This study investigates how green investment assets improve optimal portfolio diversification in terms of tail downside risk. We use the wavelet conditional value-at-risk ratio to explore the benefits of adding green assets to conventional portfolios. We quantify risk based on the contagion between conventional stock market indices and green environmental assets, including a sustainability index, clean energy, and green bonds. Our findings emphasize the high variance between conventional stock pairs, providing evidence of contagion effects before and during the COVID-19 pandemic. We show that including clean energy and green bond indices in conventional portfolios reduces the extreme risk of portfolios. In addition, we find that the diversification benefits of clean energy, green bonds, and safe-haven investments apply especially in the short term during the pandemic. Finally, we show that the considered portfolios could not decrease long-term risk during the COVID-19 crisis because of the systematic risk spread. Our portfolio optimization design supports the superiority of clean energy and green bonds in portfolio diversification over the sustainability index. These insights can be used by portfolio managers to inform diversification in different investment horizons.