Principal Eigenportfolios for U.S. Equities

39 Pages Posted: 11 Dec 2020

See all articles by Marco Avellaneda

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Brian Healy

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering

Andrew Papanicolaou

North Carolina State University - Department of Mathematics

George Papanicolaou

Stanford University - Department of Mathematics

Tony Xu

affiliation not provided to SSRN

Date Written: December 10, 2020

Abstract

We analyze portfolios constructed from the principal eigenvector of the equity returns' correlation matrix and compare how well these portfolios track the capitalization weighted market portfolio. It is well known empirically that principal eigenportfolios are a good proxy for the market portfolio. We quantify this property through the large-dimensional asymptotic analysis of a spike model, which is comprised of a rank-1 matrix and a random matrix. We show that, in this limit, the top eigenvector of the correlation matrix is close to the vector of market betas divided component-wise by returns standard deviation. Historical returns data supports this analytical explanation for the correspondence between the top eigenportfolio and the market portfolio. We further examine this correspondence using eigenvectors obtained from hierarchically constructed tensors where stocks are separated into their respective industry sectors. This hierarchical approach provides robustness in eigenportfolio construction for a large number of equity returns when a shortened time window is used. For portfolios constructed using a rolling window of only one month of daily returns, our study shows improved tracking between the returns of the market portfolio and those from hierarchically constructed portfolios.

Keywords: Eigenportfolios, Principal Component Analysis, Tensor Decomposition

JEL Classification: C20, G10

Suggested Citation

Avellaneda, Marco and Healy, Brian and Papanicolaou, Andrew and Papanicolaou, George and Xu, Tony, Principal Eigenportfolios for U.S. Equities (December 10, 2020). Available at SSRN: https://ssrn.com/abstract=3738769 or http://dx.doi.org/10.2139/ssrn.3738769

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

251 Mercer Street
New York, NY 10012
United States
212-998-3129 (Phone)
212-995-4121 (Fax)

Finance Concepts LLC ( email )

590 Madison Avenue
21st Floor
New York, NY 10022
United States

HOME PAGE: http://www.finance-concepts.com

Brian Healy

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering ( email )

Brooklyn, NY 11201
United States

Andrew Papanicolaou (Contact Author)

North Carolina State University - Department of Mathematics ( email )

Campus Box 8205
NC State University
Raleigh, NC 27695-8205
United States

George Papanicolaou

Stanford University - Department of Mathematics ( email )

Building 380
Stanford, CA 94305
United States
650-723-2081 (Phone)
650-725-4066 (Fax)

Tony Xu

affiliation not provided to SSRN

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

Paper statistics

Downloads
147
Abstract Views
628
rank
236,876
PlumX Metrics