# 13-036/III (2013-03-04)

Guorui Bian, East China Normal University; Michael McAleer, Erasmus University Rotterdam, Kyoto University, Complutense University of Madrid; Wing-Keung Wong, Hong Kong Baptist University
Maximum likelihood estimators; Modified maximum likelihood estimators; Student t family; Capital asset pricing model; Robustness
JEL codes:
C1, C2, G1

See the article in the Annals of Financial Economics (2013). Volume 8, issue 2, pages 1-18.

In this paper, we develop a modified maximum likelihood (MML) estimator for the multiple linear regression model with underlying student t distribution. We obtain the closed form of the estimators, derive the asymptotic properties, and demonstrate that the MML estimator is more appropriate for estimating the parameters of the Capital Asset Pricing Model by comparing its performance with least squares estimators (LSE) on the monthly returns of US portfolios. The empirical results reveal that the MML estimators are more efficient than LSE in terms of the relative efficiency of one-step-ahead forecast mean square error in small samples