Comments on “A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem”

doi:10.1016/j.ejor.2008.01.041

European Journal of Operational Research

Volume 194, Issue 1, 1 April 2009, Pages 339-341

https://doi.org/10.1016/j.ejor.2008.01.041 Get rights and content

Abstract

Benati and Rizzi [S. Benati, R. Rizzi, A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem, European Journal of Operational Research 176 (2007) 423–434], in a recent proposal of two linear integer programming models for portfolio optimization using Value-at-Risk as the measure of risk, claimed that the two counterpart models are equivalent. This note shows that this claim is only partly true. The second model attempts to minimize the probability of the portfolio return falling below a certain threshold instead of minimizing the Value-at-Risk. However, the discontinuity of real-world probability values makes the second model impractical. An alternative model with Value-at-Risk as the objective is thus proposed.

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Acknowledgement

The authors would like to thank the National Science Council of the Republic of China, Taiwan for financially supporting this research under Contract No. NSC 96-2416-H-182-009-MY2.

References (1)

S. Benati et al.
A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem
European Journal of Operational Research
(2007)

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A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem

European Journal of Operational Research

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Comments on “A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem”