In recent years, and especially during the last two decades, a lot of research has been made on stock returns and the relationship with their volatility, on stock market volatility and how it responds in connection with macroeconomic variables and their volatility, and on the relationship between output growth, and its volatility. Researchers have tried to interrelate the above factors and draw some useful conclusions about the past and policies of the future, regarding mostly investments and portfolio management. by including emerging markets in our sample we can address the relationship, in mean and volatility, between real stock returns and real economic activity, for which we use industrial production as our proxy, in a larger sample and work on a wider scale. No research has ever been made before that had the length of our sample (38 countries) combined with the methodology we use (see chapter IV) and especially in Matlab application. In this section (chapters I and II) we will present the literature review that supports our work and the theoretical and empirical basis of it. The remainder of our work includes the analysis of the data we collected (chapter III), the methodology of Cheung & Ng and Hong which is based on the estimation of the Cross Correlation Function for the squared standardized residuals, that are obtained from the estimation of the GARCH model (chapter IV), the presentation our empirical results and the discussion of them (chapter V). At last we conclude on our research.