Journal of Applied Mathematics and Decision Sciences
Volume 4 (2000), Issue 1, Pages 65-82
doi:10.1155/S1173912600000043
Robust estimation in Capital Asset Pricing Model
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.
Abstract
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.