Continuous-time mean-variance efficiency: the 80% rule
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.
Keywords
Cite
@article{arxiv.math/0702249,
title = {Continuous-time mean-variance efficiency: the 80% rule},
author = {Xun Li and Xun Yu Zhou},
journal= {arXiv preprint arXiv:math/0702249},
year = {2008}
}
Comments
Published at http://dx.doi.org/10.1214/105051606000000349 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)