A Protocol for Factor Identification

We propose a protocol for identifying genuine risk factors. A genuine risk factor must be related to the covariance matrix of returns, must be priced in the cross-section of returns, and should yield a reward-to-risk ratio that is reasonable enough to be consistent with risk pricing. A market factor, a profitability factor, and traded versions of macroeconomic factors pass our protocol, but many characteristic-based factors do not. Several of the underlying characteristics, however, do command premiums in the cross-section