Against the backdrop of the Covid-19 pandemic, this study explores the hedging and safe-haven potential of green bonds for conventional equity, fixed income, commodity, and forex investments. We use the cross-quantilogram approach that provides a better understanding of the dynamic relationship between assets under different market conditions. Our full sample results show that the green bond index could serve as a diversifier asset for medium- and long-term equity investors. Besides, it can also serve as a hedging and safe haven instrument for currency and commodity investments. Moreover, the sub-sample analysis of the pandemic crisis period shows a heightened short- and medium-term lead-lag association between the green bond index and conventional investment returns. However, the green bond index emerges as a significant hedging and safe-haven asset for the long-term investors of conventional financial assets. Our results offer insights for long-term investors whose portfolios comprise conventional assets such as equities, commodities, forex, and fixed income securities. Further, our findings reveal the potential role that the green bond investments could play in global financial recovery efforts without compromising the low-carbon transition targets.