On the inverse of the covariance matrix in portfolio analysis

The goal of this study is the derivation and application of a direct characterization of the inverse of the covariance matrix central to portfolio analysis. As argued below, such a specification of the inverse, in terms of a few primitive constructs, helps clarify the determinants of such key concepts as (1) the optimal holding of a given risky asset, (2) the slope of the risk-return efficiency locus faced by the individual investor, and (3) the pricing of risky assets in the Capital Asset Pricing Model. The two building blocks of the inverse turn out to be the non-diversifiable part of each asset's variance and the multiple regression and correlation coefficients obtained by regressing each asset's excess expected return on the set of excess expected returns of all other assets.