Large Dimensional Covariance Matrix Estimation Using a Factor Model

• Activity Number: 366
• Type: Topic Contributed
• Date/Time: Wednesday, August 9, 2006 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Jinchi Lv*+
• Companies: Princeton University
• Keywords: factor model ; diverging dimensionality ; covariance matrix estimation ; consistency ; asymptotic normality ; portfolio allocation and risk management

Abstract

Large dimensionality is a common feature in modern portfolio management. We examine the covariance matrix estimation in the asymptotic framework that the dimensionality p_n diverges with the sample size n. Motivated by the CAPM, we propose to use a K-factor model to reduce the dimensionality and estimate the covariance matrix among those assets. Under basic assumptions, we establish the n^b-consistency with b=min(1/2,1-a/2) when p_n=O(n^a), 0< =a< 2, and asymptotic normality for the covariance matrix estimator. The performance is compared with the sample covariance matrix. We identify the cases when the factor approach can gain substantially the performance and when the gains are only marginal. Furthermore, the impacts of the covariance matrix estimation on portfolio allocation and risk management are studied, respectively. The results are supported by a thorough simulation study.