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Portfolio Optimization - Application Of Sharpe Model Using Lagrange


  • BRATIAN Vasile

    (Lucian Blaga University of Sibiu)


This paper presents the model developed by William Sharpe regarding the determination of the structure of the effective securities portfolio and the application of this model on the Romanian capital market. In this respect, the portfolio of shares used in our analysis is a portfolio of shares of the financial investment companies (SIF), listed on the Bucharest Stock Exchange (BVB), and for determining the structure of the efficient portfolio, there is built and minimized a function of type Lagrange. Also, to support practitioners, the paper also presents a series of mathematical demonstrations of variables used in modeling.

Suggested Citation

  • BRATIAN Vasile, 2017. "Portfolio Optimization - Application Of Sharpe Model Using Lagrange," Revista Economica, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 69(5), pages 8-21, December.
  • Handle: RePEc:blg:reveco:v:69:y:2017:i:5:p:8-21

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    References listed on IDEAS

    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. A Bilbao & M Arenas & M Jiménez & B Perez Gladish & M V Rodríguez, 2006. "An extension of Sharpe's single-index model: portfolio selection with expert betas," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(12), pages 1442-1451, December.
    5. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    6. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    7. 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-.
    8. repec:agr:journl:v:9(598):y:2014:i:9(598):p:7-22 is not listed on IDEAS
    9. Gabriela Victoria ANGHELACHE & Constantin ANGHELACHE, 2014. "Diversifying the risk through portfolio investment," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(9(598)), pages 7-22, September.
    10. 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.
    11. 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.
    12. Panait, Iulian & Diaconescu, Tiberiu, 2012. "Particularități ale aplicării teoriei moderne a portofoliului in cazul acțiunilor listate la Bursa de Valori București
      [Particularities of applying Modern Portfolio Theory on the Romanian capital m
      ," MPRA Paper 44248, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    More about this item


    modern portfolio theory; Sharpe model; lagrangian;

    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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