According to the United Nations Principle for Responsible Investment, an investment in a non-ESG compliance company has 28% higher risk per annum as compared to an ESG compliance company. Such company has a positive relationship with the financial performance and the investors cannot outperform these stocks as the information about sustainability compliance is readily available in the market. This concept is of the Efficient Market Hypothesis. Employing a quantitative research design, this study considered 17 companies of BSE Green Index that has considerable ESG scores and extracted their daily, weekly and monthly data to examine and understand its stock return movement and to test whether it follows the Efficient Market Hypothesis. This study makes use of the various statistical tools such as the Run Test, Auto-correlation Function and the Unit Root Test. Summarising the results of run test, Auto-correlation Function and two-unit root test i.e., Augmented Dickey Fuller test and Philips-Perron, it statistically confirmed the findings that the daily, weekly and monthly stock return series of the 17 stocks of BSE Green Index do not obey the ‘Random Walk Hypothesis’ which is the key findings of the study and hence rejects all the three hypotheses of the study. Backing the empirical findings of this study, it would be rational to state that the concept of the Efficient Market Hypothesis does not hold good in the BSE Green Index of the Indian Stock Market and this finding would be very imperative to the investors concerned about their investment decisions with regard to sustainability practices.