Consensus reaching process for portfolio selection: a behavioral approach

A portfolio selection problem can be modeled as a group decision problem in which several experts are invited to present their ideas and judgments. In this context, the Consensus reaching process may have a central role to guarantee the selection of one of the available alternatives. Therefore, it's important to study and to analyze the process of reaching consensus among group members. In fact, due to the complexity of the context in which experts operate and due to the various diversities among experts, reaching consensus isn't always simple and easily achievable. The present contribution investigates the dynamics involved in the consensus reaching process in a group decision problem in which an investor must choose amongst a given set of portfolios, that are optimized with respect to different objective functions, and are not directly comparable to each other. By using mathematical structures, we provide the description of the experts' status, and we propose a new method to identify where the consensus precipitates. The experimental framework is divided into three different moments. In the first part, equivalent portfolios have been built by optimizing them according to different measurements of risk. In the second part, experts have expressed their preferences trough pairwise comparisons with respect to the characteristics of the proposed portfolios. This pass has allowed the construction of an AHP for everyone. Finally, the weights obtained by the AHP have been used to define the experts' probabilities in the multi-states model and to determine the Portfolio on which Consensus concords.