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Annals of Operations Research

, Volume 45, Issue 1, pp 307–317 | Cite as

Computation of mean-semivariance efficient sets by the Critical Line Algorithm

  • Harry Markowitz
  • Peter Todd
  • Ganlin Xu
  • Yuji Yamane
Article

Abstract

The general mean-semivariance portfolio optimization problem seeks to determine the efficient frontier by solving a parametric non-quadratic programming problem. In this paper it is shown how to transform this problem into a general mean-variance optimization problem, hence the Critical Line Algorithm is applicable. This paper also discusses how to implement the critical line algorithm to save storage and reduce execution time.

Keywords

Mean-variance efficient frontier mean-semivariance efficient frontier historical returns Critical Line Algorithm 

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References

  1. [1]
    A.J. King and D.L. Jensen, Linear-quadratic efficient frontiers for portfolio optimization, RC 16524, IBM Research Report (1991).Google Scholar
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    H.M. Markowitz, The optimization of the quadratic function subject to linear constraints, Naval Res. Log. Quarterly 3 (1956) 111–133.Google Scholar
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    H.M. Markowitz,Portfolio Selection, Efficiency Diversification of Investments, Cowles Foundation Monograph 16 (Yale University Press, 1959 2nd ed.: Basil Blackwell, Cambridge, 1991).Google Scholar
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    H.M. Markowitz,Mean-Variance Analysis in Portfolio Choice and Capital Markets (Basil Blackwell, Cambridge, 1987).Google Scholar
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    H.M. Markowitz, P. Todd, G.L. Xu and Y. Yamane, Fast computation of mean-variance efficient sets using historical covariance, J. Fin. Eng. (1991), to appear.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Harry Markowitz
    • 1
  • Peter Todd
    • 1
  • Ganlin Xu
    • 1
  • Yuji Yamane
    • 1
  1. 1.Global Portfolio Research DepartmentDaiwa Securities Trust CompanyJersey CityUSA

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