Alternative Specifications and Estimation Methods for Determining Random Beta Coefficients: Comparison and Extensions

Abstract

Whether beta is random or not is an important issue in the application of modern portfolio theory. In this study, we empirically compare alternative models and specifications used to estimate the random beta coefficient. Theoretically, specifications used by previous researchers based on Theil's (1971) procedure may be misspecified due to the inclusion of a non-zero intercept term and the assumption of non-zero covariance between the error term of regression and the error term of beta generating process. Empirical evidence reveals that the choice of estimation method, rather than the possible muliticollinearity problem and non-zero covariance term, significantly affect the results in detecting random beta. Regression results suggest that, when beta is random, variation of systematic risk may playa more significant role than the pure systematic risk and covariance risk in explaining abnormal return.