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A Note On Semivariance

Author

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  • Hanqing Jin
  • Harry Markowitz
  • Xun Yu Zhou

Abstract

In a recent paper (Jin, Yan, and Zhou 2005), it is proved that efficient strategies of the continuous‐time mean–semivariance portfolio selection model are in general never achieved save for a trivial case. In this note, we show that the mean–semivariance efficient strategies in a single period are always attained irrespective of the market condition or the security return distribution. Further, for the below‐target semivariance model the attainability is established under the arbitrage‐free condition. Finally, we extend the results to problems with general downside risk measures.

Suggested Citation

  • Hanqing Jin & Harry Markowitz & Xun Yu Zhou, 2006. "A Note On Semivariance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 53-61, January.
    • Handle: RePEc:bla:mathfi:v:16:y:2006:i:1:p:53-61
    DOI: 10.1111/j.1467-9965.2006.00260.x
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    Cited by:

    1. Kassimatis, Konstantinos, 2021. "Mean-variance versus utility maximization revisited: The case of constant relative risk aversion," International Review of Financial Analysis, Elsevier, vol. 78(C).
    2. Felix Fie{ss}inger & Mitja Stadje, 2023. "Time-Consistent Asset Allocation for Risk Measures in a L\'evy Market," Papers 2305.09471, arXiv.org, revised Jun 2023.
    3. Brogan, Anita J. & Stidham Jr., Shaler, 2008. "Non-separation in the mean-lower-partial-moment portfolio optimization problem," European Journal of Operational Research, Elsevier, vol. 184(2), pages 701-710, January.
    4. Černý, Aleš & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2012. "On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 386-395.
    5. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    6. Pengyu Wei & Zuo Quan Xu, 2021. "Dynamic growth-optimum portfolio choice under risk control," Papers 2112.14451, arXiv.org.
    7. Juan F. Monge & Mercedes Landete & Jos'e L. Ruiz, 2016. "Sharpe portfolio using a cross-efficiency evaluation," Papers 1610.00937, arXiv.org, revised Oct 2016.
    8. Cumova, Denisa & Nawrocki, David, 2011. "A symmetric LPM model for heuristic mean-semivariance analysis," Journal of Economics and Business, Elsevier, vol. 63(3), pages 217-236, May.
    9. Beach, Steven L., 2011. "Semivariance decomposition of country-level returns," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 607-623, October.
    10. Tong Wang & Atalay Atasu & Mümin Kurtuluş, 2012. "A Multiordering Newsvendor Model with Dynamic Forecast Evolution," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 472-484, July.

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