A Cap-Axis Integral Diagnostic of Factor Models

I propose a cap-axis zero-alpha diagnostic for factor-model evaluation. Whole-stock capitalization prefixes are paired with equal realized exposure to the aggregate market, producing a bridge-alpha curve that localizes pricing errors within the market. Finite-grid HAC-Gaussian inference and residual-block calibration provide size-controlled functional tests. In 1967-2024 CRSP data, q5’s negative daily bridge attenuates under lead-lag correction and is small monthly, whereas Fama-French and Carhart bridges become more visible monthly. Across 155 factors, cap-axis magnitude is neither a monotone transformation of maximum-Sharpe gain nor explained by exposure to FF3 SMB.