This study is aimed at investigating the volatility dynamics and the risk-return relationship in the South African market, analyzing the FTSE/JSE All Share Index returns for an updated sample period of 2009–2019. The study employed several GARCH type models with different probability distributions governing the model’s innovations. Results have revealed strong persistent levels of volatility and a positive risk-return relationship in the South African market. Given the elaborate use of the GARCH approach of risk estimation in the existing finance literature, this study highlighted several weaknesses of the model. A noteworthy property of the GARCH approach was that the innovation distributions did not affect parameter estimation. Analyzing the GARCH type models, this theory was supported by the majority of the GARCH test results with respect to the volatility dynamics. On the contrary, it was strongly unsupported by the risk-return relationship. More specifically, it was found that while the innovations of the EGARCH (1, 1) model could account for the volatile nature of financial data, asymmetry remained uncaptured. As a result, misestimating of risks occurred, which could lead to inaccurate results. This study highlighted the significance of the innovation distribution of choice and recommended the exploration of different nonnormal innovation distributions to aid with capturing the asymmetry.
<abstract> <p>This study aimed to investigate the risk-return relationship, provided volatility feedback was taken into account, in the South African market. Volatility feedback, a stronger measure of volatility, was treated as an important source of asymmetry in the investigation of the risk-return relationship. This study analyzed the JSE ALSI excess returns and realized variance for the sample period from 15 October 2009 to 15 October 2019. This study modelled the novel and robust Bayesian approach in a parametric and nonparametric framework. A parametric model has modelling assumptions, such as normality, and a finite sample space. A nonparametric approach relaxes modelling assumptions and allows for an infinite sample space; thus, taking into account every possible asymmetric risk-return relationship. Given that South Africa is an emerging market, which is subject to higher levels of volatility, the presence of volatility feedback was expected to be more pronounced. However, contrary to expectations, the test results from both the parametric and nonparametric Bayesian model showed that volatility feedback had an insignificant effect in the South African market. The risk-return relationship was then investigated free from empirical distortions that resulted from volatility feedback. The parametric Bayesian model found a positive risk-return relationship, in line with traditional theoretical expectations. However, the nonparametric Bayesian model found no relationship between risk and return, in line with early South African studies. Since the nonparametric Bayesian approach is more robust than the parametric Bayesian approach, this study concluded that there is no risk-return relationship. Therefore, investors can include South Africa in their investment portfolio with higher risk countries in order to spread their risk and derive diversification benefits. In addition, risk averse investors can find a safe environment within the South African market and earn a return in accordance to their risk tolerance.</p> </abstract>
<abstract> <p>This study investigated the All Share Index (ALSI) returns and six different risk measures of the South African market for the sample period from 17 March 2000 to 17 March 2022. The risk measures analyzed were standard deviation (SD), absolute deviation (AD), lower semi absolute deviation (LSAD), lower semivariance (LSV), realized variance (RV) and the bias-adjusted realized variance (ARV). This study made an innovative contribution on a methodological and practical level, by being the first study to extend from the novel Bayesian approach by Jensen and Maheu (2018) to methods by Karabatsos (2017)—density regression, quantile regression and survival analysis. The extensions provided a full representation of the return distribution in relation to risk, through graphical analysis, producing novel insight into the risk-return topic. The most novel and innovative contribution of this study was the application of survival analysis which analyzed the "life" and "death" of the risk-return relationship. From the density regression, this study found that the chance of investors earning a superior return was substantial and that the probability of excess returns increased over time. From quantile regression, results revealed that returns have a negative relationship with the majority of the risk measures—SD, AD, LSAD and RV. However, a positive risk-return relationship was found by LSV and the ARV, with the latter having the steepest slope. Results were the most pronounced for the ARV, especially for the survival analysis. While ARV earned the highest returns, it had the shortest lifespan, which can be attributed to the volatile nature of the South African market. Thus, investors that seek short-term high-earning returns would examine ARV followed by LSV, whereas the remaining risk measures can be used for other purposes, such as diversification purposes or short selling.</p> </abstract>
<abstract> <p>This study investigated the risk-return relationship using the Capital Asset Pricing Model (CAPM), Carhart four-factor Model (C4FM) and Fama and French Multifactor Models (FFMMs): F3FM and F5FM. This study analyzed the JSE ALSI returns of the South African market, in relation to the risk factors constructed by the data of twenty-six emerging markets, over the sample period from October 2000 to October 2021. The methodology employed was a comparison of the conventional regression analysis and novel Bayesian approach. Regression analysis estimated by Ordinary Least Squares (OLS) is one of the foremost methods used in South Africa. However, such an approach does not take into account the properties of the price data, namely, the asymmetric, volatile and random nature. While the Newey-West adjustment is one way to assist in capturing autocorrelation and volatility, it fails to consider asymmetry. The Bayesian approach accounts for all the aforementioned properties, overcoming the fundamental flaws of regression analysis. The additional model diagnostics highlighted in this study improved the Bayesian approach' robustness. The risk factors of the FFMMs estimated by regression analysis, with and without the Newey-West adjustment, were insignificant, whereas the Bayesian test results were significant. This finding clearly highlighted that model choice impacts the significance of parameter estimation and the financial decisions of investors, firms and policymakers. Jensen's alpha revealed CAPM to be optimal but none of the asset pricing models fully captured the risk premia. Thus, returns should be investigated with different risk measures for future research purposes.</p> </abstract>
<abstract> <p>The risk-return relationship is of fundamental significance in the field of economics and finance. It is used to structure investment strategies, allocate resources, as well as assist in the construction of policy and regulatory frameworks. The accurate forecast of the risk-return relationship ensures sound financial decisions, whereas an inaccurate one can underestimate risk and thus lead to losses. The GARCH-M approach is one of the foremost models used in South African literature to investigate the risk-return relationship. This study made a novel and significant contribution, on a local and international level, as it was the first study to investigate GARCH-M type models with different innovation distributions. This study analyzed the JSE ALSI returns of the South African market for the sample period from 05 October 2004 to 05 October 2021. Results revealed that the EGARCH (1, 1)-M with the Skewed Student-t distribution (Skew-t) is optimal relative to the standard GARCH, APARCH and GJR. However, the EGARCH-M Skew-t failed to capture the financial data's asymmetric, volatile and random nature. To improve forecast accuracy, this study applied different nonnormal innovation distributions: the Pearson Type Ⅳ distribution (PIVD), Generalized Extreme Value distribution (GEVD), Generalized Pareto distribution (GPD) and Stable. Model diagnostics revealed that the nonnormal innovation distributions adequately captured asymmetry. The Value at Risk and backtesting procedure found that the PIVD, followed by Stable, outperformed the Extreme Value Theory distributions (GEVD and GPD). Thus, investors, risk managers and policymakers would opt to use the EGARCH-M in combination with the PIVD when modelling the risk-return relationship. The main contribution of this study was to confirm that applying GARCH type models with the conventional and normal type distributions, to a volatile emerging market, is considered ineffective. Therefore, this study recommended the exploration of other innovation distributions, that were not included in the scope of this study, for future research purposes.</p> </abstract>
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