Portfolio selection problem is one of the most important issues in finance. It had a lot of enthusiasm from the scientific community these last decades specially after the work of the father of modern portfolio theory Harry Markowitz. The aim of this work is to find the optimal number of securities in portfolio selection problem, to get the best efficient frontier. A statistical study is conducted on a different markets. We consider issues of selection of securities under cardinality constraints, as a mixed model bi-objective variable we will solve afterwards with an exact method. Experiments are performed with major market indices, such as the Hang Seng, DAX100, FTSE 100, S&P 100, Nikkei, S&P 500 and Nasdaq.