2-Phase NSGA II: An Optimized Reward and Risk Measurements Algorithm in Portfolio Optimization

Seyedeh Eftekharian,Mohammad Shojafar,Shahaboddin Shamshirband

doi:10.3390/a10040130

Seyedeh Eftekharian, Mohammad Shojafar + Show 1 more

Open Access

https://doi.org/10.3390/a10040130

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Journal: Algorithms	Publication Date: Nov 28, 2017
Citations: 14	License type: CC BY 4.0

Affiliation: Sapienza University of Rome, Ton Duc Thang University

Abstract

Portfolio optimization is a serious challenge for financial engineering and has pulled down special attention among investors. It has two objectives: to maximize the reward that is calculated by expected return and to minimize the risk. Variance has been considered as a risk measure. There are many constraints in the world that ultimately lead to a non–convex search space such as cardinality constraint. In conclusion, parametric quadratic programming could not be applied and it seems essential to apply multi-objective evolutionary algorithm (MOEA). In this paper, a new efficient multi-objective portfolio optimization algorithm called 2-phase NSGA II algorithm is developed and the results of this algorithm are compared with the NSGA II algorithm. It was found that 2-phase NSGA II significantly outperformed NSGA II algorithm.

Highlights

Portfolio optimization is a bi-objective optimization problem aimed at maximizing the reward and at the same time, minimizing the risk
This study proposes a new evolutionary algorithm, called 2-phase non-dominated sorting genetic algorithm II (NSGA II), which is used for portfolio optimization problem
The problem of portfolio optimization with bi-objectives of risk and reward is solved by Multi-objective Evolutionary Algorithms

Summary

Introduction

Portfolio optimization is a bi-objective optimization problem aimed at maximizing the reward and at the same time, minimizing the risk. It is unlikely to come across an optimal solution in a multi-objective optimization problem since the employed objective functions often conflict with each other and it is impossible to optimize all objective functions at the same time. Apart from the constraint of ensuring that all money has been invested (budget constraint), there are some other constraints in the real-world [3]. One of these constraints is cardinality constraint that limits the number of assets in portfolio [4]

Objectives

Results

Conclusion