Volume 3 Issue 5 pp. 859-872 Summer, 2012


Multi-objective portfolio optimization of mutual funds under downside risk measure using fuzzy theory


A. Alimi M. Zandieh and M. Amiri




Mutual fund is one of the most popular techniques for many people to invest their funds where a professional fund manager invests people's funds based on some special predefined objectives; therefore, performance evaluation of mutual funds is an important problem. This paper proposes a multi-objective portfolio optimization to offer asset allocation. The proposed model clusters mutual funds with two methods based on six characteristics including rate of return, variance, semivariance, turnover rate, Treynor index and Sharpe index. Semivariance is used as a downside risk measure. The proposed model of this paper uses fuzzy variables for return rate and semivariance. A multi-objective fuzzy mean-semivariance portfolio optimization model is implemented and fuzzy programming technique is adopted to solve the resulted problem. The proposed model of this paper has gathered the information of mutual fund traded on Nasdaq from 2007 to 2009 and Pareto optimal solutions are obtained considering different weights for objective functions. The results of asset allocation, rate of return and risk of each cluster are also determined and they are compared with the results of two clustering methods.




DOI: 10.5267/j.ijiec.2012.05.005

Keywords: Clustering, Portfolio optimization, Mean-semivariance, Multi-objective non-linear programming, Fuzzy technique programming, Pareto optimal solution

References

References Ammar, E., & Khalifa, H. A. (2003). Fuzzy portfolio optimization: A quadratic programming approach. Chaos, Solitons and Fractals, 18, 1045–1054.

Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37, 1285-1297.

Basso, A., & Funari, S. (2001). A data envelopment analysis approach to measure the mutual fund performance. European Journal of Operational Research, 135, 477–492.

Chang, C. H., Lin, J. J., Lin, J. H., & Chiang, M. C. (2010). Domestic open-end equity mutual fund performance evaluation using extended TOPSIS method with different distance approaches. Expert Systems with Applications, 37, 4642-4649.

Chang, T. J., Yang, S. C., & Chang, K. J. (2009). Portfolio optimization problem in different risk measures using genetic algorithm. Expert Systems with Applications, 36, 10529-10537.

Chen, L. H., & Huang, L. (2009). Portfolio optimization of equity mutual funds with fuzzy return rates and risks. Expert Systems with Application, 36, 3720-3727.

Deb, G. S., & Banerjee, A. (2009). Downside risk analysis of Indian equity mutual funds: a value at risk approach. International Research Journal of Finance and Economics, 23, 216-230.

Decker, R., & Lenz, H. J. (2007). Advances in Data Mining. Springer, New York.

Jana, P., Roy, T. K., & Mazumder, S. K. (2009). Multi-objective possibilistic model for portfolio selection with transaction cost. Journal of Computational and Applied Mathematics, 228, 188-196.

Larose, D. T. (2005). Discovering Knowledge in Data. New Jersey: John Wiley & Sons.

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

Markowitz, H. M. (1959). Portfolio Selection: Efficient Diversification of Investments. New York: Wiley

Mobius, M. (2007). Mutual Funds: An Introduction to the Core Concepts. Singapore: John Wiley & Sons (Asia) Pte Ltd.

Murthi, B. P. S., Choi, Y. K., & Desai, P. (1997). Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach. European Journal of Operational Research, 98, 408–418.

Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39, 119–138.

Terol, A. B., Gladish, B. P., Parra, M. A., & Uria, M. V. R. (2006). Fuzzy compromise programming for portfolio selection. Applied Mathematics and Computation, 173, 251-264.

Tola, V., Lillo, F., Gallegati, M., & Mantegna, R. N. (2008). Cluster analysis for portfolio optimization. Journal of Economic Dynamics and Control, 32, 235-258.

Treynor, J. (1965). How to rate management of investment funds. Harvard Business Review, 43, 63–75

Vercher, E., Bermudez, J. D. & Segura, J. V. (2007). Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets and Systems, 158, 769-782.

Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several Objective Functions. Fuzzy Sets and Systems, 1, 45-55.

Zio, E., & Bazzo, R. (2010). Multi-objective optimization of the inspection intervals of a nuclear safety system: A clustering-based framework for reducing the Pareto Front. Annals of Nuclear Energy, 37, 798-812.