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In this article we take a recent generalized VAR-GARCH approach to examine the extent of volatility transmission between oil and stock markets in Europe and the United States at the sector-level. The empirical model is advantageous in that it typically allows simultaneous shock transmission in the conditional returns and volatilities. Insofar as volatility transmission across oil and stock sector markets is a crucial element for portfolio designs and risk management, we also analyze the optimal weights and hedge ratios for oil-stock portfolio holdings with respect to the results. Our findings point to the existence of significant volatility spillover between oil and sector stock returns. However, the spillover is usually unidirectional from oil markets to stock markets in Europe, but bidirectional in the United States. Our back-testing procedures, finally, suggest that taking the cross-market volatility spillovers estimated from the VAR …