Continuous Maturity Diversification of Default-Free Bond Portfolios and a Generalization of Efficient Diversification

Authors

  • W. JOHN HEANEY,

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    • Heaney at Simon Fraser University since August 1983, and at University of British Columbia prior to August 1983, during which time some of the results in this paper were obtained. Cheng at Simon Fraser University. The research began under a leave fellowship grant by the Social Sciences and Humanities Research Council of Canada. The research benefitted from the second author's association with the Robert Anderson School of Management, the University of New Mexico, where he developed the research idea in a graduate course on bank management.

  • PAO L. CHENG

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    • Heaney at Simon Fraser University since August 1983, and at University of British Columbia prior to August 1983, during which time some of the results in this paper were obtained. Cheng at Simon Fraser University. The research began under a leave fellowship grant by the Social Sciences and Humanities Research Council of Canada. The research benefitted from the second author's association with the Robert Anderson School of Management, the University of New Mexico, where he developed the research idea in a graduate course on bank management.


ABSTRACT

This paper presents a method for solving the mean-variance portfolio selection problem that is applicable to the case where the number of securities is nondenumerably infinite. Necessary conditions for the existence of an optimal portfolio density are obtained and an expression for the efficient frontier is derived. The conditions for the existence of an optimal portfolio of continuously maturing bonds when their covariance matrix is singular are used to derive an arbitrage-free bond pricing equation. A method for estimating the covariance matrix and the associated efficient frontier is presented.

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