Four traditional models using mean variance analysis are implemented for optimal portfolio selection disallowing short sales of securities. Historical stock data from S&P500 market are used to find out the corresponding parameters of these models. After obtaining the optimal portfolios, we examine how the models perform in actual market return by using more updated monthly historical data dated from 2001 to 2005. We then evaluate and analyze the performance of each model in terms of both their expected return, variance and the difference from the actual market return. Alternative approaches using the idea of expected utility such as geometric mean return and safety first, and approaches not using the expected utility theorem such as stochastic dominance are discussed and evaluated. Applications in the real world are discussed in the critique section.