Equilibrium Pricing Extending the Mean-Variance Theory Using Weighted Possibilistic Mean of Investor’s Subjectivity
Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan
This paper proposes an extended analytical approach to developing an equilibrium pricing vector with various types of investor’s subjectivity based on extended Mean-Variance (MV) theory. Weighted fuzzy mean and variance are introduced in order to represent investor’s subjectivity numerically. Similar to the traditional MV-based equilibrium approach, the equilibrium pricing vector of the proposed model is analytically obtained in mathematical programming. A macroeconomic index based on risky assets, which provides information with respect to the soundness of the capital market with subjectivity, is also constructed.
-  H. Markowitz, “Portfolio Selection,” Wiley, New York, 1959.
-  E. J. Elton and M. J. Gruber, “Modern Portfolio Theory and Investment Analysis,” Wiley, New York, 1995.
-  H. Konno, “Piecewise linear risk functions and portfolio optimization,” J. of Operations Research Society of Japan, Vol.33, pp. 139-159, 1990.
-  H. Konno, H. Shirakawa, and H. Yamazaki, “A mean-absolute deviation-skewness portfolio optimization model,” Annals of Operations Research, Vol.45, pp. 205-220, 1993.
-  R. T. Rockafellar and S. Uryasev, “Optimization of conditional value-at-risk,” J. of Risk, Vol.2, No.3, pp. 1-21, 2000.
-  W. F. Sharpe, “Capital asset prices: A theory of market equivalent under conditions of risk,” J. of Finance, Vol.19, No.3, pp. 425-442, 1964.
-  B. J. Lintner, “Valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets,” Rev. Econom. Statist., Vol.47, pp. 13-37, 1965.
-  J. Mossin, “Equilibrium in capital asset markets,” Econometrica, Vol.34, No.4, pp. 768-783, 1966.
-  R. Roll, “A critique of the asset pricing theory’s tests. Part I: On past and potential testability of the theory,” J. of Financial Economics, Vol.4, pp. 128-176, 1977.
-  S. A. Ross, “The current status of the Capital Asset Pricing Model (CAPM),” J. of Finance, Vol.33, pp. 885-901, 1978.
-  V. S. Bawa and E. B. Lindenberg, “Capital market equilibrium in a mean-lower partial moment framework,” J. of Financial Economics, Vol.5, pp. 189-200, 1977.
-  H. Konno and H. Shirakawa, “Equilibrium relation in the Mean-Absolute deviation capital market,” Financial Engineering and the Japanese Markets, Vol.1, pp. 21-35, 1994.
-  H. Konno and H. Shirakawa, “Existence of a Nonnegative Equilibrium Price Vector in the Mean-Variance Capital Market,” Mathematical Finance, Vol.5, pp. 233-246, 1995.
-  X. T. Deng, Z. F. Li, and S. Y.Wang, “A minimax portfolio selection strategy with equilibrium,” European J. of Operational Research, Vol.166, No.1, pp. 278-292, 2005.
-  R. T. Rockafellar, S. Uryasev, and M. Zabarankin, “Equilibrium with investors using a diversity of deviation measures,” J. of Banking and Finance, Vol.31, No.11, pp. 3251-3268, 2007.
-  L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, pp. 338-353, 1965.
-  R. Ostermark, “Fuzzy linear constraints in the capital asset pricing model,” Fuzzy Sets and Systems, Vol.30, pp. 93-102, 1989.
-  M. Inuiguchi and J. Ramik, “Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem,” Fuzzy Sets and Systems, Vol.111, pp. 3-28, 2000.
-  R. T. Leon, V. Liern, and E. Vercher, “Validity of infeasible portfolio selection problems: fuzzy approach,” European J. of Operational Researches, Vol.139, pp. 178-189, 2002.
-  H. Tanaka and P.Guo, “Portfolio selection based on upper and lower exponential possibility distributions,” European J. of Operational Researches, Vol.114, pp. 115-126, 1999.
-  H. Tanaka, P. Guo, and I. B. Turksen, “Portfolio selection based on fuzzy probabilities and possibility distributions,” Fuzzy Sets and Systems, Vol.111, pp. 387-397, 2000.
-  J.Watada, “Fuzzy portfolio selection and its applications to decision making,” Tatra Mountains Math. Pub., Vol.13, pp. 219-248, 1997.
-  H. Katagiri, M. Sakawa, and H. Ishii, “A study on fuzzy random portfolio selection problems using possibility and necessity measures,” Scientiae Mathematicae Japonocae, Vol.65, pp. 361-369, 2005.
-  T. Hasuike, H. Katagiri, and H. Ishii, “Portfolio selection problems with random fuzzy variable returns,” Fuzzy Sets and Systems, Vol.160, No.18, pp. 2579-2596, 2009.
-  K. Smimou, C. R. Bector, and G. Jacoby, “Portfolio selection subject to experts’ judgments,” Int. Review of Financial Analysis, Vol.17, pp. 1036-1054, 2008.
-  T. Hasuike, “Equilibrium pricing vector based on the hybrid mean-variance theory with investor’s subjectivity,” Proc. of 2010 IEEEWorld Congress on Computational Intelligence (WCCI2010), DOI:10.1109/FUZZY.2010.5584743, 2010.
-  R. Fuller and P. Majlender, “On weighted possibilistic mean and variance,” Fuzzy Sets and Systems, Vol.136, pp. 364-374, 2003.
-  K. Iwamura, L. Yang, and M. Horiike, “λ-credibility,” RIMS Kokyuroku, Vol.1585, pp. 38-46, 2008.