The contradiction in the previous results provides a deep avenue for researchers to take more interest in the stock market efficiency and conduct more studies. Therefore, the study objective is to decide whether the Arab Federation of Exchanges (S&P AFE 40 Index Return) is efficient at weak-form based on normality and random walk hypothesis using several statistics such as the Jarque-Bera test as a parametric technique to check the normality and the Augmented Dickey-Fuller test as a parametric method to test the random walk hypothesis. Moreover, the results are reinforced by six non-parametric techniques to test the normality hypothesis such as the Kolmogorov-Smirnov test, Shapiro-Wilk test, Lilliefors test, Cramer-von Mises test, Watson test, Anderson-Darling test, and four non-parametric techniques such as run test, variance ratio test, Phillips-Perron test, and autocorrelation test to check the random walk hypothesis for daily data after the Covid-19 vaccination program over the period from 31 March 2020 to 31 March 2023, the results of all tests indicated that the market index return is non-efficient at the weak form, and concluded that the investors could analyze the Arab Federation of Exchanges’ past stock prices or other historical data as opportunities to predict future stock prices and earn unusual profits; therefore, Policymakers may further improve access to information to prevent investors from having opportunities to predict stock movements to obtain abnormal returns.