Portfolio optimization is an important research field in financial decision making. The chief character within optimization problems is the uncertainty of future returns. Probabilistic methods are used alongside optimization techniques. Markowitz (1952, 1959) introduced the concept of risk into the problem and used a mean-variance model to identify risk with the volatility (variance) of the random objective. The mean-risk optimization paradigm has since been expanded extensively both theoretically and computationally. A single stage and two stage stochastic programming model with recourse are presented for risk averse investors with the objective of minimizing the maximum downside semideviation. The models employ the here-and-now approach, where a decision-maker makes a decision before observing the actual outcome for a stochastic parameter. The optimal portfolios from the two models are compared with the incorporation of the deviation measure. The models are applied to the optimal selection of stocks listed in Bursa Malaysia and the return of the optimal portfolio is compared between the two stochastic models. Results show that the two stage model outperforms the single stage model for the optimal and in-sample analysis.