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Revisions of modern portfolio theory optimization model

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  • Milan Vaclavik
  • Josef Jablonsky

Abstract

Among others, fluctuations in market sentiment cause step changes of correlations of financial instrument prices. This phenomenon of the correlations’ destabilization, which was markedly highlighted during the recent financial crisis, reduces the efficiency of the traditional approach to the market risk diversification based on the Markowitz Optimal Portfolio Selection Model. The original Markowitz optimization model represents a convex quadratic programming problem. Almost any efforts to its reformulation involving the above-mentioned facts lead to the loss of a positive semi-definiteness of the matrix occurring in the model’s structure. This leads to a non-convex programming problem whose solution is generally problematic. By refinement of the merits of the original model, we get into trouble with its computational, formal aspect. Therefore, it is necessary to find a way to the reconvexification of the reformulated model. Main objective of the paper is to propose a convex representation of the reformulated model. Copyright Springer-Verlag 2012

Suggested Citation

  • Milan Vaclavik & Josef Jablonsky, 2012. "Revisions of modern portfolio theory optimization model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 473-483, September.
    • Handle: RePEc:spr:cejnor:v:20:y:2012:i:3:p:473-483
    DOI: 10.1007/s10100-011-0227-2
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    References listed on IDEAS

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    1. Bernd Brandl & Christian Keber & Matthias Schuster, 2006. "An automated econometric decision support system: forecasts for foreign exchange trades," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 401-415, December.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Yong Fang & Kin Keung Lai & Shouyang Wang, 2008. "Fuzzy Portfolio Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-77926-1, December.
    4. Takashi Hasuike & Hiroaki Ishii, 2009. "Probability maximization models for portfolio selection under ambiguity," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(2), pages 159-180, June.
    5. 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.
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    Cited by:

    1. Mahdi Massahi & Masoud Mahootchi & Alireza Arshadi Khamseh, 2020. "Development of an efficient cluster-based portfolio optimization model under realistic market conditions," Empirical Economics, Springer, vol. 59(5), pages 2423-2442, November.
    2. Josef Jablonsky & Petr Fiala, 2012. "Special issue of the Czech Society for Operations Research," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 367-368, September.
    3. Vladimír Holý & Michal Černý, 2022. "Bertram’s pairs trading strategy with bounded risk," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 667-682, June.
    4. Akhter Mohiuddin Rather & V. N. Sastry & Arun Agarwal, 2017. "Stock market prediction and Portfolio selection models: a survey," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 558-579, September.

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