The issue of co-movements is still crucial and arguable in international finance. An optimum and significant level of co-movement is highly desirable to investors, and it mostly depends on investors’ decisions (behavior and psychology). We use frequency–time bands and multi-scale-based wavelet analysis to investigate the co-movement between developed and emerging countries’ stock markets for better asset allocation and portfolio diversification strategies. The results show that a significant level of co-movement is observed between conventional and Islamic stock markets in developed and emerging countries, and it varies in terms of its time–frequency domain properties. Particularly, the dependency among conventional and Islamic stock markets is strong at 4–512-band scales. However, the USA Islamic stock market illustrates a higher level of coherency with the UK, Japan and China’s Islamic stock markets, while a relatively lower level of co-movement is detected with the Chinese composite, Malaysian and Indonesian Islamic stock markets. The findings further confirm that the developed countries’ stock markets are substantially influenced by the GFC in 2007–2008 and the European debt crisis in 2012, while this trend is surprisingly not observed in the emerging markets on a similar scale. Therefore, these crises have opened the door for the grabbing of portfolio diversification benefits from the emerging countries’ stock markets. These findings give some interesting insights to policymakers, investors and fund managers for portfolio diversification and risk management strategies.