Purpose — This study examines the performance of Islamic and conventional indices during bullish (positive) and bearish (negative) markets while the economic and financial conditions are different. Design/Methodology/Approach — This study uses GARCH (1,1) and wavelet-assisted cross-spectral, cross-correlation analyses to investigate the performance of Islamic and conventional stock indices and study the presence of safe havens, which reflect low volatility in the indices during times of market turbulence, for investors during bearish and bullish periods from 2019–2021. Findings — The paper finds that there is high and persistent volatility in Islamic indices in bullish markets, while in bearish periods the Islamic indices show low volatility persistence; and conventional indices were highly volatile during crisis periods. Also, the impact of news shocks on Islamic indices was intense before COVID-19, while after that news, shocks had a high impact on the conventional indices. The wavelet coherence analysis shows that there is high coherency between Islamic and conventional indices in developed countries but in developing countries, the opposite prevails. Originality/Value — The study is the first to use both Generalised Autoregressive Conditional Heteroskedasticity (GARCH) and wavelet coherence models for examining Islamic and conventional stock indices during bearish and bullish markets, especially in the COVID-19 pandemic era. Practical Implications — The results conclude that there are safe havens present in Islamic indices in both developing and developed countries, especially the United States (US), the United Kingdom (UK), India, and Indonesia, while in other countries the presence is weak. Both GARCH and wavelet coherence models show the same results regarding the presence of volatility and safe havens for investors in different countries.