On the Class of Elliptical Distributions and their Applications to the Theory of Portfolio Choice

Abstract

ABSTRACT It is shown that the class of elliptical distributions extend the Tobin [14] separation theorem, Bawa's [2] rules of ordering uncertain prospects, Ross's [12] mutual fund separation theorems, and the results of the CAPM to non‐normal distributions, which are not necessarily stable. Further, the mean‐covariance matrix framework is generalized to a mean‐characteristic matrix framework in which the characteristic matrix is the basis for a spread or risk measure, and a generalized equilibrium pricing equation is arrived at. The implications to empirical testing of the CAPM and modeling the empirical distribution of speculative prices are discussed.