A two-stage robust model for portfolio selection by using goal programming

In portfolio selection models, uncertainty plays an important role. The parameter’s uncertainty leads to getting away from optimal solution so it is needed to consider that in models. In this paper we presented a two-stage robust model that in first stage determines the desired percentage of investment in each industrial group by using return and risk measures from different industries. One reason of this work is that general conditions of various industries is different and according to the concepts of fundamental analysis should be chosen good groups before selection assets for investment. Another reason is that the identification of several good industries helps to diversify between several groups and reduce the risk of investment. In the second stage of the model, considering assets return, systematic risk, non-systematic risk and also first stage’s result, amount of investment in each asset is determined. In both stages of the model there are uncertain parameters. To deal with uncertainty, a robust approach has been used. Since the model is a multi-objective problem, goal programming method used to solve it. The model was tested on actual data. The results showed that the portfolio formed by this model can be well-established in the conditions of high uncertainty and obtain higher returns.