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

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.