Portfolio Analysis with Symmetric Stable Paretian Returns

Abstract

We analyze a portfolio selection problem in a market where asset returns have jointly symmetric stable Paretian distribution. Univariate stable distributions are characterized by four parameters: the stability index a, the (scale or) dispersion parameterathe (mean or) location parameter p and the parameter of asymmetry ß. We consider portfolios having stable distribution with 1 < a < 2 and = 0. Since stable distributions have infinite variance, Markowitz’ mean-variance rule does not apply to this case. With stable distributions risk is measured by dispersion. The main result is given by a linear relation between expected return and the efficient level of dispersion in the single agent portfolio selection problem. Hence, the efficient set is convex, permitting us to derive an equilibrium model, called stable-CAPM. Moreover, we find that the efficient level of risk in a stable Paretian market is higher the lower the stability index, a.KeywordsPortfolio selectionrisk aversionstable Paretian distributionsminimum norm problemstable-CAPM