We consider the randomness of market trade as the origin of price and return stochasticity. We look at time series of trade values and volumes as random variables during the averaging interval Δ and describe the dependences of market-based volatilities of price and return on the volatilities...

We consider the randomness of values and volumes of market deals as a major factor that describes lower bounds of uncertainty and upper limits on the accuracy of the forecasts of macroeconomic variables, prices, and returns. We introduce random macroeconomic variables, whose average values...

This paper defines theoretical lower bounds of uncertainty of observations of macroeconomic variables that depend on statistical moments and correlations of random values and volumes of market trades. Any econometric assessments of macroeconomic variables have greater uncertainty. We consider...

We consider the consumption-based asset-pricing model, derive a new modified basic pricing equation, and present its successive approximations using the Taylor series expansions of the investor’s utility during the averaging time interval. For linear and quadratic Taylor approximations, we...

We show how time-series of random market trade values and volumes completely describe stochasticity of stock returns. We derive equation that links up returns with current and past trade values and show how statistical moments of the trade values and volumes determine statistical moments of...

The paper presents the unified theoretical description of three levels of the market-based statistical moments of “actual” returns, which Investors gain within their market sales. The market-based statistics of “actual” returns takes into account the size of the trade sale values,...

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...

This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval Δ results in the random properties of price and return. We describe how...

This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz’s definition of value weighted return of a portfolio as the definition of market-based average return of trades...

We show how time-series of random market trade values and volumes completely describe stochasticity of stock returns. We derive equation that links up returns with current and past trade values and show how statistical moments of the trade values and volumes determine statistical moments of...