Using data until 2015, we document that oil price changes no longer predict G7 country equity index returns, as has been documented based on earlier sample periods. We use a structural VAR approach to obtain an oil price change decomposition into an oil supply shock, a global demand shock, and an oil-specific demand shock and argue that these three shocks should have different effects on equity markets. The conjecture that oil supply shocks and oil-specific demand shocks (global demand shocks) predict equity returns with a negative (positive) slope is supported by the empirical evidence over the 1986-2015 period. The results are statistically and economically significant and do not appear to be consistent with time-varying risk premia.