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An extension of Sharpe's single-index model: portfolio selection with expert betas

Author

Listed:
  • A Bilbao

    (Universidad de Oviedo)

  • M Arenas

    (Universidad de Oviedo)

  • M Jiménez

    (Universidad del País Vasco, San Sebastián)

  • B Perez Gladish

    (Universidad de Oviedo)

  • M V Rodríguez

    (Universidad de Oviedo)

Abstract

This paper presents an approach to the portfolio selection problem based on Sharpe's single-index model and on Fuzzy Sets Theory. In this sense, expert estimations about future Betas of each financial asset have been included in the portfolio selection model denoted as ‘Expert Betas’ and modelled as trapezoidal fuzzy numbers. Value, ambiguity and fuzziness are three basic concepts involved in the model which provide enough information about fuzzy numbers representing ‘Expert Betas’ and that are simple to handle. In order to select an optimal portfolio, a Goal Programming model has been proposed including imprecise investor's aspirations concerning asset's proportions of both, high-and low-risk assets. Semantics of these goals are based on the fuzzy membership of a goal satisfaction set. To illustrate the proposed model a real portfolio selection problem is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:57:y:2006:i:12:d:10.1057_palgrave.jors.2602133
    DOI: 10.1057/palgrave.jors.2602133
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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.
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    9. Tanaka, Hideo & Guo, Peijun, 1999. "Portfolio selection based on upper and lower exponential possibility distributions," European Journal of Operational Research, Elsevier, vol. 114(1), pages 115-126, April.
    10. Sakawa, Masatoshi & Nishizaki, Ichiro & Uemura, Yoshio, 2001. "Fuzzy programming and profit and cost allocation for a production and transportation problem," European Journal of Operational Research, Elsevier, vol. 131(1), pages 1-15, May.
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    Cited by:

    1. 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.
    2. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    3. Aouni, Belaid & Colapinto, Cinzia & La Torre, Davide, 2014. "Financial portfolio management through the goal programming model: Current state-of-the-art," European Journal of Operational Research, Elsevier, vol. 234(2), pages 536-545.
    4. Ghahtarani, Alireza & Najafi, Amir Abbas, 2013. "Robust goal programming for multi-objective portfolio selection problem," Economic Modelling, Elsevier, vol. 33(C), pages 588-592.
    5. Cinzia Colapinto & Davide Torre & Belaid Aouni, 2019. "Goal programming for financial portfolio management: a state-of-the-art review," Operational Research, Springer, vol. 19(3), pages 717-736, September.
    6. 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.
    7. D. Pla-Santamaria & M. Bravo, 2013. "Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from Dow Jones blue chips," Annals of Operations Research, Springer, vol. 205(1), pages 189-201, May.

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