The paper investigates the time-varying correlation between stock market prices and oil prices for oilimporting and oil-exporting countries. A DCC-GARCH-GJR approach is employed to test the above hypothesis based on data from six countries; Oil-exporting: Canada, Mexico, Brazil and Oil-importing: USA, Germany, Netherlands. The contemporaneous correlation results show that i) although time-varying correlation does not differ for oil-importing and oil-exporting economies, ii) the correlation increases positively (negatively) in respond to important aggregate demand-side (precautionary demand) oil price shocks, which are caused due to global business cycle's fluctuations or world turmoil (i.e. wars). Supply-side oil price shocks do not influence the relationship of the two markets. The lagged correlation results show that oil prices exercise a negative effect in all stock markets, regardless the origin of the oil price shock. The only exception is the 2008 global financial crisis where the lagged oil prices exhibit a positive correlation with stock markets. Finally, we conclude that in periods of significant economic turmoil the oil market is not a “safe haven” for offering protection against stock market losses.