Did the pattern of US stock markets volatility change due to the COVID-19 or have the US stock markets been less volatile despite the pandemic shock? And as for tech stocks, are they even less volatile than the overall market? In this paper we provide evidence in favour of a ``quietness'' in the stock markets, interrupted by the COVID-19, by analysing dispersion, skewness and kurtosis characteristics of the empirical distribution of nine returns series including individual FATANG stocks (FAANG: Facebook, Amazon, Apple, Netflix and Google; plus Tesla) and US indices (S&P500, DJIA and NASDAQ). A new methodology based on semi-variance and semi-kurtosis is proposed. Structural breaks and conditional heteroskedasticity are also analyzed by considering the traditional symmetrical and asymmetrical GARCH models. We show that in the most recent past, despite the COVID-19 pandemic, the FATANG tech stocks are characterized mostly by conditional homoskedasticity while the returns of US stock indices are mainly conditional heteroskedastic.