Applying Markowitz’s Critical Line Algorithm

Abstract

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.