Usages of fuzzy returns on Markowitz’s portfolio selection

Abstract

© Springer International Publishing AG 2016. 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.