The aim of this research is to apply the variance and conditional value at risk (CVaR) as risk measures in portfolio selection problem. Consequently, we are motivated to compare the behavior of two different type of risk measures (variance and CVaR) when the expected returns of a portfolio vary from a low return to a higher return. To obtain an optimum portfolio of the assets, we minimize the risks using mean variance and mean CVaR models. Dataset with stocks for FBMKLCI is used to generate our scenario returns. Both models and dataset are coded and implemented in AMPL software. We compared the performance of both optimized portfolios constructed from the models in term of risk measure and realized returns. The optimal portfolios are evaluated across three different target returns that represent the low risk low returns, medium risk medium returns and high risk high returns portfolios. Numerical results show that the composition of portfolios for mean variance are generally more diversified compared to mean CVaR portfolios. The in sample results show that the seven optimal mean CVaR0:05 portfolios have lower CVaR0:05 values as compared to their optimal mean variance counterparts. Consequently, the standard deviation for mean variance optimal portfolios are lower than the standard deviation of its mean CVaR0:05 counterparts. For the out of sample analysis, we can conclude that mean variance portfolio only minimizes standard deviation at low target return. While, mean CVaR portfolios are favorable in minimizing risks at high target return.