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Prior to 1952 there was no analytical theory available that would satisfactorily explain the well-known phenomenon of asset diversification by investors. Although the portfolio selection criteria of Markowitz [3] and that of Roy [5] both explain diversification, they are based on very different objectives. The objective of Markowitz's approach is to select the portfolio of securities that maximizes the expected utility of the investor, i.e., the EV criterion. The objective of Roy's approach is economic survival through selection of the portfolio that minimizes the probability of disaster, i.e., the safety-first (SF) criterion.
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.
In his comment [4], Pashmi Thakkar raises two questions concerning our study [1] in three points. Points 1 and 3 have to do with discrediting the existence or proper measurement of our dependent variable, while point 2 argues for a technically biased regression structure resulting in biased estimates.