IDEAS home Printed from https://ideas.repec.org/p/ube/dpvwib/dp0701.html
   My bibliography  Save this paper

Applying Markowitz's Critical Line Algorithm

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://repec.vwiit.ch/dp/dp0701.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. Niedermayer, Daniel & Zimmermann, Heinz, 2007. "The Cross-Section of Positively Weighted Portfolios," Working papers 2007/15, Faculty of Business and Economics - University of Basel.
    4. Andras Niedermayer & Daniel Niedermayer, 2006. "Applying Markowitz's Critical Line Algorithm," Diskussionsschriften dp0602, Universitaet Bern, Departement Volkswirtschaft.
    5. Vic Norton, 2012. "An algorithm for the orthogonal decomposition of financial return data," Papers 1206.2333, arXiv.org, revised Nov 2014.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guerard, John, 2023. "Harry Markowitz: An appreciation," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1496-1501.
    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. Vic Norton, 2012. "An algorithm for the orthogonal decomposition of financial return data," Papers 1206.2333, arXiv.org, revised Nov 2014.
    4. Atskanov, Isuf, 2015. "Dynamic optimization of an investment portfolio on European stock markets using pair copulas," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 40(4), pages 84-105.
    5. Li, Hua & Bai, Zhidong & Wong, Wing-Keung & McAleer, Michael, 2022. "Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization," Econometrics and Statistics, Elsevier, vol. 24(C), pages 133-150.
    6. Cristiano Arbex Valle, 2024. "Portfolio optimisation: bridging the gap between theory and practice," Papers 2407.00887, arXiv.org, revised Sep 2024.
    7. Niedermayer, Daniel & Zimmermann, Heinz, 2007. "The Cross-Section of Positively Weighted Portfolios," Working papers 2007/15, Faculty of Business and Economics - University of Basel.
    8. 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.
    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.
    10. 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.
    11. Barbara Alemanni & Mario Maggi & Pierpaolo Uberti, 2021. "Unleveraged Portfolios and Pure Allocation Return," JRFM, MDPI, vol. 14(11), pages 1-11, November.
    12. Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.
    13. Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2017. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1121-1131.
    14. Tiago P. Filomena & Miguel A. Lejeune, 2014. "Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 308-329, April.
    15. Marie Briere & Ariane Szafarz, 2017. "Factor Investing: The Rocky Road from Long-Only to Long-Short," Working Papers CEB 17-013, ULB -- Universite Libre de Bruxelles.
    16. Jarrod Wilcox & Frank Fabozzi, 2009. "A Discretionary Wealth Approach to Investment Policy," Yale School of Management Working Papers amz2434, Yale School of Management.
    17. 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.
    18. Yu, Jing-Rung & Lee, Wen-Yi, 2011. "Portfolio rebalancing model using multiple criteria," European Journal of Operational Research, Elsevier, vol. 209(2), pages 166-175, March.
    19. Vrinda Dhingra & Shiv Kumar Gupta & Amita Sharma, 2023. "Norm constrained minimum variance portfolios with short selling," Computational Management Science, Springer, vol. 20(1), pages 1-35, December.
    20. 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.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ube:dpvwib:dp0701. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Franz Koelliker (email available below). General contact details of provider: https://edirc.repec.org/data/vwibech.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.