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

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.

Keywords:

portfolio selection, Markowitz model, quadratic programing, euclidean projection
[1]  Kriens J. and van Lieshout J. Th., 1998. Notes on the Markowitz portfolio selection method. Statistica Neerlandica 42 (3): 181-191.View Article
 
[2]  Li D., Ng W.L., 2000, Optimal dynamic portfolio selection: multiperiod mean-variance formulation, Mathematical Finance 10(3): 387-406.View Article
 
[3]  Markowitz H., 1952. Portfolio selection. The Journal ofFinance 7 (1): 77-91.
 
[4]  Merton R.C., 1972. An analytic derivation of the efficient portfolio frontier. Journal of Financial and Quantitative Analysis 7 (4): 1851-72.View Article
 
[5]  Best M.J. and Grauer R.R., 1992. Positively weighted minimum-variance portfolios and the structure of asset expected returns. Journal of Financial and Quantitative Analysis 27: 513-537.View Article
 
[6]  Miller M.H., 2000, The history of finance: an eyewitness account, Journal of Applied Corporate Finance 13(2): 8-14.View Article
 
[7]  Panjer H.H., editor: Boyle P.P....[et al.], 2001, Financial Economics: With Application to Investments, Insurance and Pensions. The Society of Actuaries.