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Continuous-time mean-variance efficiency: the 80% rule

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  • Xun Li
  • Xun Yu Zhou

Abstract

This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient \`{a} la Markowitz. It is shown that, when the market coefficients are deterministic functions of time, a mean-variance efficient portfolio realizes the (discounted) targeted return on or before the terminal date with a probability greater than 0.8072. This number is universal irrespective of the market parameters, the targeted return and the length of the investment horizon.

Suggested Citation

  • Xun Li & Xun Yu Zhou, 2007. "Continuous-time mean-variance efficiency: the 80% rule," Papers math/0702249, arXiv.org.
    • Handle: RePEc:arx:papers:math/0702249
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    File URL: http://arxiv.org/pdf/math/0702249
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    References listed on IDEAS

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    1. Jianming Xia, 2005. "Mean–Variance Portfolio Choice: Quadratic Partial Hedging," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 533-538, July.
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