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On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory

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  • Taras Bodnar
  • Nestor Parolya
  • Wolfgang Schmid

Abstract

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean-variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean-variance efficient. The conditions for the mean-variance efficiency of the solutions depend on the unknown parameters of the asset returns. We deal with the problem of parameter uncertainty in detail and derive the probabilities that the estimated solutions of the Markowitz problem and the quadratic utility problem are mean-variance efficient. Because these probabilities deviate from one the above mentioned quadratic optimization problems are not stochastically equivalent. The obtained results are illustrated by an empirical study.

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File URL: http://arxiv.org/pdf/1207.1029
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1207.1029.

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Date of creation: Jul 2012
Date of revision: Apr 2013
Publication status: Published in European Journal of Operational Research, Volume 229, Issue 3, 2013, pp. 637-644
Handle: RePEc:arx:papers:1207.1029

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Web page: http://arxiv.org/

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