@article{jfe2013131,
author={Zaks, Yaniv},
title={An Alternative Proof to Markowitz¡¯s Model},
journal={Journal of Finance and Economics},
volume={1},
number={3},
pages={33--35},
year={2013},
url={http://pubs.sciepub.com/jfe/1/3/1},
issn={2328-7276},
abstract={In the fundamental paper on portfolio selection, Markowitz (1952) described via geometric reasoning his innovative theory and provided the explicit optimal selection for the cases of 3 and 4 assets. Merton (1972) obtained for the general case the efficient portfolio frontiers explicitly by using Lagrange multipliers. In this paper, we suggest a geometric approach to achieve the explicit optimal selection for the general case thus generalizing Markowitz¡¯s original approach to achieve the explicit presentation of the desired selection.},
doi={10.12691/jfe-1-3-1}
publisher={Science and Education Publishing}
}