Applying the Relative Robust Approach for Selection of Optimal Portfolio in the Tehran Stock Exchange by Second-order Conic Programming

The purpose of this study was to apply the relative robust approach that minimizes the maximum regret to deal with the present uncertainty in the input data of the Markowitz mean-variance portfolio optimization model by reconstructing that model as a second-order conic program. Regret is defined as the difference between the obtained solution and the optimal solution under a specified input data set. This approach uses scenarios to consider the present uncertainty in the input data. Moreover, the robust portfolio optimization model introduced by Bertsimas and Sim, which considers uncertainty as an interval, was used to be compared with the relative robust approach and the Markowitz model.

In this research, the return of 50 more active stocks of the Tehran Stock Exchange (TSE) was used to obtain the optimal portfolio using the minimax regret method based on the Markowitz Model. Then, using the out-of-sample Sharpe criterion, the results of the minimax regret method were compared with the classic methods.

Based on the research findings, the relative robust approach in the out-of-sample test on most corresponding points of the efficient frontier showed better performance in comparison with the Markowitz model. Also, the Bertsimas and sim approach delivered better performance than the Markowitz model in the out-of-sample test. The results did not prove any significant difference for out-of-sample outputs between the relative robust and Bertsimas and sim approaches.

According to the obtained results, the relative robust approach can surpass the mean-variance approach for investors with almost all levels of risk-return preferences. The approach presented in this research can provide investors with a new risk criterion that can be considered in choosing the optimal portfolio. Furthermore, the results confirmed that investors act indifferently in choosing between the relative robust solution and the solution of Bertsimas and Sim's approach. This method can be applied as a portfolio optimization approach and also different markets can be considered under this technique to have a better understanding of its capability.