Specification Choice in Asset Pricing

If you build the factor differently, is it still priced?

2,064 construction variants, each carried through the entire asset-pricing pipeline: rebuild all five factors under the variant's choices, re-estimate betas, and re-run the cross-sectional premium test. Each dot is one variant. The horizontal axis is what the construction choice did to the factor's own mean return; the vertical axis is what survived into its cross-sectional premium. The dashed diagonal is full pass-through; the fitted line is what the data deliver. The paper's knob-level estimates put pass-through at 14–30% depending on the factor: construction choices are loud where factors live and quiet where premia live.
Loading propagation variants…
factor premium t-statistic
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variants
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pass-through (OLS slope)
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correlation
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premium > 0
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joint p (sign-aligned)
premium significant (|t| > 1.96) not significant – – full pass-through (45°) ── fitted pass-through Fama–French baseline

Joint verdicts across all 2,064 variants

factor joint p verdict, robust to construction choice
HMLpremium positive in every variant: value survives propagation
UMDpremium negative in every variant: momentum inverts at the premium layer
CMArecedes to insignificance once the lens widens beyond the published corner
SMBnot distinguishable from zero at the premium layer
RMWnot distinguishable from zero at the premium layer