Guaranteed Rate of Return for Excess Investment in a Fuzzy Portfolio Analysis
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Guaranteed Rate of Return for Excess Investment in a Fuzzy Portfolio Analysis Ruey-Chyn Tsaur1 • Chien-Liang Chiu2 • Yin-Yin Huang1
Received: 2 May 2020 / Revised: 23 September 2020 / Accepted: 15 October 2020 Taiwan Fuzzy Systems Association 2020
Abstract With increasing profit in securities investment, portfolio analysis has become a major topic for investors. We propose a fuzzy portfolio model as it is an efficient portfolio selection method associated with uncertain or vague returns. Although many researchers focus on studying the fuzzy portfolio model, they do not consider excess investment based on the selected guaranteed rates of return for some securities. To manage such an investment, a new fuzzy return function—where some securities are considered for excess investment based on the selected guaranteed rate of return—is introduced to improve the possibilistic mean and variance values, leading to a revised fuzzy portfolio model. Accordingly, to set certain securities for excess investment in the fuzzy return function, efficient portfolios for each selected guaranteed rate of return can be obtained under different levels of investment risk. Finally, we present a numerical example of a portfolio selection problem to illustrate the proposed model. This example shows that the expected rate of return of a lower guaranteed rate of return is larger than that of a higher guaranteed rate of return under different levels of investment risks. The portfolio analysis with some guaranteed rate of returns can provide more invested risk selection.
& Ruey-Chyn Tsaur [email protected] 1
Department of Management Sciences, Tamkang University, No.151, Yingzhuan Rd, Tamsui Dist, New Taipei City 25137, Taiwan, ROC
2
Department of Banking and Finance, Tamkang University, No.151, Yingzhuan Rd, Tamsui Dist, New Taipei City 25137, Taiwan, ROC
Keywords Fuzzy portfolio model Efficient portfolio Guaranteed rate of return Excess investment
1 Introduction Markowitz [15] proposed portfolio selection to maximize the expected value of a portfolio’s return under certain variability constraints or to minimize the variability in a portfolio’s return under certain expected value constraints. Investors use portfolio selection as a tool to predict investment returns accurately to manage future uncertainties, and most portfolio selection models are formulated based on the probability theory. The mean–variance portfolio selection method has been researched by Sharpe [21], Merton [16], Perold [18], Pang [17], Vo¨ro¨s [25], Best and Grauer [2], Best and Hlouskova [3]. Tanaka et al. [22] proposed a fuzzy portfolio model that extends traditional probability measures into fuzzy possibilities for investments made under uncertain economic environments. Huang [10] proposed two fuzzy mean-semi-variance models to deal with situations wherein investors intend to obtain high returns while avoiding risk by eliminating asymmetry in the degree of return distributions. Zhang and Nie [28, 29] presented the notions of lower and upper possibilistic
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