Hierarchical clustering for optimal portfolios

In Chapter 5, Portfolio Optimization and Performance Evaluation, we discussed several methods that aim to choose portfolio weights for a given set of assets to optimize the risk and return profile of the resulting portfolio. These included the mean-variance optimization of Markowitz's modern portfolio theory, the Kelly criterion, and risk parity. In this section, we cover hierarchical risk parity (HRP), a more recent innovation (Prado 2016) that leverages hierarchical clustering to assign position sizes to assets based on the risk characteristics of subgroups.

We will first present how HRP works and then compare its performance against alternatives using a long-only strategy driven by the gradient boosting models we developed in the last chapter.

How hierarchical risk parity works

The key ideas of hierarchical risk parity are to do the following:

• Use hierarchical clustering of the covariance matrix to group...