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Interactive fuzzy numbers in the evaluation of the effectiveness of investment projects and selection of efficient portfolios

100%

RĘBIASZ B.

nr 3-4

103-127

The paper presents a method for evaluating the effectiveness and risks of investment projects and the selection of efficient portfolios in a situation where parameters in the calculation of effectiveness are expressed in the form of interactive fuzzy numbers. Fuzzy model simulations are used to perform arithmetic operations on interactive fuzzy numbers. The process of selecting investment projects takes into account statistical and economic dependences between projects.

A new approach to risk assessment in fuzzy portfolio selection

100%

Dymowa L.

2006

tom R. 6, nr 10

7-18

A new approach to risk assessment in the portfolio selection optimization problem in a fuzzy setting is presented. The approach is based on the a-level representation of fuzzy values describing the stock's returns. The two-objective method based on the weighted lower and upper bounds of fuzzy portfolio return is elaborated. In the framework of proposed approach these bound represent the local criteria of risk minimization and profit maximization, respectively. Three most popular methods for local criteria aggregation are compared using the example of portfolio consist of five alternative stocks. The results are compared with those obtained with use of single criterion approaches to portfolio optimization in a fuzzy setting. It is shown that proposed method provides the results which more coincide with the practice of portfolio selection than those obtained using the fuzzy versions of reputed single criterion approaches. The method makes it possible to take into account in a natural way the local criteria of portfolio return maximization and risk minimization with their ranks. The problem is formulated as the nonlinear optimization task, so all possible forma of stock return's membership function can be used without restrictions. Since the generalized criterion is formulated as the aggregation of local criteria, the method may be easily extended by the inclusion of additional criteria such as stock's liquidity, transaction costs and so on.

Konstrukcja portfeli efektywnych z zastosowaniem Wielorównaniowych Modeli GARCH

75%

Fiszeder P.

tom 48

47-68

The purpose of this paper is to present dynamic approach to selection of efficient portfolios using a forecasts of variances and covariances from the multivariate GARCH models. Evaluation of efficiency for different methods of asset allocation is also performed for stocks from the WSE. Twelve specifications of the multivariate GARCH models, the univariate GARCH model and six other covariance matrix estimation methods are used. Taking into consideration time varying variances and covariances of stock returns in portfolio selections increases, with some exceptions, efficiency of asset allocation process. Simple specifications of them ultivariate GARCH models, w hich parameters are estimated in one stage, are the best perform ing models. From economic point of view, the differences between the models are not significant, with exception of the factor and orthogonal models. RiskMetrics methodology commonly used by practitioners does not give good results for constructions of efficient portfolios.

Metoda wyboru efektywnych portfeli przedsięwzięć inwestycyjnych

63%

Rębiasz B.

tom nr 3

96-117

W artykule przedstawiono nową metodę wyboru efektywnych portfeli przedsięwzięć inwestycyjnych. Problem wyboru portfeli sformułowano w postaci zadania optymalizacji wielokryterialnej. Opracowany algorytm umożliwia poszukiwanie niezdominowanych portfeli przedsięwzięć inwestycyjnych. Kryteriami wyboru są: maksymalizacja wartości oczekiwanej NPV i minimalizacja semiodchylenia standardowego NPV portfela. Metoda umożliwia wybór portfeli przy uwzględnieniu zależności statystycznych i ekonomicznych pomiędzy przedsięwzięciami inwestycyjnymi. Jest ona dostosowana do przedsiębiorstw o wieloetapowym cyklu produkcji, na przykład przedsiębiorstwa przemysłu metalurgicznego czy chemicznego.

A new algorithm for selecting an effective investment project portfolio from a collection of projects developed by a company has been presented in this paper. The problem of selecting an investment project was formulated as multi-objective optimization problem. The algorithm is suited for enterprises with multistage production cycles, e.g. enterprises in the metallurgical or chemical industry. During the selection process the method takes into account statistical and economic interdependencies existing among projects. Upon choosing projects the algorithm takes into account twp criteria: maximization of the expected NPV and minimization of project portfolio risk. A company may develop an effective investment project portfolio for a few years ahead. The algorithm makes it possible to search for Pareto optimal solutions. It links computer simulation methods with a genetic algorithm and standard procedure for linear optimization. An example of the use of the algorithm for selecting projects in the metallurgical industry is presented.