Robustness in portfolio optimization based on minimax regret approach

Portfolio optimization is one of the most important issues for effective and economic investment. There is plenty of research in the literature addressing this issue. Most of these pieces of research attempt to make the Markowitz’s primary portfolio selection model more realistic or seek to solve the model for obtaining fairly optimum portfolios. An efficient frontier in the typical portfolio selection problem provides an illustrative way to express the tradeoffs between return and risk. With regard to the modern portfolio theory as introduced by Markowitz, returns are usually extracted from past data. Therefore our purpose in this paper is to incorporate future returns scenarios in the investment decision process. In order to representative points on the efficient frontier, the minimax regret portfolio is calculated, on the basis of the aforementioned scenarios. In this way, the areas of the efficient frontier that are more robust than others are identified. The main contribution in this paper is related to the extension of the conventional minimax regret criterion formulation, in multi-objective programming problems. The validity of the proposed approach is verified through an empirical testing application on the top 75 companies of Tehran Stock Exchange Market in 2017.