A Mean-Variance Hybrid-Entropy Model for Portfolio Selection with Fuzzy Returns

Zhou, Rongxi; Zhan, Yu; Cai, Ru; Tong, Guanqun

doi:10.3390/e17053319

Cited by 18 publications

(12 citation statements)

References 22 publications

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“…In fuzzy space, stock yields are defined as triangular fuzzy random variables. Detail processes can be referenced in Part 2 from Reference [21]. Using Equations (1)- (6), we calculated the value of generalized entropy of the sample stocks.…”

Section: Empirical Analysis From Chinese Sample Datamentioning

confidence: 99%

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Zhou

Liu

et al. 2017

Entropy

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This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.

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Section: Empirical Analysis From Chinese Sample Datamentioning

confidence: 99%

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Zhou

Liu

et al. 2017

Entropy

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“…In order to find a diversified portfolio, the Entropy metric associated with the conventional mean-variance model was applied, according to Equations (10)- (13). The proposed model can be presented by (17)- (20):…”

Section: Proposed Methodsmentioning

confidence: 99%

“…An approach that has been widely applied to portfolio formation is the entropy concept [7,[9][10][11][12][13]. The statistics generated by the entropy provide additional information in forming optimal portfolios, particularly to increase asset diversification by reducing errors in estimating associated parameters.…”

Section: Introductionmentioning

confidence: 99%

Entropic Data Envelopment Analysis: A Diversification Approach for Portfolio Optimization

Rotela

Rocha

Áquila

et al. 2017

Entropy

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Abstract:Recently, different methods have been proposed for portfolio optimization and decision making on investment issues. This article aims to present a new method for portfolio formation based on Data Envelopment Analysis (DEA) and Entropy function. This new portfolio optimization method applies DEA in association with a model resulting from the insertion of the Entropy function directly into the optimization procedure. First, the DEA model was applied to perform a pre-selection of the assets. Then, assets given as efficient were submitted to the proposed model, resulting from the insertion of the Entropy function into the simplified Sharpe's portfolio optimization model. As a result, an improved asset participation was provided in the portfolio. In the DEA model, several variables were evaluated and a low value of beta was achieved, guaranteeing greater robustness to the portfolio. Entropy function has provided not only greater diversity but also more feasible asset allocation. Additionally, the proposed method has obtained a better portfolio performance, measured by the Sharpe Ratio, in relation to the comparative methods.

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“…Over time, Markowitz's theory has been extended and improved by different approaches to modeling uncertainty. Fuzzy sets have been widely employed in portfolio optimization because the uncertainty of return can be easily quantified by fuzzy variables [2,3]. Recently, the neutrosophic theory, which extends the fuzzy concept, has been applied for solving portfolio selection problems [4] and for characterization of both portfolio performance indicators: return and risk [5].…”

Section: Introductionmentioning

confidence: 99%

Preference Based Portfolio for Private Investors: Discrete Choice Analysis Approach

2019

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Behavioral finance literature shows that in addition to Markowitz’s rate of return and risk, private investors consider various other stock features. This paper discusses the problem of determining investors’ preferences for portfolio selection criteria, as well as the problem of optimal portfolio determination from the investors’ point of view. The study primarily focuses on private investors who are interested in one-time investments rather than stock trading. We use a discrete choice analysis and hierarchical Bayes method to measure individual investors’ preferences, and a logit model to determine individual shares of preferences. We treat the share of preferences as the share of certain stocks in an optimal portfolio. The proposed methodology is illustrated by the example of companies whose stocks are traded on the Belgrade Stock Exchange. We measure respondents’ preferences for companies, preferences for return rates, riskiness of stocks, and dividend rates. The results of comparing the performance of the resulting portfolio with the efficient frontier obtained using Markowitz’s portfolio theory indicate its high efficiency, thus validating the proposed approach.

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A Mean-Variance Hybrid-Entropy Model for Portfolio Selection with Fuzzy Returns

Cited by 18 publications

References 22 publications

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

Entropic Data Envelopment Analysis: A Diversification Approach for Portfolio Optimization

Preference Based Portfolio for Private Investors: Discrete Choice Analysis Approach

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