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Mean–Absolute Deviation Model

  • Hiroshi Konno
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 150)

Abstract

We will survey important properties of the mean–absolute deviation (MAD) portfolio optimization model, which was introduced in 1990 to cope with very large–scale portfolio optimization problems. MAD model has been used for solving huge portfolio optimization models including internationally diversified investment model, long-term ALM model, mortgage–backed security portfolio optimization model. Also, the MAD model enjoys several nice theoretical properties. In particular, all CAPM type relations for mean–variance model hold for the MAD model as well. Further, the MAD model is more compatible to the fundamental principle of rational decision making.

Keywords

Portfolio Optimization Efficient Frontier Multivariate Normal Distribution Cardinality Constraint Portfolio Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Carino, D.R., Ziemba, W.T.: Formulation of the Russell-Yasuda Kasai financial planning model. Oper. Res. 46(4), 433–449 (1998)MathSciNetMATHCrossRefGoogle Scholar
  2. Dantzig, G.: Linear Programming and Extensions. Princeton University Press, Princeton, NJ (1963)MATHGoogle Scholar
  3. Hazell, P.B.R.: A linear alternative to quadratic and semi variance to farm planning under uncertainty. Am. J. Agric. Econ. 53(4), 664–665 (1971)CrossRefGoogle Scholar
  4. Komuro, S., Konno, H.: Internationally diversified investment by stock-bond integrated model. J. Ind. Manage. Optim. 1(4), 433–442 (2005)MATHCrossRefGoogle Scholar
  5. Konno, H., Li, J.: An internationally diversified investment using a stock-bond integrated portfolio model. Int. J. Theor. Appl. Finance 1(1), 145–160 (1998)MATHCrossRefGoogle Scholar
  6. Konno, H., Shirakawa, H.: Equilibrium relations in the mean–absolute deviation capital market. Asia-Pacific Financ. Markets 1(1), 21–35 (1994)MATHGoogle Scholar
  7. Konno, H., Shirakawa, H.: Existence of a nonnegative equilibrium price vector in the mean–variance capital market. Math. Finance 5(3), 233–246 (1995)MathSciNetMATHCrossRefGoogle Scholar
  8. Konno, H., Suzuki, K.: Equilibria in the capital market with non-homogeneous investors. Jpn. J. Ind. Appl. Math. 13(3), 369–383 (1996)MathSciNetMATHCrossRefGoogle Scholar
  9. Konno, H., Wijayanayake, A.: Mean–absolute deviation portfolio optimization model under transaction costs. J. Oper. Res. Soc. Jpn 42(4), 422–435 (1999)MathSciNetMATHCrossRefGoogle Scholar
  10. Konno, H., Wijayanayake, A.: Optimal rebalancing under concave transaction costs and minimal transaction units constraints. Math. Program. 89(2), 233–250 (2001a)MathSciNetMATHCrossRefGoogle Scholar
  11. Konno, H., Wijayanayake, A.: Minimal cost index tracking under concave transaction costs. Int. J. Theor. Appl. Finance 4(6), 939–957 (2001b)MathSciNetMATHCrossRefGoogle Scholar
  12. Konno, H., Wijayanayake, A.: Portfolio optimization under d. c. transaction costs and minimal transaction unit constraints. J. Global Optim. 22(1–4), 137–154 (2002)MathSciNetMATHCrossRefGoogle Scholar
  13. Konno, H., Yamamoto, R.: Minimal concave cost rebalance of a portfolio to the efficient frontier. Math. Program. 97(3), 571–585 (2003)MathSciNetMATHCrossRefGoogle Scholar
  14. Konno, H., Yamamoto, R.: Global optimization versus integer programming in portfolio optimization under nonconvex transaction costs. J. Global Optim. 32(2), 207–219 (2005a)MathSciNetMATHCrossRefGoogle Scholar
  15. Konno, H., Yamamoto, R.: Integer programming approaches in mean–risk models. J. Comput. Manage. Sci. 2(4), 339–351 (2005b)MathSciNetMATHCrossRefGoogle Scholar
  16. Konno, H., Yamazaki, H.: Mean–absolute deviation portfolio optimization model and its applications to tokyo stock market. Manage. Sci. 37(5), 519–531 (1991)CrossRefGoogle Scholar
  17. Konno, H., Waki, H., Yuuki, A.: Portfolio optimization under lower partial risk measures. Asia-Pac. Financ. Mark. 9(2), 127–140 (2002)MATHCrossRefGoogle Scholar
  18. Markowitz, H.: Portfolio Selection: Efficient Diversification of Investments. Wiley, New York, NY (1959)Google Scholar
  19. Ogryczak, O., Ruszczyński, A.: From stochastic dominance mean–risk model. Eur. J. Oper. Res. 116(1), 33–50 (1999)MATHCrossRefGoogle Scholar
  20. Ogryczak, O., Ruszczyński, A.: On consistency of stochastic dominance and mean–semideviation models. Math. Program. 89(2), 217–232 (2001)MathSciNetMATHCrossRefGoogle Scholar
  21. Perold, A.F.: Large scale portfolio optimization. Manage. Sci. 30(10), 1143–1160 (1984)MathSciNetMATHCrossRefGoogle Scholar
  22. Zenios, S.A.: Asset liability management under uncertainty for fixed income securities. Ann. Oper. Res. 59(1), 77–97 (1995)MATHCrossRefGoogle Scholar
  23. Zenios, S.A., Kang, P.: Mean–absolute deviation portfolio optimization for mortgage-backed securities. Ann. Oper. Res. 45(1), 433–450 (1993)MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringChuo UniversityTokyoJapan

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