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Mathematics 2019, 7(3), 272; https://doi.org/10.3390/math7030272

Sharpe’s Ratio for Oriented Fuzzy Discount Factor

Department of Finance, WSB University in Poznań, 61-895 Poznań, Poland
Received: 10 January 2019 / Revised: 1 March 2019 / Accepted: 12 March 2019 / Published: 16 March 2019
(This article belongs to the Special Issue Advanced Methods in Mathematical Finance)
PDF [674 KB, uploaded 16 March 2019]

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.
Keywords: Sharpe’s ratio; ordered fuzzy number; fuzzy oriented discount factor Sharpe’s ratio; ordered fuzzy number; fuzzy oriented discount factor
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Łyczkowska-Hanćkowiak, A. Sharpe’s Ratio for Oriented Fuzzy Discount Factor. Mathematics 2019, 7, 272.

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