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

• Main Authors: Mohsen Gharakhani, Seyed Jafar Sadjadi
• Format: Article
• Language: English
• Published: Growing Science 2013-01-01
• Series: Decision Science Letters
• Subjects: MCDM; Fuzzy MCDM; COPRAS-F; Portfolio optimization; Black-Litterman optimization; Markowitz optimization; Fuzzy compromise programming
• Online Access: http://www.growingscience.com/dsl/Vol2/dsl_2013_6.pdf

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.