Hierarchical Portfolio Optimization

Abstract

The field of Portfolio Optimization has historically had a very hard time as the Mathematical Models at its availability are based on certain assumptions one can not afford to make in the financial markets, making naive approaches all-too entic-ing. In this project we have introduced the assumption that the different stocks in the financial markets have a hierarchical structure and have allowed ourselves to be inspired by it to build portfolios through a Machine Learning approach. We have employed the Hierarchical Risk Parity algorithm and tested minor variations relat-ing to the dissimilarity measure it makes use of. The tests were conducted with historical daily closing price data from 2014 to 2020 for 440 stocks in the S&P 500 index. Results suggest most of the tested Hierarchical Risk Parity variants are ro-bust and can compete with the Equal Weights Portfolio. We mainly encourage the use of two dissimilarity measures, the standard one, a correlation based metric and Dynamic Time Warping. The former is suggested to the pessimistic investor while the latter to the hopeful yet conservative investor. To optimistic investors with a high risk tolerance the recommendation would be to use the traditional Equal Weights portfolio among the asset allocation methods considered in this project.