Applied mathematics and machine learning for optimal portfolio allocation

Abstract

This research explores asset allocation techniques, leveraging mathematical methods to optimise and analyse equity portfolios for the Singapore Exchange (SGX). From 2003 to the first quarter of 2024, the study implements and compares four allocation models alongside Fama-French three-factor and five-factor models, integrating machine learning methods such as principal component regression and hierarchical agglomerative clustering to enhance the precision of factor models and risk parity strategies. Through backtesting, the three-year lookback period was deemed optimal for SGX, with analysis revealing the benefits of three and five-factor models in specific contexts. The analysis also revealed the most optimal performances with the Risk Parity and its three-factor variant when optimised for the dispersion risk measure of Mean Absolute Deviation and the downside risk measure of Semi-Standard Deviation. The findings are presented on an interactive application, offering insights into equity portfolio management strategies using value-at-risk metrics and scenario analysis to evaluate portfolio performance under various market conditions.