The study analyses the nature and behaviour of volatility, the risk–return relationship and the long‐term trend of volatility on the South African equity markets using aggregate level, industrial level and sectoral level daily data for the period 1995‐2009. By employing dummy variables for the Asian and the sub‐prime financial crises and the 11 September political shock, the study further examines whether the long‐term trend of volatility structurally breaks during financial crises and major political shocks. Three time‐varying generalised autoregressive conditional heteroskedasticity models were employed: one of them symmetric, and the other two asymmetric. Each of these models was estimated based on three error distributional assumptions. The findings of the study are as follows: First, volatility is largely persistent and asymmetric. Second, risk at both aggregate and disaggregate level is generally not a priced factor on the South Africa (SA) stock market. Third, the threshold autoregressive conditional heteroscedasticity (TARCH) model under the generalised error distribution is the most appropriate model for conditional volatility of the SA stock market. Fourth, volatility generally increases over time, and its trend structurally breaks during financial crises and major global shocks. The policy and investment implications of the findings are outlined.