Journal of Applied Mathematics and Decision Sciences
Volume 4 (2000), Issue 1, Pages 65-82

Robust estimation in Capital Asset Pricing Model

Wing-Keung Wong1 and Guorui Bian2

1Department of Economics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore
2Department of Statistics and Applied Probability, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore

Copyright © 2000 Wing-Keung Wong and Guorui Bian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Bian and Dickey (1996) developed a robust Bayesian estimator for the vector of regression coefficients using a Cauchy-type g-prior. This estimator is an adaptive weighted average of the least squares estimator and the prior location, and is of great robustness with respect to at-tailed sample distribution. In this paper, we introduce the robust Bayesian estimator to the estimation of the Capital Asset Pricing Model (CAPM) in which the distribution of the error component is well-known to be flat-tailed. To support our proposal, we apply both the robust Bayesian estimator and the least squares estimator in the simulation of the CAPM and in the analysis of the CAPM for US annual and monthly stock returns. Our simulation results show that the Bayesian estimator is robust and superior to the least squares estimator when the CAPM is contaminated by large normal and/or non-normal disturbances, especially by Cauchy disturbances. In our empirical study, we find that the robust Bayesian estimate is uniformly more efficient than the least squares estimate in terms of the relative efficiency of one-step ahead forecast mean square error, especially for small samples.