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

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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.

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References

  1. A.J. King and D.L. Jensen, Linear-quadratic efficient frontiers for portfolio optimization, RC 16524, IBM Research Report (1991).

  2. H.M. Markowitz, The optimization of the quadratic function subject to linear constraints, Naval Res. Log. Quarterly 3 (1956) 111–133.

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  3. H.M. Markowitz,Portfolio Selection, Efficiency Diversification of Investments, Cowles Foundation Monograph 16 (Yale University Press, 1959 2nd ed.: Basil Blackwell, Cambridge, 1991).

  4. H.M. Markowitz,Mean-Variance Analysis in Portfolio Choice and Capital Markets (Basil Blackwell, Cambridge, 1987).

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  5. 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.

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Authors and Affiliations

  1. Global Portfolio Research Department, Daiwa Securities Trust Company, One Evertrust Plaza, 07302, Jersey City, NJ, USA

    Harry Markowitz, Peter Todd, Ganlin Xu & Yuji Yamane

Authors
  1. Harry Markowitz
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  2. Peter Todd
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  3. Ganlin Xu
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  4. Yuji Yamane
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Markowitz, H., Todd, P., Xu, G. et al. Computation of mean-semivariance efficient sets by the Critical Line Algorithm. Ann Oper Res 45, 307–317 (1993). https://doi.org/10.1007/BF02282055

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  • DOI: https://doi.org/10.1007/BF02282055

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