The paper examines the exposure of sectoral stock returns to oil price changes in Australia, China, Germany, New Zealand and Norway over the period 2000-2015 using weekly data drawn from DataStream. The issue of volatility has important implications for the theory of finance and as is well-known accurate volatility forecasts are important in a variety of settings including option and other derivatives pricing, portfolio and risk management (e.g. in the calculation of hedge ratios and Value-at-Risk measures), and trading strategies (David and Ruiz, 2009). This study adopts GARCH and EGARCH to understand the relationship between the returns and volatility. The findings using GARCH (EGARCH) models suggests that in the case of Germany eight (nine) out of ten sectors returns can be explained by the volatility of past oil price in Germany, while in the case of Australia, six (seven) out of ten sector returns are sensitive to the oil price changes with the exception of Industrials, Consumer Goods, Health care and Utilities. While in China and New Zealand five sectors are found sensitive to oil price changes and three sectors in Norway, namely Oil & Gas, Consumer Services and Financials. Secondly, this paper also investigated the exposure of the stock returns to oil price changes using market index data as a proxy using GARCH or EGARCH model. The results indicated that the stock returns are sensitive to the oil price changes and have leverage effects for all the five countries. Further, the findings also suggests that sector with more constituents is likely to have leverage effects and vice versa. The results have implications to market participants to make informed decisions about a better portfolio diversification for minimizing risk and adding value to the stocks.