Any Axes Are Allowed: A Characteristic-Axis Integral Diagnostic of Factor Models
Abstract
This paper extends the cap-axis integral diagnostic to general characteristic axes, measuring factor-model pricing errors as bridge-alpha curves. A predetermined characteristic order generates prefix portfolios; subtracting equal-exposure aggregate portfolios yields zero-investment bridges indexed by cutoff p. The null is a zero-curve restriction on the subspace generated by the order, not a pointwise decile test. In 1967-2024 CRSP data, adding a counterpart factor shifts each curve downward, but only HML and CMA/IA overcorrect enough to be rejected, whereas RMW and UMD flatten their axes. A size-split reconstruction traces the overcorrection to 2x3 factor construction rather than the premium. Axis pricing errors relate weakly to maximum-Sharpe gains.
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