PurposeThis study examines the dynamics of the comovement and causal relationship between conventional (Bitcoin, Ethereum and Binance coin) and Islamic (OneGram, X8X token and HelloGold) cryptocurrencies.Design/methodology/approachThis study uses wavelet coherence approach to examine the time-varying lead-lag relationship between conventional and Islamic cryptocurrencies. Furthermore, the authors use BEKK-GARCH model to estimate the optimal weights, hedge ratio and hedging effectiveness in pre-COVID-19 and during the COVID-19 period.FindingsThe authors find no significant comovement in pre-COVID-19. However, the authors find significant positive comovement in conventional and Islamic cryptocurrencies at the beginning of the pandemic, and in most cases, conventional cryptocurrencies are leading. X8X and HelloGold have no/weak correlation with conventional cryptocurrencies, implying that investors can diversify the risk by making an Islamic and conventional cryptocurrencies portfolio. The authors also calculate the optimal weights, hedge ratio and hedging effectiveness using the BEKK-GARCH model. Based on the optimal weights, for the portfolios of conventional–Islamic cryptocurrencies, investors are suggested to increase their investment in Islamic cryptocurrencies during the COVID-19 than normal period. The results of hedge ratios show that hedging costs are higher during COVID-19 than before.Practical implicationsThe findings of the paper offer several practical policy implications for investors, portfolio manager, Shariah advisors and policymakers pertaining to asset allocation, risk management, forecasting and diversification. Specifically, investors can maximize the risk adjusted returns of their conventional cryptocurrencies portfolio by adding some portions of Islamic cryptocurrencies. Considering the comovement is time-varying, investors/manager should adjust their investment strategies frequently. For the entrepreneurs in crypto-industry, it is advised to introduce new Islamic cryptocurrencies, as it has a huge growth potential because of their distinct features and performance.Originality/valueThis is the first study that explores the linkages between conventional and Islamic cryptocurrencies, therefore this study extends the literature of Islamic finance, stablecoins and cryptocurrencies in pre-COVID-19 and during COVID-19 period. The study results provide insights to conventional crypto investor on how to manage their portfolio during normal and turbulent period.