Two-pass estimation of risk premiums with multicollinear and near-invariant betas

This paper investigates the reliability of the two-pass (TP) estimators of factor risk prices when betas (multifactor loadings) have high levels of cross-sectional correlation (multicollinearity) and/or when some of them have small cross-sectional variations (near-invariance). Our simulation results show the following. First, the TP estimators can have biases larger than 100% of true risk prices when data are generated by the betas with high levels of multicollinearity and invariance that can be observed from actual data. Second, the t-tests for hypotheses related to risk prices and pricing intercepts have only limited power. The levels of multicollinearity and invariance of betas can vary depending on the assets and sample periods used in estimation. Thus, we propose use of two pre-diagnostic statistics to measure these levels. Many previous studies have investigated the finite-sample properties of the TP estimators using the data generated with the estimated betas from actual data. Our results indicate that simulation outcomes can lead to quite different conclusions, depending on the levels of multicollinearity and invariance of the betas used to generate the data.