  Markets possess all available information on stock returns. The randomness of
market trade determines the statistics of stock returns. This paper describes
the dependence of the first four market-based statistical moments of stock
returns on statistical moments and correlations of current and past trade
values. The mean return of trades during the averaging period coincides with
Markowitz's definition of portfolio value weighted return. We derive the
market-based volatility of return and return-value correlations. We present
approximations of the characteristic functions and probability measures of
stock return by a finite number of market-based statistical moments. To
forecast market-based average return or volatility of return, one should
predict the statistical moments and correlations of current and past market
trade values at the same time horizon.
