A Note on a Property of the Inverse of a Bordered Matrix and Its Implication for the Theory of Portfolio Selection

Abstract

Many important results in the Neoclassical theory of consumer choice are derived from properties of the inverse of the bordered Hessian of a consumer's utility function. It is therefore not surprising that this type of matrix also plays an important part in the theory of portfolio choice. The purpose of this note is to establish a simple property of the inverse of a bordered matrix and to point out its implication for portfolio theory.