Expected Rate of Return from Financial Portfolio – the Case of Triangular Fuzzy Present Value

Krzysztof Piasecki

Abstract


The main aim of this article is to present an uncomplicated method of estimating return rate on a portfolio of securities with Present Values presented as triangular fuzzy numbers. Determined return rates on the securities are not triangular fuzzy numbers. Despite this, we achieved a solution that is based on the arithmetic of triangular fuzzy numbers. The whole considerations are illustrated by a numerical example.


Keywords


financial portfolio; present value; fuzzy number; return rate

Full Text:

PDF (Język Polski)

References


Buckley I.J., The fuzzy mathematics of finance, “Fuzzy Sets and Systems” 1987, Vol. 21, DOI: https://doi.org/10.1016/0165-0114(87)90128-X.

Caplan B., Probability, common sense, and realism: a reply to Hulsmann and Block, “The Quarterly Journal of Austrian Economics” 2001, Vol. 4(2).

Chiu C.Y., Park C.S., Fuzzy Cash Flow Analysis Using Present Worth Criterion. “The Engineering Economist” 1994, Vol. 39(2), DOI: https://doi.org/10.1080/00137919408903117.

Czerwiński Z., Matematyka na usługach ekonomii, PWN, Warszawa 1969.

Duan L., Stahlecker P., A portfolio selection model using fuzzy returns, “Fuzzy Optimization and Decision Making” 2011, Vol. 10(2), DOI: https://doi.org/10.1007/s10700-011-9101-x.

Dubois D., Prade H., Fuzzy real algebra: some results, “Fuzzy Sets and Systems” 1979, Vol. 2, DOI: https://doi.org/10.1016/0165-0114(79)90005-8.

Fang Y., Lai K.K., Wang S., Fuzzy Portfolio Optimization. Theory and Methods, Lecture Notes in Economics and Mathematical Systems 609, Springer, Berlin 2008.

Greenhut J.G., Norman G., Temponi C., Towards a fuzzy theory of oligopolistic competition, IEEE Proceedings of ISUMA-NAFIPS, 1995.

Guo S., Yu L., Li X., Kar S., Fuzzy multi-period portfolio selection with different investment horizons, “European Journal of Operational Research” 2016, Vol. 254(3), DOI: https://doi.org/10.1016/j.ejor.2016.04.055.

Gupta P., Mehlawat M.K., Inuiguchi M., Chandra S., Fuzzy Portfolio Optimization, Advances in Hybrid Multi-criteria Methodologies, Studies in Fuzziness and Soft Computing 316, Springer, Berlin 2014.

Gutierrez I., Fuzzy numbers and Net Present Value, “Scand. J. Mgmt.” 1989, Vol. 5(2), DOI: https://doi.org/10.1016/0956-5221(89)90021-3.

Huang X., Portfolio selection with fuzzy return, “Journal of Intelligent & Fuzzy Systems” 2007a, Vol. 18(4).

Huang X., Two new models for portfolio selection with stochastic returns taking fuzzy information, “European Journal of Operational Research” 2007b, Vol. 180(1), DOI: https://doi.org/10.1016/j.ejor.2006.04.010.

Kaplan S., Barish N.N., Decision-Making Allowing Uncertainty of Future Investment Opportunities, “Management Science” 1967, Vol. 13(10), B569-B577.

Knight F.H., Risk, Uncertainty, and Profit, Hart, Schaffner & Marx, Houghton Mifflin Company, Boston MA 1921.

Kolmogorov A.N., Grundbegriffe der Wahrscheinlichkeitsrechnung, Julius Springer, Berlin 1933, DOI: https://doi.org/10.1007/978-3-642-49888-6.

Kuchta D., Fuzzy capital budgeting, “Fuzzy Sets and Systems” 2000, Vol. 111, DOI: https://doi.org/10.1016/s0165-0114(98)00088-8.

Lambalgen M. von, Randomness and foundations of probability: von Mises’ axiomatization of random sequences, Institute of Mathematical Statistics Lecture Notes – Monograph Series 30, Springer, Berlin 1996.

Lesage C., Discounted cash-flows analysis. An interactive fuzzy arithmetic approach, “European Journal of Economic and Social Systems” 2001, Vol. 15(2), DOI: https://doi.org/10.1051/ejess:2001115.

