An investigation into higher and partial moment portfolio selection frameworks

This dissertation highlights the importance of considering higher moments and partial moments of the distribution when conducting portfolio optimisation and selection. This is due partly to the weaknesses of mean-variance optimisation, as discussed throughout the dissertation, and the appropriateness of considering higher moments to better meet the investors utility functions. This dissertation investigates the usage of two bi-objective optimisation frameworks, a Skewness/Semivariance framework previously suggested by Brito et al (2016), and a proposed upside and downside semivariance framework (referred to as Semivariance/Semivariance), developed from Cumova and Nawrocki’s (2014) general upper partial and lower partial moment framework. It solves the endogeneity issue present in the co-semivariance matrices, through the usage of a direct multi-search algorithm. The two frameworks were tested across multiple datasets, including one of pure stocks and one of asset classes, to test the ability to both allocate assets and select stocks. The performance was measured through nominal returns, statistical tests, Sharpe ratios, Sortino ratios, and Skewness/Semivariance ratios. The results reveal the Semivariance/Semivariance optimisation process to outperform the Skewness/Semivariance optimisation in the majority of the cases investigated. This suggests it may be a superior selection optimisation process. Furthermore, the Semivariance/Semivariance portfolios remain competitive with the benchmark portfolios selected in this dissertation, often outperforming them on an absolute return and ratio basis; however, this outperformance has not consistently proven to be statistically significant