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Black-Litterman Model with Multiple Experts’ Linguistic Views

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

This paper presents fuzzy extensions of the Black-Litterman portfolio selection model. Black and Litterman identified two sources of information about expected returns and combined these two sources of information into one expected return formula. The first source of information is the expected returns that follow from the Capital Asset Pricing Model and thus should hold if the market is in equilibrium. The second source of information is comprised of the views held by investors. The presented extension, owing to the use of fuzzy random variables, includes two elements that are important from the point of view of practice: linguistic information and the views of multiple experts. The paper introduces the model extension step-by-step and presents an empirical example.

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Notes

  1. 1.

    The concept of FRV was introduced by Feron, R., 1976. Ensembles aleatoires flous. C.R. Acad. Sci. Paris, Ser. A (282), pp. 903–906.

  2. 2.

    Variance of FRV have several definition of variance (cf. [6]).

  3. 3.

    The aggregation operator can be considered as a separate research issue. This paper illustrates a new BL algorithm; so, vector p is set in the simplest way through the frequency of the experts answers, with the assumption that all the opinions are equivalent.

  4. 4.

    The WIG20 index is based on the value of a portfolio with shares in the 20 major and most liquid companies on the Warsaw Stock Exchange Main List.

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Acknowledgments

This work was supported by the Polish National Science Center under Grant 2013/09/N/HS4/03761.

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Authors and Affiliations

  1. Department of Applied Mathematics, Poznan University of Economics and Business, Poznań, Poland

    Marcin Bartkowiak & Aleksandra Rutkowska

Authors
  1. Marcin Bartkowiak
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  2. Aleksandra Rutkowska
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Corresponding author

Correspondence to Aleksandra Rutkowska .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Bartkowiak, M., Rutkowska, A. (2017). Black-Litterman Model with Multiple Experts’ Linguistic Views. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_5

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_5

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  • Online ISBN: 978-3-319-42972-4

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