Portfolio optimization using a credibility mean-absolute semi-deviation model

Abstract

We introduce a cardinality constrained multi-objective optimization problem for generating efficient portfolios within a fuzzy mean-absolute deviation framework. We assume that the return on a given portfolio is modeled by means of LR-type fuzzy variables, whose credibility distributions collect the contemporary relationships among the returns on individual assets. To consider credibility measures of risk and return on a given portfolio enables us to work with its Fuzzy Value-at-Risk. The relationship between credibility expected values for LR-type fuzzy variables and possibilistic moments for LR-fuzzy numbers having the same membership function are analyzed. We apply a heuristic approach to approximate the cardinality constrained efficient frontier of the portfolio selection problem considering the below-mean absolute semi-deviation as a measure of risk. We also explore the impact of adding a Fuzzy Value-at-Risk measure that supports the investor’s choices. A computational study of our multi-objective evolutionary approach and the performance of the credibility model are presented with a data set collected from the Spanish stock market.