PurposeThis study attempts to examine the time-varying volatility spillovers between environmentally sustainable assets and quantify the value-at-risk of the portfolios across various frequencies.Design/methodology/approachTo accomplish these objectives, this paper utilizes a connectedness index-based TVP-VAR model and applies the wavelet-based VaR ratio to daily data spanning from January 2018 to September 2023.FindingsThe empirical findings reveal a notable increase in the connectedness index between green stocks and green bonds during the COVID-19 crisis, signifying evidence of a contagion effect. The portfolio’s risk ratio also exhibited a sharp rise amid the pandemic, particularly over medium and long-term horizons, driven by increased spillover among green assets. Notably, our analysis indicates that green bonds influence the connectedness system between green stocks and the value-at-risk ratio, reducing volatility spillover and portfolio risk ratios across various investment horizons. These results highlight the role of green bonds as an effective diversification asset against the risks associated with green equities.Originality/valueThis research investigates the dynamic connectedness and value-at-risk ratio between eight green sectoral renewable energy and non-energy equities and green bonds. We put forward some portfolio implications for green investors with an environmental consciousness who desire to decarbonize their portfolios and mitigate environmental issues.