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Fama–MacBeth: next-day returns on sentiment (cross-sectional)
Per-day cross-sectional OLS y_ret(t+1) on score_mean(t) (+ n_total). Report mean slopes and NW t-stats.
Updated: 2026-04-05
Study
Cross-sectional pricing • Status: LIVE
Updated: 2026-04-05
Dates
515
Avg CS R²
0.00377
Min XS N
120
NW lags
5
Sample ticker
AAPL
Tickers (panel)
507
Obs (panel)
261179
R² (TS)
—
R² (FE)
—
Key findings
- Fama–MacBeth estimates average cross-sectional pricing of sentiment signals using daily cross-sectional regressions.
- Average cross-sectional R² ≈ 0.003772 (dates=515).
- Interpretation: significant mean slopes suggest a systematic cross-sectional relationship rather than a single-ticker artifact.
Specification
- For each day t: r_{i,t+1} = a_t + b_t * score_{i,t} + c_t * n_total_{i,t} + ε_{i,t}.
- Then test E[b_t] using NW SE across t.
Data
- Universe: S&P 500 tickers in your snapshot pipeline.
- Frequency: Daily.
- Returns: log(P_t) − log(P_{t−1}) from ticker JSON prices.
- Sentiment: score_mean from your sentiment pipeline (ticker JSON).
Limitations
- Timing: after-close articles can contaminate same-day results; predictive tests mitigate this but do not fully solve it.
- Causality: results are descriptive; omitted variables and measurement error remain.
- Trading: no transaction costs / slippage / capacity modeled.
References (minimal)
- Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix.
- Petersen, M. A. (2009). Estimating standard errors in finance panel data sets.
- Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests.
Methodology
- Each date t: cross-sectional OLS over tickers: y_ret(t+1) ~ score_mean(t) (+ n_total(t)).
- Collect daily slope estimates; test mean slope using Newey–West standard errors.
Figures
Charts are from the sample ticker (not the full panel).
Series (sample)
No series available.
Sentiment (sample)
score_mean
No sentiment series available. Export
results.series.score_mean.Tables
Fama–MacBeth mean slopes (Newey–West t)
| Variable | Mean beta | t (NW) | p | Sig |
|---|---|---|---|---|
| score_mean | -9.788e-4 | -0.931527 | 0.351581 | 0 |
Note: exported by the Python builder; formatting is intentionally compact.
Models
This study is primarily descriptive (figures/tables). No regression model outputs were exported.
Appendix
Raw exported objects (reproducibility / debugging).
Raw exported JSON (collapsed)
{
"results": {
"sample_ticker": "AAPL",
"n_tickers": 507,
"n_obs_panel": 261179,
"famamacbeth": {
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},
"stats": {
"n_dates": 515,
"min_xs": 120,
"nw_lags": 5,
"avg_cs_r2": 0.003771716383454165
},
"table": {
"title": "Fama–MacBeth mean slopes (Newey–West t)",
"columns": [
"Variable",
"Mean beta",
"t (NW)",
"p",
"Sig"
],
"rows": [
[
"score_mean",
-0.0009787962931044752,
-0.9315273289012922,
0.3515808546761985,
""
]
]
}
},
"tables": [
{
"title": "Fama–MacBeth mean slopes (Newey–West t)",
"columns": [
"Variable",
"Mean beta",
"t (NW)",
"p",
"Sig"
],
"rows": [
[
"score_mean",
-0.0009787962931044752,
-0.9315273289012922,
0.3515808546761985,
""
]
]
}
]
},
"methodology": [
"Each date t: cross-sectional OLS over tickers: y_ret(t+1) ~ score_mean(t) (+ n_total(t)).",
"Collect daily slope estimates; test mean slope using Newey–West standard errors."
],
"sections": [
{
"title": "Specification",
"bullets": [
"For each day t: r_{i,t+1} = a_t + b_t * score_{i,t} + c_t * n_total_{i,t} + ε_{i,t}.",
"Then test E[b_t] using NW SE across t."
]
},
{
"title": "Data",
"bullets": [
"Universe: S&P 500 tickers in your snapshot pipeline.",
"Frequency: Daily.",
"Returns: log(P_t) − log(P_{t−1}) from ticker JSON prices.",
"Sentiment: score_mean from your sentiment pipeline (ticker JSON)."
]
},
{
"title": "Limitations",
"bullets": [
"Timing: after-close articles can contaminate same-day results; predictive tests mitigate this but do not fully solve it.",
"Causality: results are descriptive; omitted variables and measurement error remain.",
"Trading: no transaction costs / slippage / capacity modeled."
]
},
{
"title": "References (minimal)",
"bullets": [
"Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix.",
"Petersen, M. A. (2009). Estimating standard errors in finance panel data sets.",
"Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests."
]
}
],
"conclusions": [
"Fama–MacBeth estimates average cross-sectional pricing of sentiment signals using daily cross-sectional regressions.",
"Average cross-sectional R² ≈ 0.003772 (dates=515).",
"Interpretation: significant mean slopes suggest a systematic cross-sectional relationship rather than a single-ticker artifact."
]
}