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Equilibrium relations in a capital asset market: A mean absolute deviation approach

  • Hiroshi Konno
  • Hiroshi Shirakawa
Article

Abstract

We consider the equilibrium in a capital asset market where the risk is measured by the absolute deviation, instead of the standard deviation of the rate of return of the portfolio. It is shown that the equilibrium relations proved by Mossin for the mean variance (MV) model can also be proved for the mean absolute deviation (MAD) model under similar assumptions on the capital market. In particular, a sufficient condition is derived for the existence of a unique nonnegative equilibrium price vector and derive its explicit formula in terms of exogeneously determined variables. Also, we prove relations between the expected rate of return of individual assets and the market portfolio.

Key words

MAD model CAPM absolute deviation portfolio analysis 

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References

  1. Black, F. (1972), ‘Capital market equilibrium with restricted borrowing’,J. of Business,45, 444–454.CrossRefGoogle Scholar
  2. Chvátal, V. (1983),Linear Programming, Freeman and Co.Google Scholar
  3. Fama, E.F. (1976),Foundations of Finance, Basic Books.Google Scholar
  4. Kijima, M. and Ohnishi, M. (1992),Risk Aversion and Wealth Effects on Optimal Portfolios with Many Investment Opportunities, Technical Report No. 92-02, Graduate School of System Management, University of Tsukuba.Google Scholar
  5. Konno, H. (1990), ‘Piecewise linear risk functions and portfolio optimization’,Journal of the Operations Research Society of Japan,33, 139–156.Google Scholar
  6. Konno, H., Shirakawa, H. and Yamazaki, H. (1993), ‘A mean-absolute deviation-skewness portfolio optimization model’.Annals of Operations Research,45; 205–220.CrossRefGoogle Scholar
  7. Konno, H. and Yamashita, H. (1978),Nonlinear Programming, Japan Science and Technology Association Press.Google Scholar
  8. Konno, H. and Yamazaki, H. (1991), ‘A mean-absolute deviation portfolio optimization model and its application to Tokyo stock market’,Management Science,37; 519–531.CrossRefGoogle Scholar
  9. Lintner, J. (1965), ‘The valuation of risk assets and the selection of risky investments in stock portfolio and capital budgets’,Review of Economics and Statistics,47, 13–47.CrossRefGoogle Scholar
  10. Luenberger, D.G. (1984),Introduction to Linear and Nonlinear Programming (2nd ed.), John Wiley & Sons.Google Scholar
  11. Luenberger, D.G. (1969),Optimization by Vector Space Methods, John Wiley & Sons.Google Scholar
  12. Markowitz, H. (1959),Portfolio Selection: Efficient Diversification of Investments, John Wiley & Sons.Google Scholar
  13. Mossin, J. (1966), ‘Equilibrium in a capital asset market’,Econometrica,34, 768–783.Google Scholar
  14. Mulvey, J. and Zenois, S.A. (1992), ‘Capturing the correlations of fixed-income instruments’, To appear inManagement Science.Google Scholar
  15. Nemhauser, G. and Wolsey, L.A. (1988),Integer and Combinatorial Optimization. John Wiley & Sons.Google Scholar
  16. Press, S.J. (1982),Applied Multivariate Analysis, Robert E. Krieger Publishing Company.Google Scholar
  17. Rao, C.R. (1973),Linear Statistical Inference and Its Applications (2nd ed.), John Wiley & Sons.Google Scholar
  18. Sharpe, W.F. (1964), ‘Capital asset prices: a theory of market equilibrium under conditions of risk’,The Journal of Finance,19, 425–442.Google Scholar
  19. Sharpe, W.F. (1970),Portfolio Theory and Capital Market, McGraw Hill.Google Scholar
  20. Shirakawa, H. and Konno, H. (1993), Optimal portfolio selection for multi-factor stable distribution model,Proceedings of JAFEE Winter Meeting, 89–97.Google Scholar
  21. Worzel, K.J. and Zenios, S.A. (1992),Tracking A Mortgage Index: An Optimization Approach. Technical Report No. 92-08-01, Department of Decision Sciences, The Wharton School, University of Pennsylvania, Pennsylvania.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Hiroshi Konno
    • 1
  • Hiroshi Shirakawa
    • 1
  1. 1.Department of Industrial and Systems EngineeringTokyo Institute of TechnologyTokyoJapan

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