Submitted to the Annals of Applied Probability CONTINUOUS-TIME MEAN–VARIANCE EFFICIENCY:

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 deter-ministic 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 irrespec-tive of the market parameters, the targeted return, and the length of the investment horizon. 1. Introduction. In his seminal work Markowitz (1952), Markowitz proposed the mean–variance portfolio selection model for a single invest-ment period, where an agent seeks to maximize the risk of his investment, measured by the variance of his return, subject to a given mean return1. The dynamic extension of the Markowitz model, especially in continuous time