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Mean-variance-skewness model for portfolio selection with fuzzy returns

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  • Li, Xiang
  • Qin, Zhongfeng
  • Kar, Samarjit

Abstract

Numerous empirical studies show that portfolio returns are generally asymmetric, and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same. In order to measure the asymmetry of fuzzy portfolio return, a concept of skewness is defined as the third central moment in this paper, and its mathematical properties are studied. As an extension of the fuzzy mean-variance model, a mean-variance-skewness model is presented and the corresponding variations are also considered. In order to solve the proposed models, a genetic algorithm integrating fuzzy simulation is designed. Finally, several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm.

Suggested Citation

  • Li, Xiang & Qin, Zhongfeng & Kar, Samarjit, 2010. "Mean-variance-skewness model for portfolio selection with fuzzy returns," European Journal of Operational Research, Elsevier, vol. 202(1), pages 239-247, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:239-247
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    References listed on IDEAS

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    1. Fred D. Arditti, 1967. "Risk And The Required Return On Equity," Journal of Finance, American Finance Association, vol. 22(1), pages 19-36, March.
    2. Prakash, Arun J. & Chang, Chun-Hao & Pactwa, Therese E., 2003. "Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets," Journal of Banking & Finance, Elsevier, vol. 27(7), pages 1375-1390, July.
    3. Sharpe, William F., 1971. "A Linear Programming Approximation for the General Portfolio Analysis Problem," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1263-1275, December.
    4. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    5. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
    6. Carlos MACHADO-SANTOS & Ana Cristina FERNANDES, 2005. "Skewness in Financial Returns: Evidence from the Portuguese Stock Market (in English)," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 55(9-10), pages 460-470, September.
    7. Arenas Parra, M. & Bilbao Terol, A. & Rodriguez Uria, M. V., 2001. "A fuzzy goal programming approach to portfolio selection," European Journal of Operational Research, Elsevier, vol. 133(2), pages 287-297, January.
    8. Stone, Bernell K., 1973. "A Linear Programming Formulation of the General Portfolio Selection Problemâ€," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(4), pages 621-636, September.
    9. Tanaka, Hideo & Guo, Peijun, 1999. "Portfolio selection based on upper and lower exponential possibility distributions," European Journal of Operational Research, Elsevier, vol. 114(1), pages 115-126, April.
    10. William F. Sharpe, 1967. "A Linear Programming Algorithm for Mutual Fund Portfolio Selection," Management Science, INFORMS, vol. 13(7), pages 499-510, March.
    11. Michael J. Best & Robert R. Grauer, 1991. "Sensitivity Analysis for Mean-Variance Portfolio Problems," Management Science, INFORMS, vol. 37(8), pages 980-989, August.
    12. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
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