Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T13:32:41.709Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  06 April 2009

Peter J. Ryan  and
Jean Lefoll
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 16 , Issue 3 , September 1981 , pp. 389 - 395
Copyright
Copyright © School of Business Administration, University of Washington 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (05/06 1973), pp. 637–654.CrossRefGoogle Scholar
[2]Buser, S. A. “Mean-Variance Portfolio Selection with Either a Singular or Non-Singular Variance-Covariance Matrix.” Journal of Financial and Quantitative Analysis, Vol. 12 (09 1977), pp. 347–361.CrossRefGoogle Scholar
[3]Merton, R. C. “An Analytic Derivation of the Efficient Portfolio Frontier.” Journal of Financial and Quantitative Analysis, Vol. 7 (09 1972), pp. 1851–1872.CrossRefGoogle Scholar
[4]Roll, R. “A Critique of the Asset Pricing Theory's Tests; Part I: On Past and Potential Testability of the Theory.” Journal of Financial Economics, Vol. 4 (03 1977), pp. 129–176.CrossRefGoogle Scholar
[5]Sharpe, W.Portfolio Theory and the Capital Markets. New York: McGraw-Hill (1970).Google Scholar