Markowitz Model Investment Portfolio Optimization: a Review Theory

Nurfadhlina Abdul Hali, Ari Yuliati


In the face of investment risk, investors generally diversify and form an investment portfolio consisting of several assets. The problem is the fiery proportion of funds that must be allocated to each asset in the formation of investment portfolios. This paper aims to study the optimization of the Markowitz investment portfolio. In this study, the Markowitz model discussed is that which considers risk tolerance. Optimization is done by using the Lagrangean Multiplier method. From the study, an equation is obtained to determine the proportion (weight) of fund allocation for each asset in the formation of investment portfolios. So by using these equations, the determination of investment portfolio weights can be determined by capital.


Investment risk, diversification, portfolio, the weight of fund allocation, optimization, Lagrange multiplier

Full Text:



Ardia, D. & Boudt, K. (2013). Implied Expected Returns and the Choice of a Mean-Variance Efficient Portfolio Proxy. Working Paper. AD´epartement de Finance, Assurance et Immobilier, Universite Laval, Quebec City (Quebec), Canada.

Bjork, T., Murgoci, A. & Zhou, X.Y. (2011). Mean-Variance Portfolio Optimization with State-Dependent Risk Aversion. Working Paper. Department of Finance, StockholmSchool of Economics, Box 6501, SE-113 83 Stockholm, SWEDEN. E-mail:

Garcia, Fernando, Jairo, A., & Javier, O. (2015). Mean-Variance Investment Strategy Applied in Emerging Financial Markets: Evidence From the Colombian Stock Market. Jurnal Mykolo Romerio Universitetas, 9 (2), 22-29.

Kamil, Anton, A., Chin, Y. F., & Kin, K. (2006). Portfolio Analysis Based On Markowitz Model. Journal of Statistics and Management Systems University Sains Malaysia, 9 (3), 519-536.

Kheirollah, A. & Bjarnbo, O., (2007), A Quantitative Risk Optimization of Markowitz Model: An Empirical Investigation on Swedish Large Cap List. Master Thesis, in Mathematics/Applied Mathematics, University Sweden, Department of Mathematics and Physics, 1.16205!MasterTheses.pdf

Mangram, M. (2013). A Simplified Perspective of the Markowitz Portfolio Theory. Global Journal of Business Research SMC University Switzerland,7 (1), 59-70.

Panjer, H.H., Boyle, D.D., Cox, S.H., Dufresne, D., Gerber, H.U., Mueller, H.H., Pedersen, H.W., & Pliska, S.R. (1998). Financial Economics. With Applications to Investments, Insurance, and Pensions. Schaumberg, Illinois: the Actuarial Foundation.

Parmar, Chetna. (2014). Portfolio Selection using Min-Max Approach; Selected Bank in India: Markowitz Model. International Journal of Advanced Research in Computer Science and Management Studies RK University, 2 (1), 11-17.

Ruppert, D.(2004).Statistics and Finance: An Introduction. Springer-Verlag, New York.

Sirucek, Martin & Lukas Kren. (2015). Application of Markowitz Portfolio Theory by Building Optimal Portfolio on the Us Stock Market. Jurnal Mendel University, 63 (4), 1375-1386.



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Published By: 

IJRCS: Jalan Riung Ampuh No. 3, Riung Bandung, Kota Bandung 40295, Jawa Barat, Indonesia

Indexed By: 

width= width=  width= width= width= width=