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Stock portfolio selection under unstable uncertainty via fuzzy mean-semivariance model

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Abstract

Investment decision making, or portfolio selection, can be a complicated process affected by many factors. However, there is no doubt that two aspects are usually understood by investors most intensively—return and risk. What is the most suitable combination of return and risk for a particular investment strategy? Well-known mean–variance model can answer this question. However, this concept is burdened by some drawbacks. The main one is a type of implemented risk measure. To eliminate this shortage, a concept of semivariance was developed. However, this improvement cannot resist an instability of the typical uncertainty, i. e. unstable development of return and risk over time. This significant aspect of an investment decision making can be considered by a fuzzified mean-semivariance model. Then the vague return and risk are designed as triangular fuzzy numbers. The proposed fuzzy mean-semivariance model is solved by fuzzy programming techniques. Contribution of a designed methodological process for a portfolio selection under unstable uncertainty is demonstrated on making a portfolio from the stocks traded on the RM-SYSTÉM Czech Stock Exchange. The results are analyzed and confronted with output of more commonly used mean-semivariance model from the algorithmic-application perspective.

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Notes

  1. Asset also represents the market portfolio necessary for fuzzy semivariance concept.

  2. The market portfolio from fourteen stocks is composed under naive strategy.

  3. The matrices of semicovariances are large to be included in this paper.

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Acknowledgements

The research project was supported by Grant No. IGA F4/42/2021 of the Internal Grant Agency, Faculty of Informatics and Statistics, Prague University of Economics and Business, and also was processed with contribution of long-term institutional support of research activities by Faculty of Informatics and Statistics, Prague University of Economics and Business.

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  1. Department of Econometrics, Faculty of Informatics and Statistics, Prague University of Economics and Business, W. Churchill Sq. 4, Prague, Czech Republic

    Adam Borovička

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Correspondence to Adam Borovička.

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Borovička, A. Stock portfolio selection under unstable uncertainty via fuzzy mean-semivariance model. Cent Eur J Oper Res 30, 595–616 (2022). https://doi.org/10.1007/s10100-021-00791-0

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