Large Dimensional Covariance Matrix Estimation Via a Factor Model

55 Pages Posted: 16 Jan 2007

See all articles by Jianqing Fan

Jianqing Fan

Princeton University - Bendheim Center for Finance

Yingying Fan

Princeton University

Jinchi Lv

Princeton University

Date Written: August 12, 2006

Abstract

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to infinity as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observable and the number of factors K is allowed to grow with p. We investigate impact of p and K on the performance of the model-based covariance matrix estimator. Under mild assumptions, we have established convergence rates and asymptotic normality of the model-based estimator. Its performance is compared with that of the sample covariance matrix. We identify situations under which the factor approach increases performance substantially or marginally. The impacts of covariance matrix estimation on portfolio allocation and risk management are studied. The asymptotic results are supported by a thorough simulation study.

Keywords: Factor model, diverging dimensionality,covariance matrix estimation, consistency, asymptotic normality, ptimal portfolio, risk management

JEL Classification: G12, C13

Suggested Citation

Fan, Jianqing and Fan, Yingying and Lv, Jinchi, Large Dimensional Covariance Matrix Estimation Via a Factor Model (August 12, 2006). Available at SSRN: https://ssrn.com/abstract=957599 or http://dx.doi.org/10.2139/ssrn.957599

Jianqing Fan (Contact Author)

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

Yingying Fan

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Jinchi Lv

Princeton University

22 Chambers Street
Princeton, NJ 08544-0708
United States

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