Arbitrage pricing theory states that expected returns for a security are linear combination of exposures to risk factors and the returns on these risk factors. Betas, or the exposures of the security to a given risk factor, can be estimated via a time-series regression of the excess returns of the security on the excess returns of the factor return (single variable time-series regression).
Theory says the constant (or zero-beta excess return) in the time-series regression should be zero. However, practically speaking it is the case that some constants may be estimated that are statistically significant and different from zero. Question: Should one estimate Betas while forcing the constant equal to zero (i.e. theoretically consistent) vs. extracting Betas while allowing the constant term to exist?
What is the trade-off or which decision leads to superior accuracy? Ultimately the estimated factor exposures from the above time-series regression would be used to estimate the factor returns in a cross-sectional risk model.
Attached is a link to John Cochrane's Asset Pricing chapter 12 which describes the theory in fuller detail.