Portfolio optimization under parameter uncertainty using the risk aversion formula

The Markowitz portfolio optimization model has certain difficulties in practise since real data are rarely certain. The robust optimization is a recently developed method that is used to overcome the uncertainty situation. The technique has been recently suggested in the portfolio selection problems. In this study, two kinds of portfolio optimization problems are presented: (i) the risk aversion portfolio optimization problem based on the classical Markowitz framework, and (ii) the max-min counterpart problem based on the robust optimization framework. In the application, the two models are performed on a real-world data set obtained from BIST (Borsa Istanbul). Numerical results show that the objective function values of the classical solution and the robust solution are similar to each other. It can be said that the robust model, which works as well as the classical model in the uncertainty situations, can be used instead of the classical model and also that the optimal solution obtained in the uncertainty situation is robust to parameter perturbation.