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Portfolio Optimization. Application of the Markowitz Model Using Lagrange and Profitability Forecast

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  • Vasile BRÄ‚TIAN

    (Lucian Blaga University Sibiu, Romania)

Abstract

This paper presents the theoretical and applicative model elaborated by Harry Markowitz on the determination of the structure of the efficient securities portfolio. In this sense, in order to determine the structure of the efficient Markowitz portfolio (PE), a Lagrange function is built and minimized. Also, on the basis of the results obtained from the analysis, the profitability of the portfolio is modeled continuous time and determines the range of values in which it can be found over one year after the analysis period. The data used in our analysis are shares of financial investment companies (SIF), traded on the Bucharest Stock Exchange, and the distribution used in the analysis is lognormal. The structure of the portfolio obtained through the Markowitz model can be compared to the structure of the portfolio obtained through the Sharpe model from a previous article titled †Portfolio optimization - application of Sharpe model using Lagrange†(Brătian, 2017).

Suggested Citation

  • Vasile BRÄ‚TIAN, 2018. "Portfolio Optimization. Application of the Markowitz Model Using Lagrange and Profitability Forecast," Expert Journal of Economics, Sprint Investify, vol. 6(1), pages 26-34.
    • Handle: RePEc:exp:econcs:v:6:y:2018:i:1:p:26-34
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    References listed on IDEAS

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    1. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    2. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    3. Mark Rubinstein, 2002. "Markowitz's “Portfolio Selection”: A Fifty‐Year Retrospective," Journal of Finance, American Finance Association, vol. 57(3), pages 1041-1045, June.
    4. Edwin J. Elton & Martin J. Gruber, 1997. "Modern Portfolio Theory, 1950 to Date," New York University, Leonard N. Stern School Finance Department Working Paper Seires 97-3, New York University, Leonard N. Stern School of Business-.
    5. Elton, Edwin J. & Gruber, Martin J., 1997. "Modern portfolio theory, 1950 to date," Journal of Banking & Finance, Elsevier, vol. 21(11-12), pages 1743-1759, December.
    6. Marshall L. Fisher, 2004. "Comments on ÜThe Lagrangian Relaxation Method for Solving Integer Programming ProblemsÝ," Management Science, INFORMS, vol. 50(12_supple), pages 1872-1874, December.
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    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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