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Maximizing and minimizing investment concentration with constraints of budget and investment risk

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  • Shinzato, Takashi

Abstract

In this paper, as a first step in examining the properties of a feasible portfolio subset that is characterized by budget and risk constraints, we assess the maximum and minimum of the investment concentration using replica analysis. To do this, we apply an analytical approach of statistical mechanics. We note that the optimization problem considered in this paper is the dual problem of the portfolio optimization problem discussed in the literature, and we verify that these optimal solutions are also dual. We also present numerical experiments, in which we use the method of steepest descent that is based on Lagrange’s method of undetermined multipliers, and we compare the numerical results to those obtained by replica analysis in order to assess the effectiveness of our proposed approach.

Suggested Citation

  • Shinzato, Takashi, 2018. "Maximizing and minimizing investment concentration with constraints of budget and investment risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 986-993.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:986-993
    DOI: 10.1016/j.physa.2017.08.088
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    References listed on IDEAS

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    1. Takashi Shinzato, 2016. "Replica Analysis for the Duality of the Portfolio Optimization Problem," Papers 1609.05475, arXiv.org.
    2. Takashi Shinzato, 2016. "Portfolio Optimization Problem with Non-identical Variances of Asset Returns using Statistical Mechanical Informatics," Papers 1605.06843, arXiv.org.
    3. Stefano Ciliberti & Imre Kondor & Marc Mezard, 2007. "On the feasibility of portfolio optimization under expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 389-396.
    4. Pafka, Szilárd & Kondor, Imre, 2003. "Noisy covariance matrices and portfolio optimization II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 487-494.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Daichi Tada & Hisashi Yamamoto & Takashi Shinzato, 2017. "Random matrix approach for primal-dual portfolio optimization problems," Papers 1709.04620, arXiv.org, revised Sep 2017.
    7. Takashi Shinzato & Muneki Yasuda, 2015. "Belief Propagation Algorithm for Portfolio Optimization Problems," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-10, August.
    8. S. Ciliberti & M. Mézard, 2007. "Risk minimization through portfolio replication," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 175-180, May.
    9. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    10. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    11. Kondor, Imre & Pafka, Szilard & Nagy, Gabor, 2007. "Noise sensitivity of portfolio selection under various risk measures," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1545-1573, May.
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    Cited by:

    1. Oleg S. Sukharev, 2020. "Portfolio Theory in Solving the Problem Structural Choice," JRFM, MDPI, vol. 13(9), pages 1-21, September.

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