High-Dimensional Covariance Matrix Estimation via the Barra Model

• Activity Number: 341
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Risk Analysis
• Author(s): Yiwei Zhang*+ and Ji Zhu
• Companies: University of Michigan and University of Michigan
• Keywords: Barra model ; covariance estimation ; random effects

Abstract

The Barra model is one of the most popular risk models in financial industry for estimating the covariance matrix of financial assets, and the Barra one-step and two-step approaches are widely used to implement the estimation. In this paper, we first examine theoretical properties of the Barra approach, which have somehow been ignored in the literature. In particular, we investigate the impact of the sample size (i.e., the number of trading days) and the number of financial assets on the performance of the Barra approach. We show that as the sample size increases, the Barra approach, unlike the sample covariance, is in fact not asymptotically consistent. This result is a little surprising and has never been reported. On the other hand, when the sample size is fixed and the number of financial assets increases, which is more realistic in practice, we show that the Barra approach outperforms the sample covariance. To further improve the estimation, we re-interpret the Barra model via the framework of the random effects model and propose an EM-like method to estimate the covariance. We show that under certain conditions, the new method is asymptotically consistent when the sample siz