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Purpose The purpose of this paper is to investigate whether Islamic stock indexes outperform conventional stock indexes, in terms of informational efficiency and risk, during the recent financial instability period. Design/methodology/approach The paper uses a state space model combined with a standard GARCH(1,1) specification while taking into account structural breakpoints. The authors allow for efficiency and volatility spillovers to be time-varying and consider break dates to locate periods of financial instability. Findings Empirical results show that Islamic stock indexes are more volatile than their conventional counterparts and are not totally immune to the global financial crisis. As regards of the informational efficiency, the results show that the Islamic stock indexes are more efficient than the conventional stock indexes. Practical implications Resulting evidence of this paper has several implications for international investors who wish to invest in Islamic and/or conventional stock markets. Policy makers and even academics and Sharias researchers should as well take preventive measures in order to ensure the stability of Islamic stock markets during turmoil periods. Overall, prudent risk management and precocious financial practices are relevant and crucial for both Islamic and conventional financial markets. Originality/value The originality of this study is performed by the use of time-varying models for volatility spillovers and informational efficiency. It considers structural break dates that think about the dynamic effect of informational flows on stock markets. The study was developed in a global framework using international data. The global analysis allows avoiding country specific effects.