We implement a systematic asset allocation model using the Historical Simulation with Flexible Probabilities (HS-FP) framework developed by Meucci [142, 144, 145]. The HS-FP framework is a flexible non-parametric estimation approach that considers future asset class behavior to be conditional on time and market environments, and derives a forward-looking distribution that is consistent with this view while remaining as close as possible to the prior distribution. The framework derives the forward-looking distribution by applying unequal time and state conditioned probabilities to historical observations of asset class returns. This is achieved using relative entropy to find estimates with the least distortion to the prior distribution. Here, we use the HS-FP framework on South African financial market data for asset allocation purposes; by estimating expected returns, correlations and volatilities that are better represented through the measured market cycle. We demonstrate a range of state variables that can be useful towards understanding market environments. Concretely, we compare the out-of-sample performance for a specific configuration of the HS-FP model relative to classic Mean Variance Optimization(MVO) and Equally Weighted (EW) benchmark models. The framework displays low probability of backtest overfitting and the out-of-sample net returns and Sharpe ratio point estimates of the HS-FP model outperforms the benchmark models. However, the results are inconsistent when training windows are varied, the Sharpe ratio is seen to be inflated, and the method does not demonstrate statistically significant outperformance on a gross and net basis.

This study proposes the application of machine learning techniques to predict yield in the apple industry. Crop yield prediction is important because it impacts resource and capacity planning. It is, however, challenging because yield is affected by multiple interrelated factors such as climate conditions and orchard management practices. Machine learning methods have the ability to model complex relationships between input and output features. This study considers the following machine learning methods for apple yield prediction: multiple linear regression, artificial neural networks, random forests and gradient boosting. The models are trained, optimised, and evaluated using both a random and chronological data split, and the out-of-sample results are compared to find the best-suited model. The methodology is based on a literature analysis that aims to provide a holistic view of the field of study by including research in the following domains: smart farming, machine learning, apple crop management and crop yield prediction. The models are built using apple production data and environmental factors, with the modelled yield measured in metric tonnes per hectare. The results show that the random forest model is the best performing model overall with a Root Mean Square Error (RMSE) of 21.52 and 14.14 using the chronological and random data splits respectively. The final machine learning model outperforms simple estimator models showing that a data-driven approach using machine learning methods has the potential to benefit apple growers.

The COVID-19 pandemic has had devastating consequences across the globe, and has led many governments into completely new decision making territory. Developing models which are capable of producing realistic projections of disease spread under extreme uncertainty has been paramount for supporting decision making by many levels of government. In South Africa, this role has been fulfilled by the South African COVID-19 Modelling Consortium's generalised Susceptible-ExposedInfectious-Removed compartmental model, known as the National COVID-19 Epi Model. This thesis adapted and contributed to the Model; its primary contribution has been to incorporate the feature that resources available to the health system are limited. Building capacity constraints into the Model allowed it to be used in the resource-scarce context of a pandemic. This thesis further designed and implemented a goal programming framework to shift ICU beds between districts intra-provincially in a way that aimed to minimise deaths caused by the non-availability of ICU beds. The results showed a 15% to 99% decrease in lives lost when ICU beds were shifted, depending on the scenario considered. Although there are limitations to the scope and assumptions of this thesis, it demonstrates that it is possible to combine mathematical modelling with optimisation in a way that may save lives through optimal resource allocation.

The publication of the International Union for Conservation of Nature (IUCN) Red List of Ecosystems (RLE) standards is an important development that has received broad acceptance globally. More than 100 countries across the globe including South Africa and Myanmar have adopted the IUCN RLE standards as their national framework for assessing the risk of ecosystem collapse. The strongest motivations for the alignment include: (i) elimination of confusion and reducing the administrative burden for maintaining multiple lists of threatened ecosystems, (ii) increased legitimacy of the ecosystem threat status assessment by basing them on a body of sound scientific literature, (iii) comparable assessments across different environments and countries across the globe, (iv) for the threatened national ecosystems to be recorded under the IUCN RLE registry. Furthermore, the IUCN Red List makes it easier for countries to secure funding from international donors to achieve national biodiversity conservation objectives, and address knowledge and data gaps through focused research. The IUCN RLE standards only became available after many countries including South Africa and Australia each independently tailor-developed national indicators or standards for assessing threats to ecosystems. The Ecosystem Threat statuses (ETS) standards are developed to aid biodiversity monitoring efforts, and many have progressed into the legislated national list of the threatened ecosystems. In South Africa, the gazetted list of threatened ecosystems is ratified to inform policy development and land-use planning tools that mainstream biodiversity considerations into economic development activities. Considering the strong links between the gazetted list of threatened ecosystems and many of the policy and spatial planning tools, the change and/or update to the IUCN RLE standards may disrupt conservation and land-use plans. In addition, South Africa has limited data on ecosystem integrity with to apply the full range of the IUCN RLE functional criteria which may lead to the risk of ecosystem collapse being underestimated. However, the country has comprehensive data on threatened plant species which in many cases contain detailed information on drivers of environmental degradation and biotic disruptions. In addition, extensive efforts have been made to link threatened species and the ecosystem types in which they occur. Such efforts enable the country to look at degradation through species lenses to better understand the degree of underestimation of ecosystem risk. Nonetheless, there is a need to interrogate and holistically understand the implications that may emanate from this shift, hence the importance of this study. This thesis was focused on assessing the origins and history of the IUCN and South Africa's approach to assessing threats to ecosystems. In chapter 1, I reviewed the key concepts including the scientific basis and criteria to understand the purpose and philosophy of the South Africa (SA) ETS and IUCN RLE frameworks. In Chapter 2, I compared and contrasted the SA ETS and IUCN RLE assessment outcomes of ecosystems susceptible to only spatial threats. Finally, in Chapter 3, I tested whether the IUCN RLE is a good proxy for the distribution of threatened species in South Africa. The results revealed that the IUCN RLE and SA ETS standards have overarching similarities (e.g. spatial and functional criteria) as they both share the common ancestry (IUCN Red List of Threatened Species). Equally, there are key differences (e.g. decision thresholds) that explain the misalignments in the ecosystem threat status between the two systems. Meanwhile, the quantitative results alluded that the proportions of matching assessment outcomes are high when the risk categories (Critically Endangered: CR and Endangered: EN versus Vulnerable: VU and Least Concern: LC) are split in accordance with their policy uptake (i.e. National Environmental Management Act (NEMA) EIA regulations) but relatively low per individual risk category. Furthermore, the results suggest that not all ecosystem types undergoing spatial declines entirely reflect the status of threatened plant species they contain. Many of these threatened plant species overlap with ecosystems at immediate risk of collapse (CR and EN). Such species will indirectly benefit from broad-scale conservation interventions that are informed by the list of threatened ecosystems. However, the majority of plant species threatened by either habitat loss and/or land degradation occur within the least threatened ecosystems. These species will not benefit from conservation responses informed by the gazetted national list of threatened because spatial declines within these ecosystems are considered to either be minimal or stable to trigger conservation response. Encouragingly, there are existing legal conservation tools such as stewardship programmes, Key Biodiversity Areas, and Critical Biodiversity Areas that allow threatened and unprotected ecological features including species to be strategically targeted for conservation responses. However, there is a need for South Africa to intensify efforts that ensure that these legal tools are implemented correctly and successfully to maximise conservation impacts and arrest biodiversity loss.

