IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v25y2007i1-2007p24n4.html
   My bibliography  Save this article

An asymptotic analysis of the mean-variance portfolio selection

Author

Listed:
  • Ottucsák György
  • Vajda István

Abstract

This paper gives an asymptotic analysis of the mean-variance (Markowitz-type) portfolio selection under mild assumptions on the market behavior. Theoretical results show the rate of underperformance of the risk aware Markowitz-type portfolio strategy in growth rate compared to the log-optimal portfolio strategy, which does not have explicit risk control. Statements are given with and without full knowledge of the statistical properties of the underlying process generating the market, under the only assumption that the market is stationary and ergodic. The experiments show how the achieved wealth depends on the coefficient of risk aversion measured on past NYSE data.

Suggested Citation

  • Ottucsák György & Vajda István, 2007. "An asymptotic analysis of the mean-variance portfolio selection," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 1-24, January.
  • Handle: RePEc:bpj:strimo:v:25:y:2007:i:1/2007:p:24:n:4
    DOI: 10.1524/stnd.2007.25.1.63
    as

    Download full text from publisher

    File URL: https://doi.org/10.1524/stnd.2007.25.1.63
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1524/stnd.2007.25.1.63?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Grossman, Sanford J & Shiller, Robert J, 1981. "The Determinants of the Variability of Stock Market Prices," American Economic Review, American Economic Association, vol. 71(2), pages 222-227, May.
    4. Grauer, Robert R., 1981. "A Comparison of Growth Optimal and Mean Variance Investment Policies," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(1), pages 1-21, March.
    5. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
    6. David P. Helmbold & Robert E. Schapire & Yoram Singer & Manfred K. Warmuth, 1998. "On‐Line Portfolio Selection Using Multiplicative Updates," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 325-347, October.
    7. Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. "Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
    8. László Györfi & Gábor Lugosi & Frederic Udina, 2006. "Nonparametric Kernel‐Based Sequential Investment Strategies," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 337-357, April.
    9. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
    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. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129, arXiv.org, revised May 2013.

    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. Bin Li & Steven C. H. Hoi, 2012. "On-Line Portfolio Selection with Moving Average Reversion," Papers 1206.4626, arXiv.org.
    2. Ting-Kam Leonard Wong, 2015. "Universal portfolios in stochastic portfolio theory," Papers 1510.02808, arXiv.org, revised Dec 2016.
    3. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    4. Vajda, István & Ottucsák, György, 2006. "Empirikus portfólióstratégiák [Empirical portfolio strategies]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 624-640.
    5. Guo, Sini & Gu, Jia-Wen & Ching, Wai-Ki, 2021. "Adaptive online portfolio selection with transaction costs," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1074-1086.
    6. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129, arXiv.org, revised May 2013.
    7. John Y. Campbell & Yeung Lewis Chanb & M. Viceira, 2013. "A multivariate model of strategic asset allocation," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 39, pages 809-848, World Scientific Publishing Co. Pte. Ltd..
    8. Seung-Hyun Moon & Yong-Hyuk Kim & Byung-Ro Moon, 2019. "Empirical investigation of state-of-the-art mean reversion strategies for equity markets," Papers 1909.04327, arXiv.org.
    9. Man Yiu Tsang & Tony Sit & Hoi Ying Wong, 2022. "Adaptive Robust Online Portfolio Selection," Papers 2206.01064, arXiv.org.
    10. Joseph R. Blasi & Douglas L. Kruse & Harry M. Markowitz, 2010. "Risk and Lack of Diversification under Employee Ownership and Shared Capitalism," NBER Chapters, in: Shared Capitalism at Work: Employee Ownership, Profit and Gain Sharing, and Broad-based Stock Options, pages 105-136, National Bureau of Economic Research, Inc.
    11. David S. Jones & V. Vance Roley, 1981. "Bliss Points in Mean-Variance Portfolio Models," NBER Technical Working Papers 0019, National Bureau of Economic Research, Inc.
    12. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    13. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    14. Alessandra Carleo & Francesco Cesarone & Andrea Gheno & Jacopo Maria Ricci, 2017. "Approximating exact expected utility via portfolio efficient frontiers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 115-143, November.
    15. Ha, Youngmin & Zhang, Hai, 2020. "Algorithmic trading for online portfolio selection under limited market liquidity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1033-1051.
    16. Andrea Morone, 2008. "Comparison of Mean-Variance Theory and Expected-Utility Theory through a Laboratory Experiment," Economics Bulletin, AccessEcon, vol. 3(40), pages 1-7.
    17. Fatma Lajeri-Chaherli, 2016. "On The Concavity And Quasiconcavity Properties Of ( Σ , Μ ) Utility Functions," Bulletin of Economic Research, Wiley Blackwell, vol. 68(3), pages 287-296, April.
    18. Eckhard Platen & Renata Rendek, 2012. "Approximating the numéraire portfolio by naive diversification," Journal of Asset Management, Palgrave Macmillan, vol. 13(1), pages 34-50, February.
    19. Roujia Li & Jia Liu, 2022. "Online Portfolio Selection with Long-Short Term Forecasting," SN Operations Research Forum, Springer, vol. 3(4), pages 1-15, December.
    20. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.

    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:bpj:strimo:v:25:y:2007:i:1/2007:p:24:n:4. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.