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This study aims to analyse whether investment in green and sustainable stocks provide some cushion during current precarious time. To compare the impact of COVID-19 on the volatility of sustainable and market-capitalisation-based stocks, daily returns from Greenex, Carbonex, Large-Cap, Mid-Cap and Small-Cap index have been analysed over a period of six years from 2015 to 2021.

At the outset, logarithmic return of all selected indices has been tested for possible unit root and heteroscedastic. On confirmation of stationarity and heteroscedasticity of data, auto-regressive conditional heteroscedastic models have been applied. Thereafter, volatility is modelled through best suitable model as suggested by Akaike and Schwarz information criterions.

The findings indicate the positive impact of COVID-19 on the volatility of the indices. Asymmetric power ARCH model indicates highest significant impact of COVID-19 over the volatility of Large-Cap index, whereas exponential GARCH model detected highest significant impact of COVID-19 over the volatility of Mid-Cap Index.

To the best of the authors’ knowledge, the present study is original in the sense that it aimed at comparing the possible impact of COVID-19 over sustainable and market-capitalisation-based indices.