Solving the system of simultaneous equations as a simplifying method of Markowitz model to build the optimal stock portfolio when short selling is allowed

Analytical study of the Iraqi Stock Exchange

Abstract

Each available security 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 most widely used simplistic method to solve the portfolio selection problem for Markowitz 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, in light of allowing short selling and comparing the performance of the portfolios built in all these cases with each other.