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The risk-return relationship and volatility feedback in South Africa: a nonparametric Bayesian approach.

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The risk-return relationship is a fundamental concept in finance and economic theory and is also known as the “first fundamental law” in finance. Traditionally, the risk-return relationship is known to help assist individuals in the construction of an efficient portfolio where a desired risk and return profile is tailored to their needs. However, it is a source of much more valuable information to various market participants such as bankers, investors, policy makers and researchers alike. There are a number of investment strategies, policy frameworks, theories and asset pricing models built on the empirical result of the risk-return relationship. Hence, the topic of the risk-return relationship is of broad importance. It has been widely investigated on an international scale, especially by developed markets from as early as the 1950's, with the primary motive being to help market participants optimise their chance to earn higher returns. According to conventional economic theory, the relationship between risk and return is a positive and linear relationship – the higher the risk, the higher the return. However, there are many studies documented in literature which show a positive or negative or no relationship at all. As a result, due to the magnitude of conflicting results over the years, this has caused an international and local debate to arise regarding the risk-return relationship. International studies have explored a number of theories and models to attempt resolving the inconclusive empirical backing of the risk-return relationship. On the other hand, the methods employed by South African studies and the volume of literature on the topic is relatively limited. South Africa is becoming increasingly more recognised, liberalised, interactive and integrated into the international economy. Therefore, this study makes a significant contribution from a South African market perspective. This study identifies volatility feedback, a stronger measure of regular volatility, as an important source of asymmetry to take into account when investigating the risk-return relationship. Given that South Africa is an emerging market which is subject to higher levels of volatility, one would expect the presence of this mechanism to be more pronounced. Thus, this study investigates the risk-return relationship once volatility feedback is taken into account by its magnitude in the South African market. A valuable contribution of this study is the introduction of the novel concept “asymmetric returns exposure” which refers to the risk that arises from the asymmetric nature of returns. This measure has a certain level of uncertainty attached to it due to its latent and stochastic nature. As a result, it may be ineffectively accounted for by existing parametric methods such as regression analysis and GARCH type models which are prone to model misspecification. The results of this study are presented according to the robustness of the approaches in the build up to the final result. First, the GARCH approach is employed and consists of a symmetric and asymmetric GARCH type models. The GARCH approach is treated as a preliminary test to investigate the presence of risk-return relationship and volatility feedback, respectively. While the GARCH type models have the ability to take into account the volatile nature of returns, asymmetries and nonlinearities remain uncaptured by the probability distributions governing the model innovations. Thus, the results of the GARCH type models are inconsistent and not statistically sound. This motivates the use of a more robust method, namely, the Bayesian approach which consists of a parametric and nonparametric Bayesian model. The Bayesian approach has the ability to average out sources of uncertainty and measurement errors and thus effectively account for “asymmetric returns exposure”. The test results of both the parametric and nonparametric Bayesian model find that volatility feedback has an insignificant effect in the South African market. Consequently, the risk-return relationship is estimated free from empirical distortions that result from volatility feedback. The result of the parametric Bayesian model is a positive and linear relationship, in line with traditional theoretical expectations. However, it is noteworthy that in the context of this study that the nonparametric approach is highlighted over the parametric approach. The nonparametric approach has the ability to adjust for model misspecifications and effectively account for stochastic, asymmetric and latent properties. It has the ability to take into account an infinite number of higher moment asymmetric forms of the risk-return relationship. Thus, the nonparametric Bayesian model estimates the actual fundamental nature of the data free from any predetermined assumptions or bias. According to the nonparametric Bayesian model, the final result of this study is no relationship between risk and return, in line with early South African studies.


Masters Degree. University of KwaZulu-Natal, Durban.