This study investigates the efficiency of conventional and Islamic stock markets and their diversification potential by using multifractal de-trended fluctuation analysis (MF-DFA), wavelet squared coherence (WTC) and wavelet Value-at-Risk (VaR). Evidence from regional and country-level markets indicates Islamic stocks are less efficient than conventional ones in the short term, however more efficient in the medium term. Conventional stocks in the UK, Japan, and emerging markets are more efficient than the Islamic ones in the long term, whereas those from the US and Europe are less efficient. The wavelet VaR shows that conventional stock markets are at least as risky as the Islamic ones.