An innovative extended Bayesian analysis of the relationship between returns and different risk measures in South Africa

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.