IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v06y2003i07ns021902490300216x.html
   My bibliography  Save this article

Multiple Optimal Solutions in the Portfolio Selection Model with Short-Selling

Author

Listed:
  • A. Schianchi

    (Dipartimento di Economia dell' Università di Parma, via Kennedy 6, 43100 Parma, Italy)

  • L. Bongini

    (Institute Nazionale di Fisica della Materia, Largo E. Fermi 2, 50125 Firenze, Italy)

  • M. D. Esposti

    (Dipertimento di Matematica dell' Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy)

  • C. Giardinà

    (Dipertimento di Matematica dell' Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy)

Abstract

In this paper an extension of the Lintner model [1] is considered: the problem of portfolio optimization is studied when short-selling is allowed through the mechanism of margin requirements. This induces a non-linear constraint on the wealth. When interest on deposited margin is present, Lintner ingeniously solved the problem by recovering the unique optimal solution of the linear model (no margin requirements). In this paper an alternative and more realistic approach is explored: the nonlinear constraint is maintained but no interest is perceived on the money deposited against short-selling. This leads to a fully non-linear problem which admits multiple and unstable solutions very different among themselves but corresponding to similar risk levels. Our analysis is built on a seminal idea by Galluccio, Bouchaud and Potters [3], who have re-stated the problem of finding solutions of the portfolio optimization problem in futures markets in terms of a spin glass problem. In order to get the best portfolio (i.e. the one lying on the efficiency frontier), we have to implement a two-step procedure. A worked example with real data is presented.

Suggested Citation

  • A. Schianchi & L. Bongini & M. D. Esposti & C. Giardinà, 2003. "Multiple Optimal Solutions in the Portfolio Selection Model with Short-Selling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 703-720.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:07:n:s021902490300216x
    DOI: 10.1142/S021902490300216X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021902490300216X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021902490300216X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Szilard Pafka & Imre Kondor, 2001. "Noisy Covariance Matrices and Portfolio Optimization," Papers cond-mat/0111503, arXiv.org.
    2. V. Plerou & P. Gopikrishnan & B. Rosenow & L. A. N. Amaral & T. Guhr & H. E. Stanley, 2001. "A Random Matrix Approach to Cross-Correlations in Financial Data," Papers cond-mat/0108023, arXiv.org.
    3. B. Rosenow & V. Plerou & P. Gopikrishnan & H. E. Stanley, 2001. "Portfolio Optimization and the Random Magnet Problem," Papers cond-mat/0111537, arXiv.org.
    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. Miceli, M.A. & Susinno, G., 2004. "Ultrametricity in fund of funds diversification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 95-99.
    2. McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "On CAPM and Black–Scholes differing risk-return strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 170-177.
    3. Kondor, Imre & Pafka, Szilard & Nagy, Gabor, 2007. "Noise sensitivity of portfolio selection under various risk measures," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1545-1573, May.
    4. Wilcox, Diane & Gebbie, Tim, 2004. "On the analysis of cross-correlations in South African market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 294-298.
    5. McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "On CAPM and Black-Scholes, differing risk-return strategies," MPRA Paper 2162, University Library of Munich, Germany.
    6. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    7. Wilcox, Diane & Gebbie, Tim, 2007. "An analysis of cross-correlations in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 584-598.
    8. khoojine, Arash Sioofy & Han, Dong, 2019. "Network analysis of the Chinese stock market during the turbulence of 2015–2016 using log-returns, volumes and mutual information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1091-1109.

    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:wsi:ijtafx:v:06:y:2003:i:07:n:s021902490300216x. See general information about how to correct material in RePEc.

    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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.