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A Comment on Mean-Variance Portfolio Selection with Either a Singular or a Non-Singular Variance-Covariance Matrix

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  • Ryan, Peter J.
  • Lefoll, Jean

Abstract

The usual formulation of the portfolio selection problem through meanvariance analysis assumes that the variance-covariance matrix of the rate of returns on risky assets is non-singular. In view of the literature discussing the creation of riskless portfolio from carefully balanced quantities of risky securities (e.g., shares and warrants as in Black-Scholes [1]), the assumption of non-singularity may be challenged. Consequently, the proofs of the classical theorems of portfolio management may no longer be developed as originally presented. Buser [2] presents a means of using a singular variance-covariance matrix in the derivation of portfolio weights, which, although slightly flawed by a mathematical error, still provides some interesting insights about the efficient frontier. We present a corrected version of Buser's method in Section II; in Section III, we comment on some of the implications of his presentation and indicate some more precise results.

Suggested Citation

  • Ryan, Peter J. & Lefoll, Jean, 1981. "A Comment on Mean-Variance Portfolio Selection with Either a Singular or a Non-Singular Variance-Covariance Matrix," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(3), pages 389-395, September.
    • Handle: RePEc:cup:jfinqa:v:16:y:1981:i:03:p:389-395_00
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    Cited by:

    1. Lee, Miyoung & Kim, Daehwan, 2017. "On the use of the Moore–Penrose generalized inverse in the portfolio optimization problem," Finance Research Letters, Elsevier, vol. 22(C), pages 259-267.
    2. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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