Abstract. The classical models of portfolio selection could not be applied on a market were the efficient market hypothesis is not valid (at least in a "weak" sense). The aim of this paper is to enlighten the difficulties of portfolio construction in a financial market with institutional and structural deficiencies, like the Romanian one, and to propose an alternative approach to the problem. The main features of our analysis are: 1) an empirical test for the efficient market hypothesis in the Romanian financial market case; 2) a critical distinction between the concept of "risk" and the concept of "incertitude"; 3) the use of the individual yield/risk ratio versus the market one as a selection variable; 4) the renouncement at the use in the selection procedure of an "non-risky" asset; 5) an example of the proposed selection procedure. The output of this approach could be resumed by the thesis that, even in a situation when the financial market is affected by severe disfunctions, there is a possibility to build an "optimal" portfolio based on a yield-risk arbitrage inside an efficiency frontier and to obtain a "good" schema of an financial placement, in spite of the limited possibilities for a efficient portfolio management.

Keywords: non-efficient financial market; portfolio selection; risk; incertitude.