Robust estimation in Capital Asset Pricing Model

Abstract

Bian and Dickey (1996) developed a robust Bayesian estimator for the vector of regression coefficients using a Cauchy-type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$g$"><mml:mi>g</mml:mi></mml:math>-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.