Fuzzy Views on Black-Litterman Portfolio Selection Model

Fang, Yong; Lin, Boqiang; Zhao, Daping; Wang, Shouyang

doi:10.1007/s11424-017-6330-2

Cited by 12 publications

(18 citation statements)

References 24 publications

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“…As previously mentioned in the literature review, studies with a fuzzy approach to views [16,18] outperform both the market portfolio and the standard BL model (by less than 3 percentage points with standard constraint and no short sells). However, it should be remembered that these studies Funding: This research received no external funding.…”

Section: Discussionmentioning

confidence: 63%

“…However, the results are affected by the expert's awareness, because opinions and the fuzzification are formulated ex post, so the experts knew which events/information were important for the market. The experton in the fuzzy BL model first was presented by authors during the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology [18]. This model was shown on a simple empirical example based on a linguistic assessment of future return rate provided by Financial Engineering Students Interest Groups.…”

Section: Introductionmentioning

confidence: 99%

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Vague Expert Information/Recommendation in Portfolio Optimization-An Empirical Study

Bartkowiak

Rutkowska

2020

Axioms

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In a real market, the quantity of information and recommendations is constantly increasing. However, recommendations are often in linguistic form and no one recommendation is based on a single piece of information. Predictions of individuals and their confidence can vary greatly. Thus, a problem arises concerning different (disjointed or partially coherent) vague opinions of various experts or information from multiple sources. In this paper, we introduce extensions of the Black—Litterman model with linguistic expressed views from different experts/many sources. The study focuses on empirical analysis of proposed fuzzy approach results. In the presented modification every expert presents its opinion about particular assets according to intervals, and then an experton for each asset is built. In the portfolio optimization, we use aggregated views presented by interval, which is the mean value of the experton built on particular views. In an empirical study, we built and tested 10,000 portfolios based on recommendation from EquityRT, which was made by 14–49 experts monthly between November 2017 and June 2019 for the 29 biggest companies from the US market and different sectors. The annual average return from portfolios is 9.5–11.8%, depending on the width of the intervals and additional constraints. This approach allows people to formulate intuitive views and view the opinions of a group of experts.

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Section: Discussionmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Vague Expert Information/Recommendation in Portfolio Optimization-An Empirical Study

Bartkowiak

Rutkowska

2020

Axioms

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“…Combined return vector calculation. With matrices P, Q and Ω, we calculate the new combined return vector E(r) (10) and covariance matrix of the join distribution M (11). Similarly, in the fuzzy case, with matrices P,Q and corresponding Ω we calculate the new combined return vectorẼ (r) (19) and the covariance matrix of the join distributionM (20).…”

Section: Algorithmmentioning

confidence: 99%

“…The researchers also began a discussion on the aggregation of opinions of various experts by using the expected value of a fuzzy random variable. Fang et al [11] also use a fuzzy random approach for investor views and redefine the covariance of the views using variance of a fuzzy random variable. However, both papers use a scalar variance; such a crisp evaluation of the dispersion does not appear to match with an epistemic interpretation of fuzzy data in these cases.…”

Section: Introductionmentioning

confidence: 99%

Experton approach to vague information in portfolio selection problem with many views

Rutkowska

Bartkowiak

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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This paper presents many expert fuzzy extensions of the Black-Litterman portfolio selection model. Black and Litterman identified two sources of information regarding the expected returns, and they combined these two sources of information in one expected return formula. The first source of information is the expected returns from the Capital Asset Pricing Model and thus should hold if the market is in equilibrium. The second source of information is the views held by the investors. The presented extension, owing to the use of a fuzzy random variable and experton, includes two elements that are important from a practical perspective: linguistic information and the multiple experts' views. This paper introduces the model extension sequentially and then illustrates it by empirical example.

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“…A significant body of literature describes the use of possibility measures to construct portfolio selection problems, assuming that the returns are fuzzy variables [20][21][22][23][24][25]. Although possibility measures are useful tools to solve these problems and have been widely used, they have certain weaknesses.…”

Section: Introductionmentioning

confidence: 99%

Analytical Reduction Method for New Type-2 Fuzzy Chance-Constrained Portfolio Selection Model

Yang¹,

Mei²,

Qin³

et al. 2021

IJCIS

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In the traditional portfolio selection problem, asset returns are modeled as fuzzy variables with fuzzy return. However, this approach is limited in its ability to capture uncertainty accurately and in analytical model solving. Here, we aim to develop a new fuzzy chance-constrained portfolio model with a type-2 fuzzy return variable using a credibility measure. In real practice, an effective portfolio model under a new, more complex environment is required to improve instinctive imprecision. Here, we propose a novel analytical reduction method to transform our proposed model into a linear programing model with linear constraints, and use a linear programing tool to obtain optimal portfolio strategies. We first reformulate the portfolio model with type-2 fuzzy returns using two types of chance criteria. Next, we provide a new analytical method to solve the proposed model. Then, we present a numerical example with 20 asset returns described by a triangular membership function and use comparison testing to illustrate the advantages of our proposed method. The numerical results show that the relationship between investor tolerance of portfolio risk and the values attained for the four objective functions is in line with our expectations regarding the risk-return trade-off, and the comparison test results indicate that our proposed reduction method performs better than three existing methods. Our method provides an effective practice model for reformulating type-2 fuzzy portfolio problems using an analytical reduction method. Although a large number of existing type-2 fuzzy portfolio problems cannot be solved by our analytical method, it represents a new tool to solve these kinds of problems.

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Fuzzy Views on Black-Litterman Portfolio Selection Model

Cited by 12 publications

References 24 publications

Vague Expert Information/Recommendation in Portfolio Optimization-An Empirical Study

Vague Expert Information/Recommendation in Portfolio Optimization-An Empirical Study

Experton approach to vague information in portfolio selection problem with many views

Analytical Reduction Method for New Type-2 Fuzzy Chance-Constrained Portfolio Selection Model

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