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.

Gharakhani, M & Sadjadi, S. (2013). A fuzzy compromise programming approach for the Black-Litterman portfolio selection model.Decision Science Letters, 2(2), 11-22.

Ammar, E. (2008). On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem. Information Sciences178, 468-484.

Arenas Parra, M., Bilbao Terol, A., & Rodriguez Uria, M. (2001). A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research, 133, 287-297.

Bagnoli, C., & Smith, H. C. (1998). The theory of fuzz logic and its application to real estate valuation. Journal of Real Estate Research, 16, 169-200.

Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment, Management science, 17.

Bilbao-Terol, A., Pérez-Gladish, B., Arenas-Parra, M., & Rodríguez-Uría, M. V. (2006). Fuzzy compromise programming for portfolio selection. Applied Mathematics and Computation, 173, 251-264.

Black, F., & Litterman, R. B. (1990). Asset Allocation: Combining Investors Views with Market Equilibrium, Fixed Income Research.

Carlsson, C., Fullér, R., & Majlender, P. (2002). A possibilistic approach to selecting portfolios with highest utility score, Fuzzy sets and systems, 131, 13-21.

Ehrgott, M., Klamroth, K., & Schwehm, C. (2004). An MCDM approach to portfolio optimization. European Journal of Operational Research, 155, 752-770.

Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. Journal of Business & Economic Statistics, 22, 367-382.

Falkenbach, H. (2009). Diversification benefits in the Finnish commercial property market. International Journal of Strategic Property Management, 13, 23-35.

Fang, Y., Lai, K. K., & Wang, S. Y. (2006). Portfolio rebalancing model with transaction costs based on fuzzy decision theory. European Journal of Operational Research, 175, 879-893.

Fei, W. (2007). Optimal consumption and portfolio choice with ambiguity and anticipation. Information Sciences, 177, 5178-5190.

Fischhoff, B. (2002). Eliciting knowledge for analytical representation, Systems, Man and Cybernetics, IEEE Transactions, 19, 448-461.

French, N. (2001). Decision theory and real estate investment: an analysis of the decision-making processes of real estate investment fund managers. Managerial and Decision Economics, 22, 399–410.

Giove, S., Funari, S., and Nardelli, C. (2006). An interval portfolio selection problem based on regret function. European Journal of Operational Research, 170, 253-264.

Huang, X. (2006). Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation, 177, 500-507.

Huang, X. (2007). Two new models for portfolio selection with stochastic returns taking fuzzy information. European Journal of Operational Research, 180, 396-405.

Keeney, R. L., & Von Winterfeldt, D. (2002). On the uses of expert judgment on complex technical problems. Engineering Management, IEEE Transactions, 36, 83-86.

Ko, C. H., & Cheng, M. Y. (2003). Hybrid use of AI techniques in developing construction management tools. Automation in Construction, 12, 271-281.

Lacagnina, V., & Pecorella, A. (2006). A stochastic soft constraints fuzzy model for a portfolio selection problem. Fuzzy sets and systems, 157, 1317-1327.

Lai, K., Wang, S., Xu, J., Zhu, S., & Fang, Y. (2002). A class of linear interval programming problems and its application to portfolio selection. Fuzzy Systems, IEEE Transactions, 10, 698-704.

Lawrence, K. D., Pai, D. R., Klimberg, R. K., & Lawrence, S. M. (2009). A fuzzy programming approach to financial portfolio model. Financial Modeling Applications and Data Envelopment Applications, 53.

León, T., Liern, V., & Vercher, E. (2002). Viability of infeasible portfolio selection problems: A fuzzy approach. European Journal of Operational Research, 139, 178-189.

Li, X., Qin, Z., & Kar, S. (2010). Mean-variance-skewness model for portfolio selection with fuzzy returns. European Journal of Operational Research, 202, 239-247.

Lin, C., Tan, B., & Hsieh, P. J. (2005). Application of the uzzy weighted verage in strategic portfolio management. Decision Sciences, 36, 489-511.

Markowitz, H. M. (1952). Portfolio Selection. Journal of Finance, 7, 77–91.

Meucci, A. (2009). Enhancing the Black–Litterman and related approaches: Views and stress-test on risk factors. Journal of Asset Management, 10, 89-96.

Olaleye, A. (2008). Property market nature and the choice of property portfolio diversification strategies: The Nigeria experience. International Journal of Strategic Property Management, 12, 35-51.

Pagourtzi, E., Assimakopoulos, V., Hatzichristos, T., & French, N. (2003). Real estate appraisal: a review of valuation methods. Journal of Property Investment & Finance, 21, 383-401.

Perng, Y. H., Hsueh, S. L., & Yan, M. (2005). Evaluation of housing construction strategies in China using fuzzy-logic system. International Journal of Strategic Property Management, 9, 215–232.

Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19, 425-442.

Stanley Lee E., Li, R. (1993). Fuzzy multiple objective programming and compromise programming with Pareto optimum. Fuzzy sets and systems, 53, 275-288.

Tanaka, H., & Guo, P. (1999). Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research, 114, 115-126.

Tanaka, H., Guo, P., & Türksen, I. B. (2000). Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy sets and systems, 111, 387-397.

Wang, S., & Zhu, S. (2002). On fuzzy portfolio selection problems. Fuzzy Optimization and Decision Making, 1, 361-377.

Wang, X., Xu, W., Zhang, W., & Hu, M. (2005). Weighted possibilistic variance of fuzzy number and its application in portfolio theory. Fuzzy Systems and Knowledge Discovery, 148-155.

Watada, J. (1997). Fuzzy portfolio selection and its applications to decision making. Fuzzy structures: current trends, 219.

Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8, 338-353.

Zhang, W. G., &Wang, Y. L. (2005). Portfolio selection: Possibilistic mean-variance model and possibilistic efficient frontier. Algorithmic Applications in Management, 203-213.

Zhang, W. G., Wang, Y. L., Chen, Z. P., & Nie, Z. K. (2007). Possibilistic mean-variance models and efficient frontiers for portfolio selection problem. Information Sciences, 177, 2787-2801.