On the Inverse of the Covariance Matrix in Portfolio Analysis
Abstract
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.
Abstract The goal ofthis study is the derivation and application ofa direct characterization of the inverse ofthe covariance matrix central to portfolio analysis. As argued below, such a specification ofthe inverse, in terms ofa few primitive constructs, helps clarify the determinants ofsuch key concepts as (1) the optimal holding ofa given risky asset, (2) the slope ofthe 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 ofeach asset's variance and the multiple regression and correlation coefficients obtained by regressing each asset's excess expected return on the set ofexcess expected returns ofall other assets.
Cite this document
Guy V.G. Stevens (1995). On the Inverse of the Covariance Matrix in Portfolio Analysis (IFDP 1995-528). Board of Governors of the Federal Reserve System, International Finance Discussion Papers. https://whenthefedspeaks.com/doc/ifdp_1995-528
@techreport{wtfs_ifdp_1995_528,
author = {Guy V.G. Stevens},
title = {On the Inverse of the Covariance Matrix in Portfolio Analysis},
type = {International Finance Discussion Papers},
number = {1995-528},
institution = {Board of Governors of the Federal Reserve System},
year = {1995},
url = {https://whenthefedspeaks.com/doc/ifdp_1995-528},
abstract = {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.},
}