This paper examines the entire dependence structure of the quantile of stock return and that of oil price shocks, thereby extending the Quantile Regression to a Quantile-onQuantile Regression. Based on historical monthly data covering the period April 1994~ September 2015, it was shown that there is substantial heterogeneity in the stock returns and oil price relationship across oil importing countries and oil exporting countries. We find that the stocks of oil exporters that possess large proven oil reserves, in particular, Venezuela, Russia, and Saudi Arabia are typically more responsive toward demand-side oil shocks than those of oil importers. The intensity and the extent of these responses differ depending on the different stock market conditions and the nuances of oil price movements. profitable speculation and arbitrage strategies can be built.ⓒ