A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

Abstract

In this paper, we examine advanced optimization approach for portfolio problem introduced by Black and Litterman to consider the shortcomings of Markowitz standard Mean-Variance optimization. Black and Litterman propose a new approach to estimate asset return. They present a way to incorporate the investor's views into asset pricing process. Since the investor's view about future asset return is always subjective and imprecise, we can represent it by using fuzzy numbers and the resulting model is multi-objective linear programming. Therefore, the proposed model is analyzed through fuzzy compromise programming approach using appropriate membership function. For this purpose, we introduce the fuzzy ideal solution concept based on investor preference and indifference relationships using canonical representation of proposed fuzzy numbers by means of their correspondingα-cuts. A real world numerical example is presented in which MSCI (Morgan Stanley Capital International Index) is chosen as the target index. The results are reported for a portfolio consisting of the six national indices. The performance of the proposed models is compared using several financial criteria.

Geometric compromise programming: application in portfolio selection

“…In addition, Parra et al (2005) and Bilbao-Terol et al (2006) proposed a new CP model for portfolio selection including the imprecision and subjectivity inherent to some data. Gharakhani and Sadjadi (2013) also combined fuzzy logic and CP to integrate the investor's view about future asset returns.…”

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

“…They used fuzzy trapezoidal numbers to represent investor views and omit the aspect of consistency in combining prior probabilistic distribution and fuzzy views. Gharakhani and Sadjadi [15] assumed views as fuzzy numbers and mean asset return as well as covariance as fixed estimated parameters. They focused on a fuzzy compromise programming to find a solution of fuzzy return maximization and fuzzy beta minimization.…”

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

“…The researcher used a fuzzy trapezoidal number to represent investor views and omit the consistency aspect in combining prior probabilistic distribution and fuzzy views. Gharakhani and Sadjadi [13] assumed views as fuzzy numbers and mean asset return as well as covariance as fixed estimated parameters. The researchers focused on fuzzy compromise programming to find a solution of fuzzy return maximization and fuzzy beta minimization.…”