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Optimization in portfolio using maximum downside deviation stochastic programming model

Khlipah Ibrahim, Anton Abdulbasah Kamil and Adli Mustafa

Portfolio optimization has been one of the important research fields in financial decision making. The most important character within this optimization problem is the uncertainty of the future returns. To handle such problems, we utilize probabilistic methods alongside with optimization techniques. We develop single stage and two stage stochastic programming with recourse with the objective is to minimize the maximum downside semi deviation. We use the socalled “Here-and-Now” approach where the decision-maker makes decision”now” before observing the actual outcome for the stochastic parameter. We compare the optimal portfolios between the single stage and two stage models 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. The results show that the two stage model outperforms the single stage model in the optimal and in-sample analysis