Portfolio optimization using the generalized reduced gradient nonlinear algorithm

Abstract

Purpose This study aims to utilize the mean–variance optimization framework of Markowitz (1952) and the generalized reduced gradient (GRG) nonlinear algorithm to find the optimal portfolio that maximizes return while keeping risk at minimum. Design/methodology/approach This study applies the portfolio optimization concept of Markowitz (1952) and the GRG nonlinear algorithm to a portfolio consisting of the 30 leading stocks from the three different sectors in Amman Stock Exchange over the period from 2009 to 2013. Findings The selected portfolios achieve a monthly return of 5 per cent whilst keeping risk at minimum. However, if the short-selling constraint is relaxed, the monthly return will be 9 per cent. Moreover, the GRG nonlinear algorithm enables to construct a portfolio with a Sharpe ratio of 7.4. Practical implications The results of this study are vital to both academics and practitioners, specifically the Arab and Jordanian investors. Originality/value To the best of the author’s knowledge, this is the first study in Jordan and in the Arab world that constructs optimum portfolios based on the mean–variance optimization framework of Markowitz (1952) and the GRG nonlinear algorithm.