The paper focuses on econometrically justified robust analysis of the effects of the COVID-19 pandemic on financial markets in different countries across the World. It provides the results of robust estimation and inference on predictive regressions for returns on major stock indexes in 23 countries in North and South America, Europe, and Asia incorporating the time series of reported infections and deaths from COVID-19. We also present a detailed study of persistence, heavy-tailedness and tail risk properties of the time series of the COVID-19 infections and death rates that motivate the necessity in applications of robust inference methods in the analysis. Econometrically justified analysis is based on heteroskedasticity and autocorrelation consistent (HAC) inference methods, recently developed robust $t$-statistic inference approaches and robust tail index estimation.