IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0133846.html
   My bibliography  Save this article

Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model

Author

Listed:
  • Takashi Shinzato

Abstract

In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always result in the best rate of return on assets. Prior to making investment decisions, it is important to an investor to know the potential minimal investment risk (or the expected minimal investment risk) and to determine the strategy that will maximize the return on assets. We use the self-averaging property to analyze the potential minimal investment risk and the concentrated investment level for the strategy that gives the best rate of return. We compare the results from our method with the results obtained by the operations research approach and with those obtained by a numerical simulation using the optimal portfolio. The results of our method and the numerical simulation are in agreement, but they differ from that of the operations research approach.

Suggested Citation

  • Takashi Shinzato, 2015. "Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-24, July.
    • Handle: RePEc:plo:pone00:0133846
    DOI: 10.1371/journal.pone.0133846
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0133846
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0133846&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0133846?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    4. 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.
    5. Takashi Shinzato & Muneki Yasuda, 2010. "Belief Propagation Algorithm for Portfolio Optimization Problems," Papers 1008.3746, arXiv.org, revised Sep 2010.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aekkachai NITTAYAGASETWAT & Jiroj BURANASIRI, 2016. "Performance Comparison Between Real Estate Securities and Real Estate Investment Using Stochastic Dominance and Mean-Variance Analysis," International Conference on Economic Sciences and Business Administration, Spiru Haret University, vol. 3(1), pages 208-219, October.
    2. Takashi Shinzato, 2017. "Property Safety Stock Policy for Correlated Commodities Based on Probability Inequality," Papers 1701.02245, arXiv.org.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Takashi Shinzato, 2014. "Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model," Papers 1404.5222, arXiv.org, revised Apr 2014.
    2. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    3. 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.
    4. Varga-Haszonits, Istvan & Caccioli, Fabio & Kondor, Imre, 2016. "Replica approach to mean-variance portfolio optimization," LSE Research Online Documents on Economics 68955, London School of Economics and Political Science, LSE Library.
    5. Jerome Garnier-Brun & Michael Benzaquen & Stefano Ciliberti & Jean-Philippe Bouchaud, 2021. "A new spin on optimal portfolios and ecological equilibria," Papers 2104.00668, arXiv.org, revised Oct 2021.
    6. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    7. 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.
    8. 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.
    9. Fabio Caccioli & Imre Kondor & G'abor Papp, 2015. "Portfolio Optimization under Expected Shortfall: Contour Maps of Estimation Error," Papers 1510.04943, arXiv.org.
    10. Jerome Garnier-Brun & Michael Benzaquen & Stefano Ciliberti & Jean-Philippe Bouchaud, 2021. "A new spin on optimal portfolios and ecological equilibria," Post-Print hal-03378915, HAL.
    11. Sefair, Jorge A. & Méndez, Carlos Y. & Babat, Onur & Medaglia, Andrés L. & Zuluaga, Luis F., 2017. "Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry," Omega, Elsevier, vol. 68(C), pages 39-48.
    12. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    13. Caccioli, Fabio & Kondor, Imre & Papp, Gábor, 2015. "Portfolio optimization under expected shortfall: contour maps of estimation error," LSE Research Online Documents on Economics 119463, London School of Economics and Political Science, LSE Library.
    14. Ben Abdallah, Skander & Lasserre, Pierre, 2016. "Asset retirement with infinitely repeated alternative replacements: Harvest age and species choice in forestry," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 144-164.
    15. Oscar Gutiérrez & Francisco Ruiz-Aliseda, 2011. "Real options with unknown-date events," Annals of Finance, Springer, vol. 7(2), pages 171-198, May.
    16. Timothy Erickson & Toni M. Whited, 2000. "Measurement Error and the Relationship between Investment and q," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 1027-1057, October.
    17. Arve, Malin & Zwart, Gijsbert, 2023. "Optimal procurement and investment in new technologies under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    18. Shively, Gerald E., 2001. "Price thresholds, price volatility, and the private costs of investment in a developing country grain market," Economic Modelling, Elsevier, vol. 18(3), pages 399-414, August.
    19. Marks, Phillipa & Marks, Brian, 2007. "Spectrum Allocation, Spectrum Commons and Public Goods: the Role of the Market," MPRA Paper 6785, University Library of Munich, Germany.
    20. Stern, Nicholas, 2018. "Public economics as if time matters: Climate change and the dynamics of policy," Journal of Public Economics, Elsevier, vol. 162(C), pages 4-17.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0133846. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.