445786a262401410VgnVCM100000c2b1d38dRCRDapproved/UMICH/stats/Home/News & Events/Dissertations and Oral Preliminary ExaminationsYiwei Zhang###@###(Thu, 5 Sep 2013)Yiwei Zhang###@###(Thu, 5 Sep 2013)438 WHHigh Dimensional Covariance Matrix Estimation via the Barra Modelstats137840040000013784004000001:00PM<p>The Barra model is one of the most popular risk models in financial industry for estimating<br> the covariance matrix of financial assets. In this report, we first examine theoretical properties<br> of the Barra model, which has somehow been ignored in the literature. In particular, we<br> investigate the impact of the sample size (i.e., the number of trading days) and the number<br> of financial assets on the performance of the Barra model. We show that as the sample size<br> increases, the Barra model, unlike the sample covariance, is in fact not asymptotically consistent.<br> This result is a little surprising and has never been reported. On the other hand,<br> when the sample size is fixed and the number of financial assets increases, which is more<br> realistic in practice, we show that the Barra model outperforms the sample covariance. To<br> further improve the estimation, we re-interpret the Barra model via the framework of the<br> random effects model and propose a new method to estimate the covariance. We show that<br> under certain conditions, the new method is asymptotically consistent when the sample size<br> increases, and when the sample size is fixed while the number of financial assets increases,<br> the new method performs as well as the traditional Barra model. Extensive simulation studies<br> are used to support the theoretical results and compare the Barra model, the new method<br> and the sample covariance.</p>Njkmcdonjjsantos1378755804573145786a262401410VgnVCM100000c2b1d38d____once11112newnewHigh Dimensional Covariance Matrix Estimation/UMICH/stats/Home/News & Events/Dissertations and Oral Preliminary Examinations/Yiwei Zhang PreLim Flyer.pdf