The ex-ante and ex-post information of an asset return

If realized return is not the ex-post realization of the ex-ante expectation, can we use average realized return to estimate the expected return? In text books, the authors treat realized return as a sample of return. In this paper, we redefine realized return and the ex-post return, and we argue that realized return cannot be the sample of return. This paper is the first to explain the difference between ex-post and realized return; and we show the inability of the realized return to be the ex-post realization of the ex-ante expectation of return. In this paper we go back to the basic of the asset-pricing model, for example, and we focus on the reason behind the failure of realized return as an estimator for expected return. We show that, in general, realized return cannot be a sample of return and using the average realized return as the estimator for the expected return has been misleading over the years.