Robust multiobjective portfolio optimization: A minimax regret approach

An efficient frontier in the typical portfolio selection problem provides an illustrative way to express the tradeoffs between return and risk. Following the basic ideas of modern portfolio theory as introduced by Markowitz, security returns are usually extracted from past data. Our purpose in this paper is to incorporate future returns scenarios in the investment decision process. For representative points on the efficient frontier, the minimax regret portfolio is calculated, on the basis of the aforementioned scenarios. These points correspond to specific weight combinations. In this way, the areas of the efficient frontier that are more robust than others are identified. The underlying key-contribution is related to the extension of the conventional minimax regret criterion formulation, in multiobjective programming problems. The validity of the approach is verified through an illustrative empirical testing application on the Eurostoxx 50.