Robust Estimation and Forecasting of the Capital Asset Pricing Model

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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.
The third author would like to thank Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement. For financial support, the first author is grateful to East China Normal University, the second author acknowledges the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science, and the third author wishes to acknowledge Hong Kong Baptist University.
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