An Answer to Roll’s Critique (1977) 45 Years Later

We implement a new framework to mitigate the errors-in-variables (EIV) problem in the estimation of asset pricing models. Considering an international data of portfolio stock returns from 1990 to 2021 widely used in empirical studies, we highlight the importance of the estimation method in time-series regressions. We compare the traditional ordinary-least squares (OLS) method to an alternative estimator based on a compact genetic algorithm (CGA) in the case of the CAPM. Based on intercepts, betas, adjusted R2, and the Gibbons et al. (1989) test, we find that the CGA-based method outperforms overall the OLS method. In particular, we obtain less statistically significant intercepts, smoother R2 across different portfolios, and lower GRS test statistics. Specifically, in line with Roll's critique (1977) on the unobservability of the market portfolio, we reduce the attenuation bias in market risk premium estimates. Moreover, our results are robust to alternative methods such as instrumental variables estimated with generalized-method of moments (GMM). Our findings have several empirical and managerial implications related to the estimation of asset pricing models as well as their interpretation as a popular tool in terms of corporate financial decision-making.