The volatility of stock markets has important implications for investment decision making, financial stability and overall macroeconomic stability. This study examines the risk-return relationship as well as the behaviour of volatility of the South African equity markets using both aggregate, industrial level and sector level data. The study is divided into three parts. The first part investigates the behaviour of volatility in each of the industries, sectors and the benchmark series focussing on whether volatility is symmetric or asymmetric. Subsequently we investigate which, among the GARCH family of models appropriately captured the riskreturn relationship under which distributional assumption. The second part examines the riskreturn relationship on the SA stock market. The third part examines the long term trend of volatility and whether volatility significantly increases during financial crises and during major global shocks. The GARCH-M, EGARCH-M and TARCH-M models under the Gaussian, Student –t and the GED are used. The findings this study makes are as follows: firstly, there is no clear relationship between risk and return. Secondly, volatility is asymmetrical, implying that bad news has a greater effect on volatility than good news in the South African equity market. Thirdly, the TARCH-M model under the GED was found to be the most appropriate model. Fourthly, volatility increases during financial crises and major global shocks. Overall, volatility is generally not priced on the South African equity markets. Thus, both local and international investors need to consider other factors that influence returns such as skewness. The general increase in volatility during financial crises and major global shocks poses a major concern for policy makers as this may cause financial instability. Thus policy makers need to be mindful of the behaviour of volatility in the South African equity market in response to external shocks.

Submitted in fulfillment of the requirements of the degree of Doctor of Technology: Business Administration, Durban University of Technology, Durban, South Africa, 2014. / The performance of portfolios of a fixed-rate asset and a risky asset of major companies in a South African market index the FTSE/JSE with strategies which rebalances fixed proportions of wealth in every rebalancing period is analysed in a long term. Recent findings in portfolio management theory by Dempster, Evstigneev and Schenk-Hoppé (2010, 2008, 2007, 2003) and by Browne (1988) note optimality of fixed-mix portfolios which assert fast exponential growth in stationary markets. A quantitative analysis is performed to analyse quantifiable measures in order to optimize the application of self-financing constant rebalanced portfolio strategies that contribute to the financial engineered prospects suggested by Dempster et al. (2010) for fixed-mix portfolios. The comparative performance of fixed-mix portfolios with a proxy strategy and without proxy strategy relative to a buy and hold strategy shows the superiority of fixed-mix portfolios in generic market conditions. The research extends the utilization of constant rebalanced self-financing portfolio investment strategies by assessing the market price of risk under the mean-variance model of Markowitz (1952). Effective implementation tactics of the strategy are examined by focusing on the market risk and the financial risk. The frequent reversals and trending of stochastic asset prices in the financial market are analysed to adjust the market price of risk by considering tradable financial securities to determine the financial proxy of de-trending. The proxy hypothesis which evaluates the stationary financial condition in a fixed-mix portfolio is validated by an option-based myopic strategy using a lookback straddle option. A myopic strategy is a strategy which considers a single period ahead, Fabozzi, Forcardi and Kolm (2006). The realised growth under a financial proxy is found to have a linear strategic asset allocation with a low degree of concavity relative to a buy and hold performance in the market risk of self-financing portfolio strategies. / D

Value and size related equity investment strategies are supported by a large body of empirical research that shows a persistent premium, both longitudinally and crosssectionally. However, the competing rational and behavioural finance explanations for the success of these strategies are a subject of debate. The rational explanation is that the premium earned on value shares or shares of small companies can be attributed to higher risk. Behaviouralists argue that such shares are not riskier and attribute the premium to cognitive errors and biases in human decision making. The purpose of this study is to determine, firstly, whether the value and size premium exist in South Africa during the period July 2006 to June 2012, which includes one of the worst equity market crises in history. Secondly, this study sets out to determine whether the premium earned on value and size strategies are adequately explained by the principles of rational finance theory. To provide evidence regarding the existence of the value premium and size effect, returns are analysed, cross-sectionally, on portfolios of shares sorted by value and size. For evidence of a rational explanation, returns are regressed on value and size variables, and the relative riskiness of value and small companies is analysed. The results show evidence of a value premium in portfolios of small companies, but not big companies. The size effect is found not to be statistically significant. While regressions do show significant relationships between value and size variables and returns, these variables are found not to be associated with higher levels of risk. The conclusion is that the evidence does not support a rational, risk based explanation of the returns

The agricultural sector plays an important role in the South African economy through job creation and earning foreign exchange. The role of agricultural co-operatives increased substantially over the last few decades. The research focuses firstly on the identification of derivative instruments in the market and their applicability to mitigate financial risks co-operatives experience. Secondly, research is conducted about the extent to which co-operatives use these derivatives to hedge financial risks. The research shows that most co-operatives are exposed to financial risks through different activities. It is, however, evident that although the derivative instruments are available, not all co-operatives make use of these instruments. Recommendations for further research include the development of a risk management framework and determining the different economic factors that have an influence on the use of derivatives by South African agricultural co-operatives. / Business Management / M.Comm.

The agricultural sector plays an important role in the South African economy through job creation and earning foreign exchange. The role of agricultural co-operatives increased substantially over the last few decades. The research focuses firstly on the identification of derivative instruments in the market and their applicability to mitigate financial risks co-operatives experience. Secondly, research is conducted about the extent to which co-operatives use these derivatives to hedge financial risks. The research shows that most co-operatives are exposed to financial risks through different activities. It is, however, evident that although the derivative instruments are available, not all co-operatives make use of these instruments. Recommendations for further research include the development of a risk management framework and determining the different economic factors that have an influence on the use of derivatives by South African agricultural co-operatives. / Business Management / M.Comm.