Principal Eigenportfolios for U.S. Equities
39 Pages Posted: 11 Dec 2020
Date Written: December 10, 2020
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: Suggested Citation