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Entropy 2013, 15(11), 4607-4621; doi:10.3390/e15114607
Article

On the Diversity Constraints for Portfolio Optimization

Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Chungli, Taoyuan 32003, Taiwan
Received: 30 August 2013 / Revised: 19 October 2013 / Accepted: 23 October 2013 / Published: 28 October 2013
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Abstract

In the literature, Markowitz’s mean-variance model and its variants have been shown to yield portfolios that put excessive weights on only a few assets. Many diversity constraints were proposed and added to these models to avoid such overly concentrated portfolios. However, since these diversity constraints are formulated differently, it becomes difficult to compare them and study their relationships. This paper proposes a canonical form for the commonly used diversity constraints in the literature, and shows how to transform these diversity constraints into this canonical form. Furthermore, this paper compares these diversity constraints (in the canonical form with the same upper bound) on their ability to shrink the feasible region of the portfolio optimization problem. The results show a subset relation among their feasible regions.
Keywords: portfolio optimization; diversity constraint; norm; entropy portfolio optimization; diversity constraint; norm; entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Lin, J.-L. On the Diversity Constraints for Portfolio Optimization. Entropy 2013, 15, 4607-4621.

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