Open Access Peer-reviewed

An Alternative Proof to Markowitz’s Model

Yaniv Zaks
Department of Mathematics, Bar-Ilan University, Israel
Journal of Finance and Economics. 2013, 1(3), 33-35. DOI: 10.12691/jfe-1-3-1
Published online: August 25, 2017


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.


portfolio selection, Markowitz model, quadratic programing, euclidean projection
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