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Sharpe’s Ratio for Oriented Fuzzy Discount Factor

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  • Anna Łyczkowska-Hanćkowiak

    (Department of Finance, WSB University in Poznań, 61-895 Poznań, Poland)

Abstract

The analysis presented in this paper regards the security of a present value given as an ordered fuzzy number. The present value was estimated in an imprecise manner and supplemented by the forecast of its coming changes. A discount factor of such security is an ordered fuzzy number of the orientation identical to the oriented present value that determines it. All classical methods of portfolio analysis are based on the definition of the return rate. In the case of securities with a fuzzy present value, a discount factor is a better tool for portfolio analysis than the return rate, which implies the chosen methods of management of securities should be revised and transformed to equivalent methods based on a discount factor. This would enable the use of those methods in the case of a financial instrument of the oriented fuzzy present value. This paper presents example results of the realization of such a postulate. The main aim of the paper is to generalize Sharpe’s ratio to a case of investment recommendations management formulated for a security characterized by an oriented discount factor. A five-degree rating scale was used. The whole deliberation is illustrated by broad numerical examples.

Suggested Citation

  • Anna Łyczkowska-Hanćkowiak, 2019. "Sharpe’s Ratio for Oriented Fuzzy Discount Factor," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:272-:d:214492
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    References listed on IDEAS

    as
    1. Krzysztof Piasecki & Anna Łyczkowska-Hanćkowiak, 2019. "Representation of Japanese Candlesticks by Oriented Fuzzy Numbers," Econometrics, MDPI, vol. 8(1), pages 1-24, December.
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    7. Krzysztof Piasecki, 2013. "Behavioural present value," Papers 1302.0539, arXiv.org.
    8. Piasecki, Krzysztof, 2011. "Effectiveness of securities with fuzzy probabilistic return," MPRA Paper 46214, University Library of Munich, Germany.
    9. Krzysztof M. Piasecki, 2011. "Effectiveness of securities with fuzzy probabilistic return," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(2), pages 65-78.
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