A comparative analysis of generic models to an individualised approach in portfolio selection

Abstract

The portfolio selection problem has been widely understood and practised for millennia, but it was rst formalised by Markowitz (1952) with the proposition of a risk-reward trade-o model. Since then, portfolio selection models have continued to evolve. The general consensus is that three objectives, to maximise the uncertain Rate Of Return (ROR), to maximise liquidity and to minimise risk, should be considered. It was found that there are opportunities for improvement within the existing portfolio selection models. This can be attributed to three gaps within the existing models. Generally, existing portfolio selection models are generic, especially in how they incorporate risk, they generally do not incorporate Socially Responsible Investing (SRI), and generally they are considered to be unvalidated. This dissertation set out to address these gaps and compare the real-world performance of generic and individualised portfolio selection models. A new method of accounting for risk was developed that consolidates the portfolio's market risk with the investor's nancial risk tolerance. Two portfolio selection models that incorporate individualised risk and SRI objectives were developed. These two models were called the risk-adjusted and social models, respectively. These individualised models were compared to an existing generic Markowitz model. These models were formulated using stochastic goal programming. A sample of 208 companies JSE Limited companies was selected and two independent datasets were extracted for these companies, a training (2010/01/01 { 2016/12/31) and testing (2017/01/01 { 2019/12/31) dataset. The models solved were in LINGO using the training dataset and tested on an unknown future by using the testing dataset. It was found that in the training period, the individualised risk-adjusted model outperformed the generic Markowitz model and the individualised social model. Furthermore, it was found that it would not be bene cial for an investor to be Socially Responsible (SR). Nevertheless, investors invest to achieve their ROR and SRI goals in the future, not in the present. Thus, it was necessary to evaluate how the portfolios selected by all three models would have performed in an unknown future. In the testing period, both the generic Markowitz model and the risk-adjusted models had dismal performance and were signi cantly outperformed by the South African market and unit trusts. Thus, these models are not useful or suitable for their intended purpose. On the contrary, the social model portfolios achieved high ROR values, were SR, and outperformed the market and the unit trusts. Thus, this model was useful and suitable for its intended purpose. The individualised social model signi cantly outperformed the other two models. Thus, it was concluded that an individualised approach that incorporates SRI outperforms a generic portfolio selection approach. Given its unparalleled performance and novel model formulation, the social model makes a contribution to the eld of portfolio selection. This dissertation also highlighted the importance of testing portfolio selection models on an unknown future and demonstrated the potentially horri c consequences of neglecting this analysis.