Includes bibliographical references (leaves 72-75). / A key feature of the local bond market is that trade is concentrated in a few liquid government bonds. We review and implement the filtered term structure model proposed by Gombani, Jaschke and Runggaldier that defines an arbitrage free pricing system that is consistent with liquid bond prices. The model is derived in two stages called the underlying and perturbed models. The underlying model defines the theoretical arbitrage free term structure. It is assumed to be a multi-factor, affine HNM type model where the stochastic factors satisfy a linear diffusion equation. Gombani et al. argue that the differences between the theoretical and market prices should be interpreted as unobserved errors. The perturbed model the prices of the observed bonds as their theoretical values distorted by noise. Assuming that the information at any point in time is the market prices of a finite number of liquidly traded bonds, the perturbed model is used to derive a continually updated pricing system that is arbitrage free with respect to the observed prices. The method is based on the Kalman filter. We implement a particular three-factor version of the model and calibrate it to the South African market. We discuss the relevant data and numerical and statistical techniques including principal component analysis and yield curve construction. We apply the formulas for pricing European options on zero-coupon and coupon bearing bonds for Gaussian HJM models to the perturbed model and present two examples to demonstrate the application of the model to bond and option pricing.

Includes bibliographical references (leaves 75-77).

Includes bibliographical references. / Portfolio construction with quantitative and qualitative forecasts is described through the exposition of two asset allocation models. The two models arc the Black-Litterman Asset Allocation moodel and the Qualitative Forecasts : Model developed by Herold Ulf. The models are developed theoretically and made intuitively accessible with real market data examples. Methodology is developed using the two models to transport alpha across benchmarks.

Includes bibliographical references (leaves 62-66). / The Analysis of variance is a robust technique whereby the total variation present in a set of data is partitioned into two or more components (Wayne, 1999). In this thesis, ANOVA was used to uncover the differences in goby length preyed on by three different colonies of fur seals at the Namibian coast. Moreover, ANOVA was used to investigate temporal differences in lengths of goby preyed on by fur seals in each location of the seal colonies. Results of the analysis are shown in the Analysis and results section, and the findings are discussed in the discussion section. But before these two sections, there are three sections of the thesis. The first section is the general introduction that explains about the general situation and the targets of this thesis. The second section gives a general background on the ANOVA technique. The third section explains the nature of the data and gives background information on gobies.

The purpose of this thesis is to examine a regime-based asset allocation strategy and evaluate whether accounting for regime-dependent risk and return of asset classes provides any significant improvement on portfolio performance. The South African market and economy are considered as a proxy for the analysis. Motivation of this thesis stems from the growing body of research by practitioners devoted to models that are reflective of the interdependency between financial assets and the real economy. The asset classes under consideration for the analysis are domestic and foreign cash, domestic and foreign bonds, domestic and foreign equity, inflation linked bonds, property, gold and commodities. In order to evaluate the performance of the regime-based strategy, this thesis proposes a framework based on Principal Component Analysis and Fuzzy Cluster Analysis for regime identification and asset allocation. The performance of the strategy is tested against two strategies that are not cognizant of regime changes. These are an equally weighted portfolio and a buy-and-hold strategy. Furthermore, relative performance analysis was performed by comparing the regime-based strategy proposed in this thesis against the Alexander Forbes Large Manager Watch Index. Due to data limitations, the analysis is done on an in-sample basis without an out-of-sample testing. The results from the analysis showed the extent of outperformance of the proposed regime-based strategy relative to an equally weighted strategy and a buy-and-hold strategy. These results were consistent with existing literature on regime-based strategies. Furthermore, the results provided strong motivation for the use of the regime identification framework together with tactical asset allocation proposed in this thesis.

Includes bibliographical references.