Portfolio Selection: Markowitz Mean-variance Model

2012 ◽  
Keyword(s):  
Portfolio Selection ◽  
Variance Model ◽  
Mean Variance

scholarly journals Mean-Variance Model for Portfolio Selection

2012 ◽  
Author(s):  
Frank J. Fabozzi ◽  
Harry M. Markowitz ◽  
Petter N. Kolm ◽  
Francis Gupta
Keyword(s):  
Portfolio Selection ◽  
Variance Model ◽  
Mean Variance

scholarly journals A Simple View on the Interval and Fuzzy Portfolio Selection Problems

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 932
Author(s):  
Krzysztof Kaczmarek ◽  
Ludmila Dymova ◽  
Pavel Sevastjanov
Keyword(s):  
Portfolio Selection ◽  
Portfolio Risk ◽  
Bicriteria Optimization ◽  
Variance Model ◽  
Fuzzy Portfolio Selection ◽  
Optimization Task ◽  
Maximal Profit ◽  
Mathematical Formalization ◽  
Mean Variance ◽  
Fuzzy Setting

In this paper, first we show that the variance used in the Markowitz’s mean-variance model for the portfolio selection with its numerous modifications often does not properly present the risk of portfolio. Therefore, we propose another treating of portfolio risk as the measure of possibility to earn unacceptable low profits of portfolio and a simple mathematical formalization of this measure. In a similar way, we treat the criterion of portfolio’s return maximization as the measure of possibility to get a maximal profit. As the result, we formulate the portfolio selection problem as a bicriteria optimization task. Then, we study the properties of the developed approach using critical examples of portfolios with interval and fuzzy valued returns. The α-cuts representation of fuzzy returns was used. To validate the proposed method, we compare the results we got using it with those obtained with the use of fuzzy versions of seven widely reputed methods for portfolio selection. As in our approach we deal with the bicriteria task, the three most popular methods for local criteria aggregation are compared using the known example of fuzzy portfolio consist of five assets. It is shown that the results we got using our approach to the interval and fuzzy portfolio selection reflect better the essence of this task than those obtained by widely reputed traditional methods for portfolio selection in the fuzzy setting.

scholarly journals A Novel Framework for Portfolio Selection Model Using Modified ANFIS and Fuzzy Sets

Computers ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 57 ◽  
Author(s):  
Chanchal Kumar ◽  
Mohammad Najmud Doja
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Portfolio Selection ◽  
Layered Structure ◽  
Value At Risk ◽  
Conditional Value At Risk ◽  
Variance Model ◽  
Portfolio Selection Model ◽  
Mean Variance ◽  
Existing Structure

This paper proposes a novel framework for solving the portfolio selection problem. This framework is excogitated using two newly parameters obtained from an existing basic mean variance model. The scheme can prove entirely advantageous for decision-making while using computed values of these significant parameters. The framework combines effectiveness of the mean-variance model and another significant parameter called Conditional-Value-at-Risk (CVaR). It focuses on extracting two newly parameters viz. αnew and βnew, which are demarcated from results obtained from mean-variance model and the value of CVaR. The method intends to minimize the overall cost, which is computed in the framework using quadratic equations involving these newly parameters. The new structure of ANFIS is designed by changing existing structure of ANFIS and this new structure contains six layers instead of existing five-layered structure. Fuzzy sets are harnessed for the design of the second layer of this new ANFIS structure. The output parameter acquired from the sixth layer of the new ANFIS structure serves as an important index for an investor in the decision-making. The numerical results acquired from the framework and the new six-layered structure is presented and these results are assimilated and compared with the results of the existing ANFIS structure.

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