On the Inverse of the Covariance Matrix in Portfolio Analysis

Authors

  • Guy V. G. Stevens

    1. Board of Governors of the Federal Reserve System
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    • Board of Governors of the Federal Reserve System. My thanks go to Michael Adler, John Ammer, Neil Ericsson, William Helkie, and, especially, Michael McCarthy, Charles Thomas, and the referee for very helpful discussions and comments. The views expressed in this paper are mine alone and should not be interpreted as reflecting those of the Board of Governors or other members of its staff.

Abstract

The goal of this paper is the derivation and application of a direct characterization of the inverse of the covariance matrix central to portfolio analysis. Such a characterization, in terms of a few primitive constructs, provides the basis for new and illuminating expressions for key concepts as the optimal holding of a given risky asset and the slope of the risk-return efficiency frontier faced by the individual investor. The building blocks of the inverse turn out to be the regression coefficients and residual variance obtained by regressing the asset's excess return on the set of excess returns for all other risky assets.

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