Mean-variance-skewness model for portfolio selection with fuzzy returns

Li, Xiang; Qin, Zhongfeng; Kar, Samarjit

doi:10.1016/j.ejor.2009.05.003

Cited by 251 publications

(85 citation statements)

References 29 publications

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“…The characterization of the first-order dominance allows us to write an optimization model describing elements of its set of the best portfolios. The numerical implementation of the model with the example of seven triangular assets, introduced by Huang (2008) and used by Li et al (2010) and Sadefo Kamdem et al (2012), displays the best portfolios which have better parameters than those obtained by Huang (2008), Li et al (2010) and Sadefo Kamdem et al (2012). This new approach (qualitative approach) for portfolio selection with fuzzy returns, based on dominances of fuzzy variables, is flexible (it is not restricted to target values) and it improves previous approach (quantitative approach) by providing the best portfolios with better parameters.…”

Section: Discussionmentioning

confidence: 99%

“…In the following, we implement the previous multiobjective program for the usual family A ¼ ðn i Þ 1 i 7 of seven assets with returns described by the following triangular fuzzy variables (see Huang 2008;Li et al, 2010;Sadefo Kamdem et al, 2012): n 1 ¼ ðÀ0:3; 1:8; 2:3Þ, n 2 ¼ ðÀ0:4; 2:0; 2:2Þ, n 3 ¼ ðÀ0:5; 1:9; 2:7Þ, n 4 ¼ ðÀ0:6; 2:2; 2:8Þ, n 5 ¼ ðÀ0:7; 2:4; 2:7Þ, n 6 ¼ ðÀ0:8; 2:5; 3:0Þ and n 7 ¼ ðÀ0:6; 1:8; 3:0Þ.…”

Section: Application In Finance: Set Of Best Portfolios Of a Finite Nmentioning

confidence: 99%

“…Therefore, scholars ( Liu and Liu 2002;Huang 2008;Li et al, 2010;Sadefo Kamdem et al, 2012) studied, by means of the credibility measure, moments and semi-moments of fuzzy variables and they used the obtained theoretical results to propose portfolio optimization models when returns are fuzzy. In that approach based on parameters of fuzzy variables (namely quantitative approach), we have the mean-variance model proposed by Huang (2008), the mean-variance-skewness model proposed by Li et al, (2010) and the mean-variance-skewnesssemi-kurtosis model proposed by Sadefo Kamdem et al (2012). More recently, Chen and Tsaur (2016) proposed a weighted fuzzy portfolio model based on a weighted function of possibility mean and variance in order to approach portfolio selection differently in response to the varying investment return.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns

Tassak

Kamdem

Fono

et al. 2017

Journal of the Operational Research Society

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Peng et al (Int J Uncertain Fuzziness Knowl Based Syst 15:29-41, 2007) introduced, by means of the credibility measure, two dominance relations on fuzzy variables, namely the first-and the second-order dominances. In this paper, we characterize each of these dominance relations, and we justify that they satisfy six well-known properties of comparison methods. We propose a Game Theory approach for the determination of optimal portfolios when returns are fuzzy by introducing the set of best portfolios with respect to the first-and the second-order dominances. Based on the characterization of the first-order dominance, we numerically display some of the best portfolios of the classical set of portfolios of seven independent assets described by triangular fuzzy numbers.

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Section: Discussionmentioning

confidence: 99%

Section: Application In Finance: Set Of Best Portfolios Of a Finite Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns

Tassak

Kamdem

Fono

et al. 2017

Journal of the Operational Research Society

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“…A Moderna Teoria das Carteiras (Modern Portfolio Theory -MPT) foi firmada pelo trabalho seminal de Harry Markowitz, em 1952, intitulado "Portfolio Selection" (LAI;YU;WANG, 2006;QIN;KAR, 2010;KOLM;TÜTÜNCÜ;FABOZZI, 2014) e considera o investidor como sendo racional, avesso ao risco e maximizador de sua própria utilidade esperada. Desse modo, baseado, principalmente, em premissas sobre a distribuição dos retornos dos ativos e sobre o comportamento dos investidores, Markowitz (1952) tinha como principal objetivo diversificar carteiras de investimento, de forma a determinar uma composição que minimizasse o risco ou maximizasse o retorno esperado pelo investidor, dado que este é racional.…”

Section: Introductionunclassified

Análise da eficácia da variância e de medidas Downside Risk para formação de carteiras

Bezerra

Machado

2016

Enf.:Ref. Cont.

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O objetivo deste artigo é analisar a eficácia da variância e de medidas de downside risk para formação de carteiras de investimentos no mercado de ações brasileiro. Utilizando as metodologias de Ang (1975), Markowitz et al. (1993), Ballestero (2005), Estrada (2008) e Cumova e Nawrocki (2011), foi verificado qual o melhor método para resolução do problema de matriz assimétrica e endógena e, inspirando-se nos trabalhos de Markowitz (1952) e Lohre, Neumann e Winterfeldt (2010), foi constatada qual métrica de risco é mais indicada para a realização da alocação mais eficiente dos recursos disponíveis no mercado acionário do Brasil. A amostra utilizada foi composta pelas ações do IBrX 50, no período de 2000 a 2013. Os resultados indicaram que, ao empregar a semivariância como medida de risco assimétrico, caso o investidor possua meios para utilizar modelos mais requintados para resolução do problema da matriz de semivariância-cosemivariância assimétrica, será mais eficaz o modelo de Cumova e Nawrocki (2011). Além disso, a partir dos dados brasileiros, o VaR apresentou-se mais eficaz do que a variância e outras medidas de downside risk no que tange à minimização do risco de perda. Assim, dada a premissa de que o investidor possui preferências assimétricas em relação ao risco, a formação de carteiras de ações no mercado brasileiro é mais eficiente ao se utilizar critérios de minimização de downside risk do que a abordagem tradicional de média-variância.

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“…Considering the complexity of the security market in the real world, the non-uniqueness of randomness as a kind of uncertainty and the lack of enough historical data to reflect the future performances of security returns in some real life cases, many scholars began to regard security returns as fuzzy variables which rely on experienced experts' evaluations instead of historical data. Thus, fuzzy portfolio optimization theory is developed and has been mainly studied based on following three methods: (i) Fuzzy set theory [5]; (ii) Possibility measure [6,7]; (iii) Credibility measure [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

Gao

Huicheng

2017

Entropy

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This paper aims to develop a risk-free protection index model for portfolio selection based on the uncertain theory. First, the returns of risk assets are assumed as uncertain variables and subject to reputable experts' evaluations. Second, under this assumption, combining with the risk-free interest rate we define a risk-free protection index (RFPI), which can measure the protection degree when the loss of risk assets happens. Third, note that the proportion entropy serves as a complementary means to reduce the risk by the preset diversification requirement. We put forward a risk-free protection index model with an entropy constraint under an uncertainty framework by applying the RFPI, Huang's risk index model (RIM), and mean-variance-entropy model (MVEM). Furthermore, to solve our portfolio model, an algorithm is given to estimate the uncertain expected return and standard deviation of different risk assets by applying the Delphi method. Finally, an example is provided to show that the risk-free protection index model performs better than the traditional MVEM and RIM.

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Mean-variance-skewness model for portfolio selection with fuzzy returns

Cited by 251 publications

References 29 publications

Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns

Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns

Análise da eficácia da variância e de medidas Downside Risk para formação de carteiras

A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

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