  We discuss the economic reasons why the predictions of price and return
statistical moments in the coming decades, in the best case, will be limited by
their averages and volatilities. That limits the accuracy of the forecasts of
price and return probabilities by Gaussian distributions. The economic origin
of these restrictions lies in the fact that the predictions of the market-based
n-th statistical moments of price and return for n=1,2,.., require the
description of the economic variables of the n-th order that are determined by
sums of the n-th degrees of values or volumes of market trades. The lack of
existing models that describe the evolution of the economic variables
determined by the sums of the 2nd degrees of market trades results in the fact
that even predictions of the volatilities of price and return are very
uncertain. One can ignore existing economic barriers that we highlight but
cannot overcome or resolve them. The accuracy of predictions of price and
return probabilities substantially determines the reliability of asset pricing
models and portfolio theories. The restrictions on the accuracy of predictions
of price and return statistical moments reduce the reliability and veracity of
modern asset pricing and portfolio theories.
