Selecting Optimal Portfolio Using Multi-objective Extended Markowitz Model and Harmony Search Algorithm

Abstract

Morkowitz model is one of the well-known models in portfolio selection problem. This paper presents an extended version of Markowitz mean semi variance portfolio selection model. The extended model considers sets of constraints including cardinality, bounds on holdings, sector capitalization, an entropy constraints. It also considers transaction costs. The problem model has a combinatorial structure. Due to the NP-hard characteristic of the resulting mathematical model, Harmony Search Meta-heuristic algorithm was used to solve the model. Since the proposed mathematical model is a multi-objective one, the Pareto solution approach was applied. To investigate the applicability of the proposed model, a data set of ten stocks from Tehran Stock Exchange, from March 2011 to December 2015, is used as a case study. The obtained efficient frontier indicates the applicability of the harmony algorithm in the optimization model. Research results show that the proposed model is efficiently is capable to consider the investment portfolio requirements quite well.

Keywords

• portfolio optimization
• markowitz model
• harmony search algorithm
• pareto approach