Using the nonlinear GRG algorithm to build the optimal stock portfolio

Maitham Rabee Hadi Al-Hassnawi, Sara Arif Abnea Al-Jubouri

THE IRAQI MAGAZINJE FOR MANAGERIAL SCIENCES
2022, Volume 18, Issue 72, Pages 36-55

Abstract

The concept of diversification is the essence of what was brought by Markowitz’s modern portfolio theory in 1952, if Markowitz gave a description of the efficient frontier that constitutes a group of efficient portfolios that lead to the highest return at a certain level of risk or that lead to the lowest risk at a certain level of return in preparation for determining the portfolio optimal risk. Despite the development brought about by the modern portfolio theory, it suffers from the difficulty of its practical application represented by the problem of quadratic programming. In this study, we will solve the problem of quadratic programming in preparation for enabling the investor to choose the optimal portfolio through the nonlinear optimization algorithm called the nonlinear generalized reduced gradient algorithm (GRG).

Keywords

portfolio optimum, nonlinear generalized reduced gradient, GRG algorithm, efficient frontier, modern portfolio theory.