The stochastic nature of financial markets is a barrier for successful portfolio management. Besides traditional Markowitz's model, many other portfolio selection models in Bayesian and Non-Bayesian frameworks have been developed. Starting with the basic Markowitz model, several cardinal models are used to find optimum portfolios with select stock set. Having developed the regression model of the return of each stock with the market return, the unsystematic part of the uncertainty was used to find the optimum portfolio and efficient risk-return frontier within each portfolio selection model. The average stock return as estimated from its historical data and the forecasted stock return were used for maximizing return with quadratic programming formulation in Markowitz model. In the models involving Fuzzy probability and possibility distributions, the future return was estimated using the similarity grade of past returns. In the interval coefficient models, future return was estimated as interval variable. The optimum portfolios of different models were widely divergent and DEA was used to identify the model giving the best portfolio with higher appraisal, both overall and by peers, and least Maverick behavior. Use of Signal to Noise ratio proved equally efficient for model discrimination and yielded identical results. © 2013, IGI Global.