Applying Markowitz’s Critical Line Algorithm


This paper derives a numerically enhanced version of Markowitz’s Critical Line Algorithm for computing the entire mean variance frontier with arbitrary lower and upper bounds on weights. We show that this algorithm computationally outperforms standard software packages and a recently developed quadratic optimization algorithm. As an illustration: For a 2,000-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.


Covariance Matrix Turning Point Portfolio Optimization Portfolio Selection Expected Return 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Kellogg School of Management, Managerial Economics and Decision SciencesNorthwestern UniversityEvanstonUSA
  2. 2.Credit Suisse, Asset Management and WWZUniversity of BaselBaselSwitzerland

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