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.

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.

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This paper examines properties of mean-variance inefficient proxies with respect to producing a linear relation between expected returns and betas. The numerical results of a Monte Carlo simulation show that in the CAPM slightly inefficient, positively weighted proxies cause an almost perfect linear expected return-beta relation. Moreover, we show that a strong linearity among a predefined subset of assets exists. These implications are important for the interpretation of empirical tests as well as for asset pricing and for the improvement of proxies' benchmark properties. In contrast to current literature the results suggest that the CAPM's pricing error is small when slightly inefficient, positively weighted proxies are used.