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The aim of this study focuses on the theory of Efficient Market Hypothesis and the related investment risks associated with it. It examines various types of theories, analyzes potential anomalies, and investigates the investment risks affecting these markets. Furthermore, it provides an extensive review of significant research works that explore the analysis and prediction of stocks return, adopting both classical and modern methodologies. The analysis was conducted through daily observations of the closing price performance of Coca-Cola's stock and the General Index of the Athens Stock Exchange (ASE). Data was sourced from Yahoo Finance, covering the period from April 2016 to April 2023, and the estimations were calculated using the econometric software Eviews12. Initially, fundamental concepts and methodologies essential for understanding economic analysis were analyzed, along with the descriptive statistics of the examined stock's performance and the General Index. Subsequently, an augmented Dickey-Fuller (ADF) test was performed on the aforementioned variables, concluding that both variables are stationary at their levels. Then, using the single-factor Capital Asset Pricing Model (CAPM), the systematic risk of Coca-Cola's stock performance was analyzed, concluding that it is a defensive stock showing a positive correlation with the market. Finally, using ARIMA models and ARCH-GARCH models, a suitable ARIMA-ARCH, ARIMA-GARCH model was selected and constructed, used in the analysis and prediction of the data. From the data analysis, it was found that both the stock returns of the examined stock and the General Index do not follow a random walk process, and thus, the hypothesis of the ASE efficiency in its weak form needs to be rejected. Moreover, it was revealed that the ARIMA(6,0,1)-GARCH(1,2) model exhibits the best performance in predicting Coca Cola's prices. Specifically, the static prediction method demonstrated better results compared to the dynamic one, as it provided a better approximation of the actual values.