This paper examines the impact of oil price shocks on global equities. The focus is on the heterogeneity of responses to stocks depending on three characteristics: the type of the shock; whether the country is an oil importer/exporter; the bull/bear state of the stock market. We utilise the Kilian (2009) structural VAR to distil the oil price shocks and regress stock returns on these oil shocks using a quantile regression. In addition to oil price shocks, we consider the role of both economic policy uncertainty and stock market volatility. The results reveal that equity markets in oil-importing economies do not exhibit specific patterns in response to oil shocks, whereas those in oil-exporting economies are affected by precautionary oil demand shocks. Across these markets, precautionary demand shocks have a positive effect on stock markets, although for the GCC nations it predominantly impacts only during bear markets.