Presenting a fuzzy model for fuzzy portfolio optimization with the mean absolute deviation risk function

Abstract

The main purpose of this paper is portfolio optimization with the use of fuzzy method based on the mean absolute deviation risk function in firms listed in Tehran Stock Market. In the present research, for the purpose of fuzzy portfolio optimization the stock portfolio Value at Risk criterion and for calculation of this value the parametric method and for fuzzy optimization also the Hybrid intelligent algorithms (genetic algorithms and neural networks) have been used. For selecting the portfolio with 15 during the research time span (2005-2011) fuzzy optimization based on the following six criteria were used including Asymmetric Value at Risk, Symmetric Value at Risk , Interval Value at Risk (interval of 5%-95%), Interval Value at Risk (interval of 10%-90%), and Normal Value at Risk. Since the calculated probability ratio statistic Kupiec based on fuzzy optimization for the 6 above mentioned models is larger than the obtained critical value from chi-square distribution at the confidence level of 95%, the research hypothesis stating that the application of fuzzy optimization method improves the efficiency of portfolio in the actual world problems with lack of certainty was confirmed. Also, the results of the Kupiec probability ratio statistic indicate that the model of value at risk based on the mean absolute deviation risk function (MVAR) is more successful and have less failure comparing to other models, hence; the research hypothesis stating that fuzzy variables have a higher ability in modeling asymmetric uncertainties in financial domains is also confirmed.