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Applying Markowitz's Critical Line Algorithm

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  • Andras Niedermayer
  • Daniel Niedermayer

Abstract

We provide a Matlab quadratic optimization tool based on Markowitz's critical line algorithm that significantly outperforms standard software packages and a recently developed operations research algorithm. As an illustration: For a 2000 asset universe our method needs less than a second to compute the whole frontier whereas the quickest competitor needs several hours. This paper can be considered as a didactic alternative to the critical line algorithm such as presented by Markowitz and treats all steps required by the algorithm explicitly. Finally, we present a benchmark of different optimization algorithms' performance.

Suggested Citation

  • Andras Niedermayer & Daniel Niedermayer, 2007. "Applying Markowitz's Critical Line Algorithm," Diskussionsschriften dp0701, Universitaet Bern, Departement Volkswirtschaft.
    • Handle: RePEc:ube:dpvwib:dp0701
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    References listed on IDEAS

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    1. Andras Niedermayer & Daniel Niedermayer, 2006. "Applying Markowitz's Critical Line Algorithm," Diskussionsschriften dp0602, Universitaet Bern, Departement Volkswirtschaft.
    2. Bruce I. Jacobs & Kenneth N. Levy & Harry M. Markowitz, 2005. "Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions," Operations Research, INFORMS, vol. 53(4), pages 586-599, August.
    3. Michael Wolf, 2006. "Resampling vs. Shrinkage for Benchmarked Managers," IEW - Working Papers 263, Institute for Empirical Research in Economics - University of Zurich.
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    Cited by:

    1. Andras Niedermayer & Daniel Niedermayer, 2006. "Applying Markowitz's Critical Line Algorithm," Diskussionsschriften dp0602, Universitaet Bern, Departement Volkswirtschaft.
    2. MohammadAmin Fazli & Parsa Alian & Ali Owfi & Erfan Loghmani, 2021. "RPS: Portfolio Asset Selection using Graph based Representation Learning," Papers 2111.15634, arXiv.org.
    3. Ralph Steuer & Markus Hirschberger & Kalyanmoy Deb, 2016. "Extracting from the relaxed for large-scale semi-continuous variable nondominated frontiers," Journal of Global Optimization, Springer, vol. 64(1), pages 33-48, January.
    4. Clarence C. Y. Kwan, 2018. "What really happens if the positive definiteness requirement on the covariance matrix of returns is relaxed in efficient portfolio selection?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 32(1), pages 77-110, February.
    5. Niedermayer, Daniel & Zimmermann, Heinz, 2007. "The Cross-Section of Positively Weighted Portfolios," Working papers 2007/15, Faculty of Business and Economics - University of Basel.
    6. Vic Norton, 2012. "An algorithm for the orthogonal decomposition of financial return data," Papers 1206.2333, arXiv.org, revised Nov 2014.
    7. Yue Qi & Ralph E. Steuer, 2020. "On the analytical derivation of efficient sets in quad-and-higher criterion portfolio selection," Annals of Operations Research, Springer, vol. 293(2), pages 521-538, October.
    8. Markus Hirschberger & Ralph E. Steuer & Sebastian Utz & Maximilian Wimmer & Yue Qi, 2013. "Computing the Nondominated Surface in Tri-Criterion Portfolio Selection," Operations Research, INFORMS, vol. 61(1), pages 169-183, February.
    9. Yue Qi, 2017. "On the criterion vectors of lines of portfolio selection with multiple quadratic and multiple linear objectives," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(1), pages 145-158, March.

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    More about this item

    Keywords

    finance; portfolio selection; efficient frontier; critical line algorithm; quadratic optimization; numerical methods;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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