We provide a Matlab quadratic optimization tool based on Markowitz’s citical 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.