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PurposeThis paper aims at examining the co-movement dependent regime and causality relationships between conventional and Islamic returns for emerging, frontier and developed markets from November 2008 to August 2020.Design/methodology/approachFirst, the authors used the Markov-switching autoregression (MS–AR) model to capture the regime-switching behavior in the stock market returns. Second, the authors applied the Markov-switching regression and vector autoregression (MS-VAR) models in order to study, respectively, the co-movement and causality relationship between returns of conventional and Islamic indexes across market states.FindingsResults show the presence of two different regimes for the three studied markets, namely, stability and crisis periods. Also, the authors found evidence of a co-movement relationship between the conventional and Islamic indexes for the three studied markets whatever the regime. For the Granger causality, it is proved only for emerging and developed markets and only during the stability regime. Finally, the authors conclude that Islamic indexes can act as diversifiers, or safe-haven assets are not strongly supported.Originality/valueThis paper is the first study that examines the co-movement and the causal relationship between conventional and Islamic indexes not only across different financial markets' regimes but also during the COVID-19 period. The findings may help investors in making educated decisions about whether or not to add Islamic indexes to their portfolios especially during the recent outbreak.

PurposeThe objective of this paper is twofold. First, to study the safe-haven characteristic of the Islamic stock indexes and Sukuk during the crises time. Second, to evaluate this property in the last pandemic. This study employs the daily dataset from June 15, 2015, to June 15, 2020, for the most affected countries by the earlier disease.Design/methodology/approachThis study uses the Markov-switching Capital Asset Pricing Model (CAPM) approach and the basic CAPM for the main analysis and the safe haven index (SHI) recently developed by Baur and Dimpfl (2021) for the robustness test.FindingsBased on Baur and Lucey's (2010) definition, empirical findings indicate that Islamic stock indexes cannot be a refuge throughout the crisis regime for all selected conventional markets. However, Sukuk are a strong refuge in Brazilian, Russian and Malaysian markets. For the remainder countries, except Italy, the USA and Spain, the Sukuk index offers weak protection against serious conventional market downturns. Similar conclusions are obtained during the COVID-19 global crisis period. Finally, results are confirmed by using the SHI.Originality/valueTo the best of the authors’ knowledge, this paper is the first study that evaluates the safe haven effectiveness of the Islamic index and Sukuk using the SHI in the most impacted countries by the COVID-19 outbreak.