A Cap-Axis Integral Diagnostic of Factor Models
General Finance
2026-07-02 v1 Computational Finance
Mathematical Finance
Pricing of Securities
Statistical Finance
Abstract
I propose a cap-axis integral diagnostic for factor-model evaluation. Low-dimensional factor models can improve the maximum-Sharpe frontier while leaving zero-alpha violations on economically fixed subspaces. The diagnostic studies one such subspace by lifting pricing errors into a bridge-alpha curve along the market-capitalization rank axis. Under an aggregate-market gate, a zero curve is equivalent to pricing the market's internal cap-rank subspace. In 1967-2024 CRSP data, q5's daily negative bridge attenuates under lead-lag correction, while Fama-French and Carhart bridges are more visible monthly. Across 154 factors, the cap-axis norm is distinct from Sharpe gain and size exposure.
Cite
@article{arxiv.2607.01765,
title = {A Cap-Axis Integral Diagnostic of Factor Models},
author = {Useong Shin},
journal= {arXiv preprint arXiv:2607.01765},
year = {2026}
}