The Excluded-Coordinate Return Signature: A Public-Data Test of SAPM

The return-side test is no longer a queue note; it is a mixed empirical result

Paper 7 tests SAPM with public SEC issuer metadata, Yahoo Finance adjusted monthly returns, Fama-French factors, a sin-industry factor, a litigation-risk factor, and a green-minus-brown transition factor. Two predictions survive and two fail.

• Sample: 13,523 domain-firm rows and 4,989 unique tickers.
• Event side: 197,014 event-return rows joined to returns and factors.
• P4 side: 3,928,873 pairwise covariance rows.

High beta-W portfolios do not show a detected normal-period premium

The high-minus-low beta-W portfolio has no statistically detected normal-period alpha. That supports the pre-paradigm claim: before W is legible, the excluded coordinate is not priced as an ordinary premium.

• Reported alpha = -0.00193548.
• Reported t = -1.41.
• The result supports no detected normal-period premium, not a broad market-efficiency victory claim.

Beta-W exposure loads on restoration-event return magnitude

The event-side result is the strongest positive finding. Beta-W loads positively on absolute event excess returns after composite controls, which is exactly where SAPM expects the excluded coordinate to become return-relevant.

• Reported beta-W coefficient = 0.00268427.
• Reported t = 23.09.
• The claim is restoration-loading, not an ordinary risk-premium claim.

The negative-skew prediction does not survive this run

The high-versus-low skew delta is positive rather than negative. That failure matters: the public-data result does not support beta-W as a broad hidden tail-risk factor in this specification.

• Reported skew delta = 0.282295.
• The sign is the wrong direction for the original P3 prediction.
• The honest conclusion narrows SAPM rather than overclaiming it.

The within-system covariance prediction also fails

The shared-system coefficient on event covariance is negative and not statistically supportive. This run does not establish beta-W as a non-diversifiable within-system covariance factor.

• Reported shared-system coefficient = -0.163922.
• Reported t = -1.00.
• The covariance claim remains an open hypothesis, not a demonstrated result.

The delisting-stress check does not rescue P3 or P4

The rerun assigns the eight pre-specified missing delisted, bankrupt, or acquired supplement tickers domain-peer histories and terminal losses. Even under severe terminal-loss assumptions, P3 and P4 still do not flip.

• Stress levels: -30 percent, -55 percent, and -100 percent.
• The check addresses missing delisted/bankrupt/acquired supplement tickers.
• The failed predictions remain failed in this public-data run.

SAPM survives as no-premium and restoration-loading theory, not as a full hidden-tail-risk factor

The paper's conclusion is stronger because it narrows. Historical public data support two distinctive claims: W was not priced as a normal premium before it was legible, and beta-W exposure becomes return-relevant around restoration events.

• Supported: pre-paradigm no-premium.
• Supported: restoration-event loading.
• Not supported here: broad hidden tail risk or non-diversifiable within-system covariance.

The next falsifiable step is diffusion

The next paper should test whether W begins to price when beta-W-style disclosure, litigation analysis, activist research, or institutional adoption makes the coordinate legible to investors.

• The empirical posture is bounded and testable.
• The return-side theory is not protected from failure.
• The website should present this as a disciplined mixed result.