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

Authors

  • Marwa Abdel Sattar Jabbar Economics and Administration College - Karbala University
  • Maitham Rabie Hadi Economics and Administration College - Karbala University

Keywords:

optimum stock portfolio, system of simultaneous equations

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.

Author Biographies

Marwa Abdel Sattar Jabbar , Economics and Administration College - Karbala University

مدرس مساعد

 

Maitham Rabie Hadi , Economics and Administration College - Karbala University

استاذ دكتور 

ادارة مالية 

References

Adams, Andrew T., Booth, Philip M., Bowie, David C., Freeth, Della S., Investment Mathematics, John Wiley & Sons Ltd,2003.

AYGoREN, Hakan, SARITAŞ, Hakan, IS A CORRECTION NECESSARY FOR BETA ESTIMATION?, Akdeniz İ.İ.B.F. Dergisi (14) 2007.

BODIE, ZVI, KANE, ALEX& ALAN J. MARCUS, Investments, tenth ed, McGraw-Hill Education, New York,2014.

Brealey, Richard A., Myers, Stewart C., Allen, Franklin, Principles of Corporate Finance, TENTH EDITION, McGraw-Hill/Irwin,2011.

Brealey, Richard A., Myers, Stewart C., Principles of Corporate Finance, Seventh ed, The McGraw−Hill Companies, 2003.

Chen ,Son-Nan , Brown, Stephen J. , Estimation Risk and Simple Rules for Optimal Portfolio Selection, The Journal of Finance, Vol. 38, No. 4,1983.

Chincarini,Ludwig B.,Kim, Daehwan ,Quantitave Equity portfolio management An Active Approach to portfolio construction and management, McGraw-Hill, united states of America,2004.

Corter ,James E. , Chen, YuhJia, DO INVESTMENT RISK TOLERANCE ATTITUDES PREDICT PORTFOLIO RISK?, Journal of Business and Psychology, Vol. 20, No. 3, 2005.

CUTHBERTSON, KEITH, NITZSCHE, DIRK, QUANTI T A T I V E F I N A N C I A L E C O N O M I C S STOCKS, BONDS AND FOREIGN EXCHANGE, Second Edition, John Wiley & Sons Ltd,2004.

Djamaluddin, Said, Kurnia, Nanang, Djumarno, Analysis of Return to Beta in Forming the Optimal Portfolio of Stocks on LQ45 in Indonesia Stock Exchange, International Journal of Business Marketing and Management, Volume 2 Issue 9,2017.

ELTON, EDWIN J., GRUBER, MARTIN J., BROWN, STEPHEN J., GOETZMANN, WILLIAM N.,MODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS, NINTH EDITION, John Wiley & Sons, Inc.,2014.

Elton, Edwin J., Gruber, Martin J., Modern Portfolio Theory ,1950 to Date, Working Paper series ,1997.

FABOZZI ,FRANK J., GUPTA ,FRANCIS, MARKOWITZ, HARRY M., The Legacy of Modern Portfolio Theory, THE JOURNAL OF INVESTING,2002.

Faisal ,Syed Mohammad , Khan, Ahmad Khalid , Estimating Beta (β) Values of Stocks in the Creation of Diversified Portfolio - A Detailed Study Applied Economics and Finance, Vol. 5, No. 3,2018.

Garcia ,Teresa, Borrego, Daniel, MARKOWITZ EFFICIENT FRONTIER AND CAPITAL MARKET LINE – EVIDENCE FROM THE PORTUGUESE STOCK MARKET, The European Journal of Management Studies, Vol 22, Issue 1, 2017.

Garivaltis, Alex, Game-Theoretic Optimal Portfolios for Jump Diffusions, games journal,2019.

Haubner ,Georges , The Generalized Treynor Ratio: A Note,2003.

Ivanova, M., Dospatliev, L., APPLICATION OF MARKOWITZ PORTFOLIO OPTIMIZATION ON BULGARIAN STOCK MARKET FROM 2013 TO 2016, International Journal of Pure and Applied Mathematics ,Vol. 117, No. 2 2017.

Jared, Adam, The Alpha and the Beta of Investing, Advisor Perspectives, Inc,2014.

اداء المحفظة المبنية بأسلوب حل المعادلات الانية  مقابل اداء محفظة السوق المرجعية ومحفظة التدريج البسيط بظل السماح بالبيع القصير

Published

2024-07-01

How to Cite

مروة عبد الستار جبار, & ميثم ربيع هادي. (2024). 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. Iraqi Journal for Administrative Sciences, 17(70), 25–51. Retrieved from https://mail.journals.uokerbala.edu.iq:8443/index.php/ijas/article/view/1888