Prominent financial stock pricing models are built on assumption that asset returns follow a normal (Gaussian) distribution. However, many authors argue that in the practice stock returns are often characterized by skewness and kurtosis, so we test the existence of the Gaussian distribution of stock returns and calculate the kurtosis of several stocks at the Macedonian Stock Exchange (MSE). Obtaining information about the shape of distribution is an important step for models of pricing risky assets. The daily stock returns at Macedonian Stock Exchange (MSE) are characterized by high volatility and non-Gaussian behaviors as well as they are extremely leptokurtic. The analysis of MSE time series stock returns determine volatility clustering and high kurtosis. The fact that daily stock returns at MSE are not normally distributed put into doubt results that rely heavily on this assumption and have significant implications for portfolio management. We consider this stock market as good representatives of emerging markets. Therefore, we argue that our results are valid for other similar emerging stock markets.