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Purpose The purpose of this study is to investigate the dynamic return volatility connectedness among S&P, Dow Jones (DJ) sustainability indices and their conventional counterparts. Design/methodology/approach This study uses time-series daily data for 10 S&P and DJ indices over the period of December 1, 2012 to December 8, 2021. The authors divide the data into three periods; over the whole sample, pre and during the Covid-19 pandemic. The study adopts the connectedness approach developed by Diebold and Yilmaz (2014). Findings The results reveal a high degree of connectedness between S&P and DJ indices and their relative sustainability indices over the whole sample, pre and during the Covid-19 pandemic, indicating that the sustainability indices converge toward their conventional peers. The results further show that the conventional S&P500, S&P Euro 50 and DJWI are the main transmitters of shocks, whereas the S&P400, S&P500 and S&P50 sustainability indices are the main receivers of shocks. Originality/value The study provides novel insights in terms of shock transmission of S&P and DJ sustainability indices and their conventional counterparts, where there is a lack of investigation of the connectedness between indices in this field. Practical implications The study has significant implications for investors and portfolio managers to devise portfolio strategies to minimize risk and trace the cause, the direction and the magnitude of risk transmission among different indices. Also, the results help policymakers to manage diverse types of risks associated with S&P and DJ indices. Finally, faith-based and ethical investors would be able to predict the pairwise spillover connectedness between these indices.