High Dimensional Covariance Matrix Estimation <br>via the Barra Model
The Barra model is one of the most popular risk models in financial industry for estimating
the covariance matrix of financial assets. In this report, we first examine theoretical properties
of the Barra model, which has 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 model. We show that as the sample size
increases, the Barra model, 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 model 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 a new method to estimate the covariance. We show that
under certain conditions, the new method is asymptotically consistent when the sample size
increases, and when the sample size is fixed while the number of financial assets increases,
the new method performs as well as the traditional Barra model. Extensive simulation studies
are used to support the theoretical results and compare the Barra model, the new method
and the sample covariance.
