This paper investigates the properties of South African stock returns and the underlying variance. The investigation into the properties of stock returns and the behaviour of the variance underlying returns is undertaken using model-free approaches and through the application of ARCH/GARCH models. The results indicate that, as with other stock markets, returns on the South African stock market depart from normality and that variance displays evidence of heteroscedasticity, long memory, persistence, and asymmetry. Applying the EGARCH(p,q,m) and IGARCH(p,q) specifications confirms these findings and the application of these models suggests differing characteristics for variance structures underlying the South African stock market. In light of the findings relating to the properties of stock returns and the characteristics of variance and its structure, implications are outlined, and recommendations on how time-series specifications may be estimated are made.