Building the optimal stock portfolio by solving the system of simultaneous equations
“An Analytical study in the Iraq Stock Market”
Thesis submitted by
Marwa Abdul Sattar Jabbar
To the Council of the College of Administration and Economics – Karbala University It is part of the requirements for a Philosophy Doctorate degree of sciences in Banking and Financial sciences
Supervised by
Prof. Dr.Maitham Rabee Hadi Al-Hassnawi
Abstract
The choice of the optimal portfolio is one of the most important arguments in the field of contemporary finance and investment. The first solution to this argument is Markowitz (1952). The simplistic models and expansions followed to reach the optimal portfolio with a combination of components that achieve the best exchange between return and risk. Each security available for investment has uncertain results, which implies that it is risky and since the portfolio is a combination of securities, the main argument is to choose the optimal portfolio from among the possible portfolios, and the simplistic method most widely used to solve the portfolio selection problem for Marquitz was the simple staging method which Establishing specific assumptions about why stocks moved with one another, which simplified the Marquitz entry covariance matrix. This method and other simplistic methods have been proposed with the aim of simplifying the inputs required to predict the correlation matrix between stocks, but the empirical evidence about the extent to which these methods are capable of superior or at minimum match the accuracy of the Markowitz model has been different and confusing. So far, no method has been proposed that is capable of that, since the simplification of all these methods came at the expense of the accuracy and optimization of the construction.
This study attempts to propose and test the efficacy of the latest method in construction, represented by the method of solving simultaneous equations. The idea of this method is based on the idea of converting the properties of individual papers into equations according to precise mathematical scientific rules and procedures, and then adopting a distinct method for solving these simultaneous equations, and the goal behind that is to determine the identity of the papers to be included in the optimal portfolio as well as the optimal weight to be invested in each A component of this portfolio, under the condition that short selling is not allowed and in the event that it is permitted according to the two different definitions (Standard and Lintner) and comparing the performance of the portfolios built in all these cases with each other. For the purpose of achieving the objectives of this study, the monthly closing price data was collected for a sample consisting of (41) stocks listed on the Iraq Stock Exchange during the period from March 2015 to March 2020, and by using a number of financial, mathematical and statistical methods, the study reached many conclusions. One of the most important of them is the ability of the method of solving the system of simultaneous equations to build a portfolio of risky stocks outperforming both the reference market portfolio and the portfolio based on the most simple methods, namely the simple ranking method, in all cases of short selling (disallow and allow according to the standard and Lintner definitions). In light of this, the study came out with a number of recommendations, perhaps the most important of which is the necessity of adopting investors in the Iraq Stock Exchange on the outputs of this study and adopting them as a roadmap in building their investment portfolios as it showed from the results of the sign in the field of optimal construction of risky stock portfolios.
