The electricity sector is one of the most important participants in the European Union Emissions Trading Scheme (EU-ETS). This study provides further evidence on the effect of the carbon pricing on the stock returns of electricity companies in the EU-ETS. The investigation is undertaken in both phases I and II of the EU-ETS using multivariate Generalised AutoRegressive Conditional Heteroskedasticity (M-GARCH) approaches which include a multivariate Constant Conditional Correlation Generalised AutoRegressive Conditional Heteroskedasticity (CCC-GARCH) and a Dynamic Conditional Correlation Multivariate Generalised AutoRegressive Conditional Heteroskedasticity (DCC-M-GARCH) methods. The results show that the carbon market significantly affected the returns of electricity companies in Phase 1, but not in phase II of the EU-ETS. The relationship between carbon prices and electricity prices was found to be positive and symmetric. However, no volatility spillover effect between the carbon market and electricity returns was found in Phase I, whereas such effect existed in Phase II and one which was positive. These results imply that in the short run, electricity companies are significantly affected by the carbon market but this effect diminishes over the long run. These also imply that the risk-return relationship does not seem to be in full operation in relation to the link between the carbon market and capital markets.