The Stationary Distribution of Returns and Portfolio Separation in Capital Markets: A Fundamental Contradiction

Abstract

In a general equilibrium model of risky assets, prices would be determined by the interaction of the supply and demand. Unpredictable events would impact one or both sides of the asset market and thereby influence the return on assets. The probability distribution of returns would thus be endogenous. Since expectations as to subsequent asset returns influence asset demand, the probability distribution of returns is a crucial element in the general equilibrium system; it is the consequence of the demand and supply of assets and, at the same time, a central determinant of expectations and, hence, of the demand for assets. Nevertheless, it is possible to undertake a partial equilibrium analysis in which the behavior of asset demand, conditional upon a postulated probability distribution of returns, is examined. In such a limited context, it is natural to postulate a “convenient” probability distribution of returns, namely, one that facilitates the analysis of demand. A leading assumption has been that returns are serially independent and obey a stationary distribution.