The Quantitative Diversity Index in Multi-Objective Portfolio Model

Seyed Babak Ebrahimi,Nasser Safaie,Mostafa Abdollahi Moghadam

doi:10.30699/ijf.2021.125101

Seyed Babak Ebrahimi, Nasser Safaie + Show 1 more

Open Access

https://doi.org/10.30699/ijf.2021.125101

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Abstract

The primary purpose of investors is maximizing the utility that is characterized by two essential criteria include risk and return. Regarding investors' uncertainty about the future, one of the main ways to reduce risk is to diversify the investment portfolio. In this research, we proposed an index conducted by Euclidean distance for assessing portfolio diversity. Besides, we designed a multi-objective model to select optimal stock portfolios with considering value at risk (VaR), which is one of the critical indicators of unacceptable risk, portfolio Beta as systematic risk, and portfolio variance as unsystematic risk simultaneously. The model presented in this paper aims to maximize diversification while minimizing value at risk and stock risks. Furthermore, maximizing returns are considered as a limitation of this model. Since the proposed model is nonlinear and concerning computational complexity, it is NP-hard; therefore, we utilized the PSO and the GE metaheuristic algorithms that are improved for solving multi-objective problems to solve the model. The results of the model implementation in multiple iterations showed that the average yield of selected portfolios by the model is higher than the desirable condition. The evaluation of stock performance indicators also shows the satisfactory performance of the multi-objective model.

Highlights

The current literature highlights the importance of choosing the optimal set of investments in the capital market to maximize the expected wealth of investors
This study contributes to the literature as follows: First, we develop an innovative multi-objective mathematical model by combining value at risk (VaR) and portfolio diversification as a task to optimize portfolio, stock returns, and risks
This study introduces the Euclidean distance criterion as a measure of stock portfolio diversification and uses a multi-objective model attempts to select optimal stock portfolios

Summary

Introduction

The current literature highlights the importance of choosing the optimal set of investments in the capital market to maximize the expected wealth of investors. An investor needs proper methods or criteria to identify and measure the potential value of each investment opportunity. These criteria should be sufficiently reliable and accurate so that investors can decide with high confidence and low risk. Risk and returns are two main critical factors in capital market decisions. The selection of a set of stocks, called portfolio, is usually driven by the interaction between risk and return. The higher the risk of an investment, demands a higher return (Jones, 2010)

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