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

Xun Li·Xun Yu Zhou
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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 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.

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Xun Li, Xun Yu Zhou. 2007-02-09. Continuous-time mean-variance efficiency: the 80% rule. https://doi.org/10.1214/105051606000000349

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