Abstract
Backtests are difficult to assess when specification searches and overlapping events are not disclosed. We examine a fixed single-stock rule that calls a direction at a random-day percentile of ≥ .95 or ≤ .05, nominally two-sided 10%. Across 124 stocks, circular shifts of persistent condition masks by at least 252 trading days yield a random-day rejection rate of 0.314 (95% CI 0.302–0.324), compared with 0.102 for a shift-based placebo. Thinning events to at least 20 trading days apart retains a median 0.366 of the nominal sample (95% CI 0.356–0.376). Most initially directional readings lose their direction after thinning. This does not establish that genuine return effects disappear: thinning removes information, and the shift placebo shares the mechanism used to construct the null. General false-positive control remains unverified. The stock pool is selected, thinned events may remain dependent, and stock-resampling intervals have unverified coverage under a shared calendar. This retrospective exploratory study was not prospectively preregistered. Evaluation requires the search history and event-overlap accounting; neither is replaced by a small reported p-value. A planned simulation comparison will test calibration and power against established methods.
Results and limitations
- Under the circular-shift procedure in 124 stocks, the random-day rule rejects in 0.314 of cases (95% CI 0.302–0.324); a shift-based placebo rejects in 0.102.
- With events at least 20 trading days apart, the median stock retains 0.366 of its nominal sample (95% CI 0.356–0.376). This is not an effective sample size.
- In the real-mask thinning comparison, 37 of 43 initially directional readings lose their direction; 11 stocks remain directional overall. This concerns classifications, not proof that genuine return effects disappear.
- This study was not prospectively preregistered. The original timestamp is retrospective and was obtained after the original results.
- The stock pool is not random; shared-calendar dependence and the coverage of stock-resampling intervals remain unverified.
- The reported 0.314 concerns the fixed final rule; it does not include feature or threshold selection.
- The accepted prospective protocol is locked. The October 30, 2026 receipt readback recorded calendar attestations with Bitcoin confirmation pending; this is a dated observation, not a fresh confirmation check.
- The smoke replay used two stocks and twenty replicates per stock. H1b failed with a 90% interval [0.10, 0.15]; the stop rule had no smoke exemption, but results were written and drafting continued. The unchanged full-sample estimates are not thereby overturned.
- The 28 documented attempt groups do not establish an exhaustive trial denominator. Original T01 smoke files remain unavailable.
Prospective protocol registration for a future extension; this does not retrospectively preregister the paper.
Declaration of Generative AI and AI-Assisted Technologies in the Writing Process
During the preparation of this work, the author used Claude (Anthropic) and Codex (OpenAI) for code development, drafting assistance and language editing. The author designed the study, determined the principal arguments and interpretations, reviewed and revised all content, verified all data and citations, and takes full responsibility for the content of this article.
Citation
@techreport{cai2026placebo,
author = {Cai, Peilun},
title = {An Exploratory Study of Random-Day Placebos Under Persistent Conditioning: Calibration and Non-Overlapping Event Retention in Single-Stock Conditional Event Studies},
year = {2026},
note = {Working paper v1, October 30, 2026},
url = {https://axiocairn.com/en/research/ax-p-001}
}
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