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

Xun Li, Xun Yu Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

41 Citations (Scopus)


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 à 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.
Original languageEnglish
Pages (from-to)1751-1763
Number of pages13
JournalAnnals of Applied Probability
Issue number4
Publication statusPublished - 1 Nov 2006
Externally publishedYes


  • Continuous time
  • Goalachieving
  • Hitting time
  • Mean-variance efficiency
  • Portfolio selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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