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.
Highlights
Both financial economists and statisticians have been concerned with the distributions of stock market returns. Fama (1963, 1965a, 1965b) and many others analyzed the empirical data and concluded that the normality assumption in the distribution of a security or portfolio return is violated such that the distribution is ‘flat-tailed’
They suggested the family of stable Paretian distributions between normal and Cauchy distributions for the stock returns
Based on the simulation results, we find that the proposed Bayesian estimator is superior to least squares estimator (LSE) when the Capital Asset Pricing Model (CAPM) model is contaminated by large normal and/or non-normal disturbances, especially by Cauchy disturbances
Summary
Both financial economists and statisticians have been concerned with the distributions of stock market returns. Fama (1963, 1965a, 1965b) and many others analyzed the empirical data and concluded that the normality assumption in the distribution of a security or portfolio return is violated such that the distribution is ‘flat-tailed’. Based on the simulation results, we find that the proposed Bayesian estimator is superior to LSE when the CAPM model is contaminated by large normal and/or non-normal disturbances, especially by Cauchy disturbances. To overcome these difficulties, Harvey and Zhou (1990) imposed a prior on all the parameters of the multivariate regression model and used Monte Carlo numerical integration to accurately evaluate 90-dimensional integrals to estimate the parameters in the posterior distribution They developed a Bayesian framework to test the mean-variance efficiency of a given portfolio. This shows that βC is considerably robust relative to both βN and β
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