This paper aims to examine and compare the effect of black swan events on the performance of companies with strong Environmental, Social, and (Corporate) Governance (ESG) backgrounds with that of other companies. Compared to established firms, companies with ESG backgrounds are perceived to be stable that will help them outperform established companies that are volatile during times of crisis. This research focuses on SENSEX for conventional market index and BSE GREEENEX and S&P BSE CARBONEX for ESG indices. We evaluated performances of the three indices during U.S. Debt Ceiling Crisis (2011-12), Black Monday China, BREXIT and Demonetization (2015-16), and COVID-19 (2020) crisis. We checked whether ESG indices outperformed conventional index significantly using Student's T-test. We have also compared the volatility of the three indices during the different black swan periods using the GARCH model.