Fuzzy compromise programming for portfolio selection

The aim of this paper is to solve a portfolio selection problem using Sharpe's single index model in a soft framework. Estimations of subjective or imprecise future beta for every asset can be represented through fuzzy numbers constructed on the basis of statistical data and the relevant knowledge of the financial analyst; the model, therefore, works with data that contain more information than any classical model and dealing with it does not involve a great extra computational effort. In order to solve the portfolio selection problem we have formulated a Fuzzy Compromise Programming problem. For this task we have introduced the fuzzy ideal solution concept based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their @a-cuts. The accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and using discrepancy between fuzzy numbers in our analysis. A major feature of this model is its sensitivity to the analyst's opinion as well as to the decision-maker's preferences. This allows interaction with both when it comes to design the best portfolio.

[1]  H. Konno,et al.  Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market , 1991 .

[2]  Amelia Bilbao-Terol,et al.  Solving a multiobjective possibilistic problem through compromise programming , 2005, Eur. J. Oper. Res..

[3]  Julián Molina Luque.  Toma de decisiones con criterios múltiples en variable continua y entera. Implementación computacional y aplicaciones a la economía , 2000 .

[4]  Simon French,et al.  Applied Decision Analysis. , 1985 .

[5]  Stephen A. Marglin.  Public Investment Criteria , 1967 .

[6]  Amelia Bilbao-Terol,et al.  Solving the multiobjective possibilistic linear programming problem , 1999, Eur. J. Oper. Res..

[7]  F. Blasco,et al.  On the Monotonicity of the Compromise Set in Multicriteria Problems , 1999 .

[8]  M. Blume,et al.  BETAS AND THEIR REGRESSION TENDENCIES , 1975 .

[9]  Mariano Jiménez,et al.  Ranking fuzzy numbers through the Comparison of its Expected Intervals , 1996, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[10]  Wei-Guo Zhang,et al.  On admissible efficient portfolio selection problem , 2004, Appl. Math. Comput..

[11]  Carlos Romero,et al.  Portfolio Selection: A Compromise Programming Solution , 1996 .

[12]  E. Elton.  Modern portfolio theory and investment analysis , 1981 .

[13]  Shouyang Wang,et al.  Criteria, Models and Strategies in Portfolio Selection , 2002 .

[14]  P. Yu.  A Class of Solutions for Group Decision Problems , 1973 .

[15]  Yazid M. Sharaiha,et al.  Heuristics for cardinality constrained portfolio optimisation , 2000, Comput. Oper. Res..

[16]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[17]  Peijun Guo,et al.  Portfolio selection based on upper and lower exponential possibility distributions , 1999, Eur. J. Oper. Res..

[18]  L. A. Zadeh,et al.  From Circuit Theory to System Theory , 1962, Proceedings of the IRE.

[19]  Stanisław Heilpern,et al.  The expected value of a fuzzy number , 1992 .

[20]  H. Markowitz.  Portfolio Selection: Efficient Diversification of Investments , 1971 .

[21]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[22]  Wei-Guo Zhang,et al.  On admissible efficient portfolio selection policy , 2005, Appl. Math. Comput..

[23]  Kathrin Klamroth,et al.  An MCDM approach to portfolio optimization , 2004, Eur. J. Oper. Res..

[24]  Edwin J. Elton,et al.  Are Betas Best , 1978 .

[25]  Oldrich A Vasicek,et al.  A NOTE ON USING CROSS‐SECTIONAL INFORMATION IN BAYESIAN ESTIMATION OF SECURITY BETAS , 1973 .

[26]  Amelia Bilbao-Terol,et al.  An extension of Sharpe's single-index model: portfolio selection with expert betas , 2006, J. Oper. Res. Soc..

[27]  Barr Rosenberg,et al.  Prediction of Beta from Investment Fundamentals , 1995 .

[28]  A. G. Malliaris,et al.  Chapter 1 Portfolio theory , 1995, Finance.

[29]  Kin Keung Lai,et al.  A model for portfolio selection with order of expected returns , 2000, Comput. Oper. Res..