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We study the relation between oil prices and stock market returns for a set of six countries, including important oil consumers and demanders. We study interconnectedness between oil and stock markets and characterize the dynamics of transmission and reception between them. We test for Granger causality between markets dynamically, endogenously identifying periods for which oil prices have responded to innovations in financial markets. Our results on connectedness show that the direction of transmission is mainly from stock markets to crude petroleum prices. Additionally, connectedness increased importantly around the global financial crisis, and reports high levels until 2014. Regarding causality, we find evidence of bidirectional relations between stock market returns and crude petroleum prices. Causality is stronger during times of financial volatility as well. Our results have important implications both for investors and policy makers.