Correlation and the omitted variable: A tale of two prices

We offer a new perspective on the low-beta anomaly by acknowledging the omitted-variable problem in the correlation component of beta: Correlation is “plagued” by firm size (the omitted variable) to exhibit a negative price. Once isolating the size impact, a hidden positive price emerges for the size-orthogonalized component of correlation. Further analyses suggest that (a) the positive price of the size-orthogonalized component is not due to mispricing, supporting the return comovement-based pricing channel; (b) the negative price of the size-explained component is related to illiquidity and coskewness.; (c) the omitted-variable problem also applies to the pricing of beta.