With the spread of Covid-19, investors’ expectations changed during 2020, as well as financial markets’ policy responses and the structure of global financial intermediation itself. These dynamics are studied in this paper, which analyzes quarterly changes in herding behavior by quantifying the self-similarity intensity of six stock markets in Asia and Europe. A multifractal detrended fluctuation analysis (MFDFA) is applied, using intraday trade prices with a 15-min frequency from Jan-2020 to Dec-2020. The empirical results confirm that Covid-19 had a significant impact on the efficiency of the stock markets under study, although with a quarterly varying impact. During the first quarter of the year, European stock markets remained efficient compared to Asian markets; in the subsequent two quarters, the Chinese stock market showed significant improvement in its efficiency and became the least inefficient market, with a decline in the market efficiency of the UK and Japan. Furthermore, European markets are more sensitive to asset losses than Asian markets, so investors are more likely to show herding in the former. Herding was at its peak during the 2nd quarter of 2020. These findings could be related to possible market inefficiencies and herding behavior, implying the possibility of investors forming profitable trading strategies.