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A Cap-Axis Integral Diagnostic of Factor Models

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  • Useong Shin

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.

Suggested Citation

  • Useong Shin, 2026. "A Cap-Axis Integral Diagnostic of Factor Models," Papers 2607.01765, arXiv.org, revised Jul 2026.
  • Handle: RePEc:arx:papers:2607.01765
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