Abstract
Given the unavailability of historical data, selecting portfolio by the Markowitz’s becomes difficult, if not impossible. In this particular situation expert opinion is the inevitable option. To cope with the nature of subjective data and their different types of inherent risks, we have developed the fuzzy-set based approach following the direction of the modern theory. Instead of the deployment of traditional probability distribution, six possibilistic shapes of fuzzy numbers have been proposed in order to simplify the translation of linguistic terms into fuzzy returns. The returns on assets are scaled according to their allocation percentages and combined by operations on fuzzy restrictions while optimized on centroids and other indices in fuzzy set theory. The demonstration has been carried out on several asset types and solved by the general-purpose genetic algorithm. The structure of fuzzy number is still preserved throughout the process and, as a result, breeds the resultant portfolio distinct.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Markowitz, H.: Portfolio selection. J. Finance 7(1), 77–91 (1952)
Markowitz, H.: Portfolio Selection: Efficient Diversification of Investments. Cowles Foundation for Research in Economics at Yale University, Wiley (1959). Monograph
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Hahn, J., Todd, P., Van der Klaauw, W.: Identification and estimation of treatment effects with a regression-discontinuity design. Econometrica 69(1), 201–209 (2001)
Aubin, J.P.: Cooperative fuzzy games. Math. Oper. Res. 6(1), 1–13 (1981)
Liu, Y., Liu, B.: Expected value operator of random fuzzy variable and random fuzzy expected value models. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 11(2), 195–215 (2003)
Huang, X.: A new perspective for optimal portfolio selection with random fuzzy returns. Inf. Sci. 177(23), 5404–5414 (2007)
Sirisrisakulchai, J., Autchariyapanitkul, K., Harnpornchai, N., Sriboonchitta, S.: Portfolio optimization of financial returns using fuzzy approach with NSGA-II algorithm. JACIII 19(5), 619–623 (2015)
Draeseke, R., Giles, D.E.: A fuzzy logic approach to modelling the New Zealand underground economy. Math. Comput. Simul. 59(1), 115–123 (2002)
Autchariyapanitkul, K., Hanpornchai, N., Sriboonchitta, S.: On tax management for unobserved utility using fuzzy logic: An investigation from Thailand underground economy. In: The Eleventh International Symposium on Management Engineering, pp. 36–42, July 2014
Breiman, L., et al.: Statistical modeling: The two cultures (with comments and a rejoinder by the author). Stat. Sci. 16(3), 199–231 (2001)
Boswell, S.B., Taylor, M.S.: A central limit theorem for fuzzy random variables. Fuzzy Sets Syst. 24(3), 331–344 (1987)
Shaheen, A.A., Fayek, A.R., AbouRizk, S.: Fuzzy numbers in cost range estimating. J. Constr. Eng. Manag. 133(4), 325–334 (2007)
Kaufmann, A., Gupta, M.M.: Fuzzy Mathematical Models in Engineering and Management Science. Elsevier Science Inc., New York (1988)
Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1(1), 3–28 (1978)
Puri, M.L., Ralescu, D.: A possibility measure is not a fuzzy measure. Fuzzy Sets Syst. 7(3), 311–313 (1982)
Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning–I. Inf. Sci. 8(3), 199–249 (1975)
Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning–II. Inf. Sci. 8(4), 301–357 (1975)
Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning–III. Inf. Sci. 9(1), 43–80 (1975)
Hanss, M.: Applied Fuzzy Arithmetic: An Introduction with Engineering Applications. Springer, Heidelberg (2005)
Meriam, J.L., Kraige, L.G.: Engineering Mechanics: Statics, 7th edn. Wiley, New York (2011)
American Heritage Dictionary of the English Language. 5 edn. Houghton Mifflin Harcourt Publishing Company, New York (2016)
Scrucca, L.: GA: A package for genetic algorithms in R. J. Stat. Softw. 53(4), 1–37 (2013)
Acknowledgements
The authors would like to express much of our appreciations to Ms. Duangthip Sirikanchanarak, Senior Economist - Bank of Thailand (BOT), for her contributions on the data used in the examples and to the Faculty of Economics, Chiang Mai University for financial support.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Rattanadamrongaksorn, T., Sirisrisakulchai, J., Sriboonjitta, S. (2016). Usages of Fuzzy Returns on Markowitz’s Portfolio Selection. In: Huynh, VN., Inuiguchi, M., Le, B., Le, B., Denoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2016. Lecture Notes in Computer Science(), vol 9978. Springer, Cham. https://doi.org/10.1007/978-3-319-49046-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-49046-5_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49045-8
Online ISBN: 978-3-319-49046-5
eBook Packages: Computer ScienceComputer Science (R0)