s Top Ten Blog Posts in 2020. See an excerpt below.

Various risk parity methodologies are a popular choice for the construction of better diversified and balanced portfolios. It is notoriously hard to predict the future performance of the majority of asset classes. Risk parity approach overcomes this shortcoming by building portfolios using only assets’ risk characteristics and correlation matrix. A new research paper written by Lohre, Rother and Schafer builds on the foundation of classical risk parity methods and presents hierarchical risk parity technique. Their method uses graph theory and machine learning to build a hierarchical structure of the investment universe. Such structure allows better division of assets/factors into clusters with similar characteristics without relying on classical correlation analysis. These portfolios then offer better tail risk management, especially for skewed assets and style factor strategies.

Authors: Lohre, Rother and Schafer

Title: Hierarchical Risk Parity: Accounting for Tail Dependencies in Multi-Asset Multi-Factor Allocations



We investigate portfolio diversification strategies based on hierarchical clustering. These hierarchical risk parity strategies use graph theory and unsupervised machine learning to build diversified portfolios by acknowledging the hierarchical structure of the investment universe. In this chapter, we consider two dissimilarity measures for clustering a multi-asset multi-factor universe. While the Pearson correlation coefficient is a popular choice, we are especially interested in a measure based on the lower tail dependence coefficient. Such innovation is expected to achieve better tail risk management in the context of allocating to skewed style factor strategies. Indeed, the corresponding hierarchical risk parity strategies seem to have been navigating the associated downside risk better, yet come at the cost of high turnover. A comparison based on block-bootstrapping evidences alternative risk parity strategies along economic factors to be on par in terms of downside risk with those based on statistical clusters.

Notable quotations from the academic research paper:

“The recent literature has presented risk parity allocation paradigms guided by hierarchical clustering techniques|prompting Lopez de Prado (2016) to label the technique hierarchical risk parity (HRP). Given a set of asset class and style factor returns, the corresponding algorithm would cluster these according to some distance metric and then allocate equal risk budgets along these clusters. Such clusters might be deemed more natural building blocks than the aggregate risk factors in that they automatically pick up the dependence structure and form meaningful ingredients to aid portfolio diversication.

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