Hierarchical risk parity: Efficient implementation and real world analysis

Abstract

In this paper, we present an efficient implementation of the Hierarchical Risk Parity (HRP) portfolio optimization algorithm. HRP was designed to allocate portfolio weights by building a hierarchical tree of asset clusters and reducing risk through inverse variance allocation across the clusters. Our implementation improves the performance of the original algorithm by reducing its time complexity and making it more suitable for real-time systems. We evaluate the performance of our implementation on various constituents of the S&P 500 index, a market-capitalization-weighted index of 500 leading publicly traded companies in the U.S., using historical price data from 2005 to 2023. We compare the out-of-sample risk-adjusted returns of the HRP algorithm to those of a simple 1/N allocation method and find that the 1/N method outperforms HRP across all experimental setups. However, the HRP generated portfolios had a lower standard deviation by approximately 1% across all experimental setups. These results show that HRP can be of great use in generating portfolios when risk is the primary concern.