IDEAS home Printed from https://ideas.repec.org/a/blg/reveco/v69y2017i5p8-21.html
   My bibliography  Save this article

Portfolio Optimization - Application Of Sharpe Model Using Lagrange

Author

Listed:
  • BRATIAN Vasile

    (Lucian Blaga University of Sibiu)

Abstract

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 Sciencess, vol. 69(5), pages 8-21, December.
  • Handle: RePEc:blg:reveco:v:69:y:2017:i:5:p:8-21
    as

    Download full text from publisher

    File URL: http://economice.ulbsibiu.ro/revista.economica/archive/69501bratian.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    3. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    4. 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.
    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. Mark Rubinstein, 2002. "Markowitz's "Portfolio Selection": A Fifty-Year Retrospective," Journal of Finance, American Finance Association, vol. 57(3), pages 1041-1045, June.
    7. 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.
    8. 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.
    9. 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.
    10. 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-.
    11. 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.
    12. repec:agr:journl:v:9(598):y:2014:i:9(598):p:7-22 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Kourtis, Apostolos & Dotsis, George & Markellos, Raphael N., 2012. "Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2522-2531.
    3. Jitka Janová, 2012. "Crop planning optimization model: the validation and verification processes," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 451-462, September.
    4. Panos Xidonas & George Mavrotas, 2014. "Comparative issues between linear and non-linear risk measures for non-convex portfolio optimization: evidence from the S&P 500," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1229-1242, July.
    5. Jongbin Jung & Seongmoon Kim, 2017. "Developing a dynamic portfolio selection model with a self-adjusted rebalancing method," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 766-779, July.
    6. Zhao Zhao & Olivier Ledoit & Hui Jiang, 2019. "Risk reduction and efficiency increase in large portfolios: leverage and shrinkage," ECON - Working Papers 328, Department of Economics - University of Zurich, revised Jan 2020.
    7. Hannart, Alexis & Naveau, Philippe, 2014. "Estimating high dimensional covariance matrices: A new look at the Gaussian conjugate framework," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 149-162.
    8. Leon, T. & Liern, V. & Vercher, E., 2002. "Viability of infeasible portfolio selection problems: A fuzzy approach," European Journal of Operational Research, Elsevier, vol. 139(1), pages 178-189, May.
    9. Maurizio Daniele & Winfried Pohlmeier & Aygul Zagidullina, 2018. "Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices," Working Paper Series of the Department of Economics, University of Konstanz 2018-07, Department of Economics, University of Konstanz.
    10. Santos, André A.P. & Nogales, Francisco J. & Ruiz, Esther & Dijk, Dick Van, 2012. "Optimal portfolios with minimum capital requirements," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1928-1942.
    11. Menezes, Mozart B.C. & Ruiz-Hernández, Diego & Verter, Vedat, 2016. "A rough-cut approach for evaluating location-routing decisions via approximation algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 89-106.
    12. Francesco Lautizi, 2015. "Large Scale Covariance Estimates for Portfolio Selection," CEIS Research Paper 353, Tor Vergata University, CEIS, revised 07 Aug 2015.
    13. Yanling Chu & Xiaoju Zhang & Zhongzhen Yang, 2017. "Multiple quay cranes scheduling for double cycling in container terminals," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-19, July.
    14. Cinzia Colapinto & Raja Jayaraman & Simone Marsiglio, 2017. "Multi-criteria decision analysis with goal programming in engineering, management and social sciences: a state-of-the art review," Annals of Operations Research, Springer, vol. 251(1), pages 7-40, April.
    15. An, Yu & Zhang, Yu & Zeng, Bo, 2015. "The reliable hub-and-spoke design problem: Models and algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 103-122.
    16. Dollevoet, Twan & van Essen, J. Theresia & Glorie, Kristiaan M., 2018. "Solution methods for the tray optimization problem," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1070-1084.
    17. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2015. "A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 238-255.
    18. Iloglu, Suzan & Albert, Laura A., 2018. "An integrated network design and scheduling problem for network recovery and emergency response," Operations Research Perspectives, Elsevier, vol. 5(C), pages 218-231.
    19. Marco Neffelli, 2018. "Target Matrix Estimators in Risk-Based Portfolios," Risks, MDPI, Open Access Journal, vol. 6(4), pages 1-20, November.
    20. Xie, Siyang & Ouyang, Yanfeng, 2019. "Reliable service systems design under the risk of network access failures," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 1-13.

    More about this item

    Keywords

    modern portfolio theory; Sharpe model; lagrangian;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:blg:reveco:v:69:y:2017:i:5:p:8-21. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/feulbro.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Eduard Alexandru Stoica (email available below). General contact details of provider: https://edirc.repec.org/data/feulbro.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.