We examine the nature of the time-varying market risk of investment in green stocks across US, Europe, and the Asia-Pacific region, particularly during the periods of two recent global crises, 2007e08’s great recession and the recent SARS-CoV-2 crisis. We further explore the transmission mechanism of such risks, through both exogenous and endogenous channels. Time varying beta (TVB) is used to capture the risk. Suitable multivariate-GARCH model and CMAX method are used to locate exogenous channels in local and global markets. Finally, we explore the endogenous volatility channel examining deterministic chaos in the data. Results show that the US and European green stocks have significant volatility spillover from the local market. They are also strongly integrated with global market. For the Asia-Pacific green stocks, there is no spillover from the local market. However, they are weakly integrated with the global market. In US and Europe, global crisis weakens financial integration, insulating from global market fluctuations. But in Asia-Pacific market, global crises strengthen financial integration. The defensive green stocks exhibited remarkable resilience during both crises. The apparent resilience may attract investment in green stocks. Green stocks may be safe, but only apparently. The risk of green stocks lies in its chaotic nature that makes it endogenous to the system. With such chaotic market risks, an unfavorable reversal in investment optimism is possible. This calls for more caution for investors before investing in green stocks