Correlation Matrices with the Perron-Frobenius Property

43 Pages Posted: 11 Sep 2014

See all articles by Phelim P. Boyle

Phelim P. Boyle

Wilfrid Laurier University - School of Business & Economics; University of Waterloo

Shui Feng

Department of Mathematics and Statistics, McMaster University, Canada

David Melkuev

Department of Statistics and Actuarial Science, University of Waterloo

Johnew Zhang

Columbia University, Columbia Business School, Finance and Economics, Students; Department of Statistics and Actuarial Science, University of Waterloo

Date Written: August 25, 2014

Abstract

The first principal component of stock returns is often identified with the market factor. If this portfolio is to represent the market portfolio, then all its weights must be positive. From the classical Perron-Frobenius theorem, a sufficient condition for the dominant eigenvector to be positive is that all the off diagonal elements are positive. Stock return correlation matrices typically contain negative elements and the frequency of negative elements has varied during the last 20 years. However, it is possible for a correlation matrix with some negative elements to have a positive dominant eigenvector. This paper explores the conditions under which the dominant eigenvector of a correlation matrix has strictly positive weights.

Keywords: Perron-Frobenius, Correlation-matrices

JEL Classification: G1

Suggested Citation

Boyle, Phelim P. and Feng, Shui and Melkuev, David and Zhang, Johnew, Correlation Matrices with the Perron-Frobenius Property (August 25, 2014). Available at SSRN: https://ssrn.com/abstract=2493844 or http://dx.doi.org/10.2139/ssrn.2493844

Phelim P. Boyle (Contact Author)

Wilfrid Laurier University - School of Business & Economics ( email )

Waterloo, Ontario N2L 3C5
Canada
519 884 1970 (Phone)
519 888 1015 (Fax)

University of Waterloo

Waterloo, Ontario N2L 3G1
Canada

Shui Feng

Department of Mathematics and Statistics, McMaster University, Canada ( email )

Canada

David Melkuev

Department of Statistics and Actuarial Science, University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Johnew Zhang

Columbia University, Columbia Business School, Finance and Economics, Students ( email )

3022 Broadway
New York, NY 10027
United States

Department of Statistics and Actuarial Science, University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
215
Abstract Views
1,191
rank
174,514
PlumX Metrics