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The objective of this paper is to investigate the volatility spillovers between oil and stock markets in Europe. As not all industries are expected to be equally affected by oil price changes, we conduct our study at both the aggregate as well as sector levels. Empirically, we make use of a recently developed VAR–GARCH approach which allows for transmissions in volatilities. In addition, we analyze the optimal weights and hedge ratios for oil–stock portfolio holdings based on our results. On the whole, our findings show significant volatility spillovers between oil price and sector stock returns, and suggest that a better understanding of those links is crucial for portfolio management in the presence of oil price risk.