Li C., Jin J., Fuzzy Portfolio Optimization Model with Fuzzy Numbers, Advances in Intelligent and Soft Computing 100, Springer, Berlin 2011.

Liu Y.-J., Zhang W.-G., Fuzzy portfolio optimization model under real constraints, “Insurance: Mathematics and Economics” 2013, Vol. 53(3), DOI: https://doi.org/10.1016/j.insmatheco.2013.09.005.

Markowitz H.S.M., Portfolio Selection, “Journal of Finance” 1952, Vol. 7(1), DOI: https://doi.org/10.1111/j.1540-6261.1952.tb01525.x.

Mehlawat M.K., Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels, “Information Science” 2016, Vol. 345, DOI: https://doi.org/10.1016/j.ins.2016.01.042.

Mises L. von, The Ultimate Foundation of Economic Science An Essay on Method, D. Van Nostrand Company, Inc., Princeton 1962.

Mises R. von, Probability, statistics and truth, The Macmillan Company, New York 1957.

Piasecki K., Behavioural present value, “SSRN Electronic Journal” 2011a, DOI: https://doi.org/10.2139/ssrn.1729351.

Piasecki K., Rozmyte zbiory probabilistyczne jako narzędzie finansów behawioralnych, Wydawnictwo UE, Poznań 2011b, DOI: https://doi.org/10.13140/2.1.2506.6567.

Piasecki K., Siwek J., Behavioural Present Value Defined as Fuzzy Number – a New Approach, “Folia Oeconomica Stetinensia” 2015, Vol. 23(2), DOI: https://doi.org/10.1515/foli-2015-0033.

Piasecki K., Siwek J., Oczekiwana stopa zwrotu z portfela – przypadek trójkątnych rozmytych wartości bieżących, „Przegląd Statystyczny” 2017, t. 64.

Saborido R., Ruiz A.B., Bermúdez J.D., Vercher E., Luque M., Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection, “Applied Soft Computing” 2016, Vol. 39, DOI: https://doi.org/10.1016/j.asoc.2015.11.005.

Sadowski W., Decyzje i prognozy, PWN, Warszawa 1997.

Sheen J.N., Fuzzy financial profitability analyses of demand side management alternatives from participant perspective, “Information Sciences” 2005, Vol. 169, DOI: https://doi.org/10.1016/j.ins.2004.05.007.

Siwek J., Portfel dwuskładnikowy – studium przypadku dla wartości bieżącej danej jako trójkątna liczba rozmyta, „Studia Ekonomiczne. Zeszyty Naukowe Uniwersytetu Ekonomicznego w Katowicach” 2015, z. 241.

Tsao C.-T., Assessing the probabilistic fuzzy Net Present Value for a capital. Investment choice using fuzzy arithmetic, “Journal of Chinese Institute of Industrial Engineers” 2005, Vol. 22(2), DOI: https://doi.org/10.1080/10170660509509282.

Ustawa z dnia 24 września 1994 r. o rachunkowości (Dz.U. 2017, nr 0, poz. 1089 z późn. zm.).

Ward T.L., Discounted fuzzy cash flow analysis, Fall Industrial Engineering Conference Proceedings, 1985.

Wu X.-L., Liu Y.K., Optimizing fuzzy portfolio selection problems by parametric quadratic programming, “Fuzzy Optimization and Decision Making” 2012, Vol. 11(4), DOI: https://doi.org/10.1007/s10700-012-9126-9.

Zadeh L., Fuzzy sets, “Information and Control” 1965, Vol. 8, DOI: https://doi.org/10.1016/s0019-9958(65)90241-x.

Zhang X., Zhang W.-G., Xiao W., Multi-period portfolio optimization under possibility measures, “Economic Modelling” 2013, Vol. 35, DOI: https://doi.org/10.1016/j.econmod.2013.07.023.




DOI: http://dx.doi.org/10.17951/h.2017.51.5.221
Date of publication: 2017-12-22 12:02:51
Date of submission: 2017-05-02 20:05:57


Statistics


Total abstract view - 692
Downloads (from 2020-06-17) - PDF (Język Polski) - 0

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Krzysztof Piasecki

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.