Portfolio Selection and Asset Pricing—Three-Parameter Framework

Abstract

Idiosyncratic security risks are modelled as following a joint spherical distribution characterized by a mean vector and a generalized covariance matrix. Skewness is generated by a single factor for the whole economy, but upon which different securities have different loadings. This results in three-fund separation—two funds to span the spherical risk and one more fund to span the additional skewness risk. A three-parameter normative portfolio analysis that allows short sales restrictions is developed. In addition, a three-parameter capital asset pricing model is provided.