Although it is widely assumed that the stock market is efficient, some empirical studies have already tried to address the issue of forecasting stock returns. As far as is known, it is hard to find a paper involving not only the forecasting statistics but also the forecasting profitability. This paper aims to provide an empirical evidence of the market inefficiency and to present some simple realistic strategies based on forecasting stocks returns. In order to achieve this study, some linear and non linear algorithms are used to prove the predictability of returns. Many regularization methods are introduced to enhance the linear regression model. In particular, the RIDGE method is used to address the colinearity problem and the LASSO method is used to perform variable selection. The different obtained results show that the stock market is inefficient and that profitable strategies can be computed based on forecasting returns. Empirical tests also show that simple forecasting methods perform almost as well as more complicated methods.