According to the conventional theory, portfolio management models are exclusively based on the twain criteria of expected return and risk, with the latter being generally measured by the variance. Nonetheless, such models have been shown to be fraught with anomalies. Hence, we propose in this paper an original methodology for the assessment of stock market shares using multicriteria decision methods. We consider an exhaustive set of criteria accredited in the financial literature and used by the professional of portfolio management to boot. The ranking of financial securities as well as their sorting out into three different categories involving attractive shares (to buy), uncertain shares (to keep) and non-attractive shares (for sale) are both a common practice for portfolio managers. This paper focuses on the application of multicriteria decision aid for the ranking and sorting out of 194 shares listed on the U.S. market. Key Words: Portfolio Management, Multicriteria Decision Aid, ranking, sorting out, MINORA and ELECTRE TRI.