We examine the risk minimization utility of Islamic stock and sukuk (bond) indices by studying their linkages against traditional global counterparts. We first employ an asymmetric power ARCH-based ADCC model on an extended dataset employed by Kenourgios et al. (2016). Our sample ranges from July 2007 to June 2021 covering the Global Financial Crisis (GFC), the European Sovereign Debt Crisis (ESDC), and the COVID-19 pandemic. Econometric tests suggest strong evidence of coupling in the bulk of Islamic equity indices. A handful of emerging market indices constitute exceptions. Qualitatively similar results emerge from time–frequency analysis via wavelet tools, revealing pervasive coupling in both returns and volatility series. The linkages are scale-dependent in only a few pairs. In contrast, sukuk indices are uncoupled from their global fixed income counterparts and relevant risky debt portfolios. In sum, the risk-return characteristics of Islamic equities (especially in developed economies) remain coupled to major global benchmarks and therefore are unlikely to appeal as safe haven candidates. The converse applies to sukuk, which promises potential portfolio diversification benefits and safe haven status in ‘normal’ and crisis periods.