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An asymptotic analysis of the mean-variance portfolio selection

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  • 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), pages 63-86, January.
    • Handle: RePEc:bpj:strimo:v:25:y:2007:i:1/2007:p:24:n:4
    DOI: 10.1524/stnd.2007.25.1.63
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    References listed on IDEAS

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    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.
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    5. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, 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.
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    Cited by:

    1. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129, arXiv.org, revised May 2013.

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