We study the relation between oil and stock market returns for a set of seven countries that are important participants in commodity markets. Observed oil prices are decomposed into a supply related factor, a demand related factor and a risk factor. Total and directional spillover indicators are computed using forecast error variance decomposition from vector autoregressions, and their dynamic nature is explored. Studying time-varying spillovers between commodity and traditional financial markets is crucial for the design of effective portfolio composition and risk diversification strategies in global financial markets. Our findings suggest that oil markets are net volatility receptors. While some recent studies suggest that results may depend on whether supply or demand factors are considered, this study finds major stock markets are net volatility transmitters to oil markets. Transmission intensities and net positions present, however, considerable time variation being substantially larger in moments of financial distress with respect to normal times. Furthermore, results from dynamic predictive causality tests show the existence of bidirectional relations, which are stronger from stock to oil markets. Our findings provide empirical evidence supporting the oil markets financialization hypothesis.