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.

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Tinbergen Institute
Tinbergen Institute Discussion Paper Series
Discussion paper / Tinbergen Institute
Erasmus School of Economics

Bian, G, McAleer, M.J, & Wong, W.-K. (2013). Robust Estimation and Forecasting of the Capital Asset Pricing Model (No. TI 13-036/III). Discussion paper / Tinbergen Institute (pp. 1–26). Tinbergen Institute. Retrieved from