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 i). The positive price of the size-orthogonalized component is not due to mispricing, supporting the return comovement-based pricing channel. ii). The negative price of the size-explained component is related to illiquidity and coskewness. iii). The omitted-variable problem also applies to the pricing of beta.