← Back to Research

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 pricingStatus: 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)
VariableMean betat (NW)pSig
score_mean-9.788e-4-0.9315270.3515810
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": {
      "series": {
        "dates": [
          "2024-11-04",
          "2024-11-05",
          "2024-11-06",
          "2024-11-07",
          "2024-11-08",
          "2024-11-09",
          "2024-11-10",
          "2024-11-11",
          "2024-11-12",
          "2024-11-13",
          "2024-11-14",
          "2024-11-15",
          "2024-11-16",
          "2024-11-17",
          "2024-11-18",
          "2024-11-19",
          "2024-11-20",
          "2024-11-21",
          "2024-11-22",
          "2024-11-23",
          "2024-11-24",
          "2024-11-25",
          "2024-11-26",
          "2024-11-27",
          "2024-11-28",
          "2024-11-29",
          "2024-11-30",
          "2024-12-01",
          "2024-12-02",
          "2024-12-03",
          "2024-12-04",
          "2024-12-05",
          "2024-12-06",
          "2024-12-07",
          "2024-12-08",
          "2024-12-09",
          "2024-12-10",
          "2024-12-11",
          "2024-12-12",
          "2024-12-13",
          "2024-12-14",
          "2024-12-15",
          "2024-12-16",
          "2024-12-17",
          "2024-12-18",
          "2024-12-19",
          "2024-12-20",
          "2024-12-21",
          "2024-12-22",
          "2024-12-23",
          "2024-12-24",
          "2024-12-25",
          "2024-12-26",
          "2024-12-27",
          "2024-12-28",
          "2024-12-29",
          "2024-12-30",
          "2024-12-31",
          "2025-01-01",
          "2025-01-02",
          "2025-01-03",
          "2025-01-04",
          "2025-01-05",
          "2025-01-06",
          "2025-01-07",
          "2025-01-08",
          "2025-01-09",
          "2025-01-10",
          "2025-01-11",
          "2025-01-12",
          "2025-01-13",
          "2025-01-14",
          "2025-01-15",
          "2025-01-16",
          "2025-01-17",
          "2025-01-18",
          "2025-01-19",
          "2025-01-20",
          "2025-01-21",
          "2025-01-22",
          "2025-01-23",
          "2025-01-24",
          "2025-01-25",
          "2025-01-26",
          "2025-01-27",
          "2025-01-28",
          "2025-01-29",
          "2025-01-30",
          "2025-01-31",
          "2025-02-01",
          "2025-02-02",
          "2025-02-03",
          "2025-02-04",
          "2025-02-05",
          "2025-02-06",
          "2025-02-07",
          "2025-02-08",
          "2025-02-09",
          "2025-02-10",
          "2025-02-11",
          "2025-02-12",
          "2025-02-13",
          "2025-02-14",
          "2025-02-15",
          "2025-02-16",
          "2025-02-17",
          "2025-02-18",
          "2025-02-19",
          "2025-02-20",
          "2025-02-21",
          "2025-02-22",
          "2025-02-23",
          "2025-02-24",
          "2025-02-25",
          "2025-02-26",
          "2025-02-27",
          "2025-02-28",
          "2025-03-01",
          "2025-03-02",
          "2025-03-03",
          "2025-03-04",
          "2025-03-05",
          "2025-03-06",
          "2025-03-07",
          "2025-03-08",
          "2025-03-09",
          "2025-03-10",
          "2025-03-11",
          "2025-03-12",
          "2025-03-13",
          "2025-03-14",
          "2025-03-15",
          "2025-03-16",
          "2025-03-17",
          "2025-03-18",
          "2025-03-19",
          "2025-03-20",
          "2025-03-21",
          "2025-03-22",
          "2025-03-23",
          "2025-03-24",
          "2025-03-25",
          "2025-03-26",
          "2025-03-27",
          "2025-03-28",
          "2025-03-29",
          "2025-03-30",
          "2025-03-31",
          "2025-04-01",
          "2025-04-02",
          "2025-04-03",
          "2025-04-04",
          "2025-04-05",
          "2025-04-06",
          "2025-04-07",
          "2025-04-08",
          "2025-04-09",
          "2025-04-10",
          "2025-04-11",
          "2025-04-12",
          "2025-04-13",
          "2025-04-14",
          "2025-04-15",
          "2025-04-16",
          "2025-04-17",
          "2025-04-18",
          "2025-04-19",
          "2025-04-20",
          "2025-04-21",
          "2025-04-22",
          "2025-04-23",
          "2025-04-24",
          "2025-04-25",
          "2025-04-26",
          "2025-04-27",
          "2025-04-28",
          "2025-04-29",
          "2025-04-30",
          "2025-05-01",
          "2025-05-02",
          "2025-05-03",
          "2025-05-04",
          "2025-05-05",
          "2025-05-06",
          "2025-05-07",
          "2025-05-08",
          "2025-05-09",
          "2025-05-10",
          "2025-05-11",
          "2025-05-12",
          "2025-05-13",
          "2025-05-14",
          "2025-05-15",
          "2025-05-16",
          "2025-05-17",
          "2025-05-18",
          "2025-05-19",
          "2025-05-20",
          "2025-05-21",
          "2025-05-22",
          "2025-05-23",
          "2025-05-24",
          "2025-05-25",
          "2025-05-26",
          "2025-05-27",
          "2025-05-28",
          "2025-05-29",
          "2025-05-30",
          "2025-05-31",
          "2025-06-01",
          "2025-06-02",
          "2025-06-03",
          "2025-06-04",
          "2025-06-05",
          "2025-06-06",
          "2025-06-07",
          "2025-06-08",
          "2025-06-09",
          "2025-06-10",
          "2025-06-11",
          "2025-06-12",
          "2025-06-13",
          "2025-06-14",
          "2025-06-15",
          "2025-06-16",
          "2025-06-17",
          "2025-06-18",
          "2025-06-19",
          "2025-06-20",
          "2025-06-21",
          "2025-06-22",
          "2025-06-23",
          "2025-06-24",
          "2025-06-25",
          "2025-06-26",
          "2025-06-27",
          "2025-06-28",
          "2025-06-29",
          "2025-06-30",
          "2025-07-01",
          "2025-07-02",
          "2025-07-03",
          "2025-07-04",
          "2025-07-05",
          "2025-07-06",
          "2025-07-07",
          "2025-07-08",
          "2025-07-09",
          "2025-07-10",
          "2025-07-11",
          "2025-07-12",
          "2025-07-13",
          "2025-07-14",
          "2025-07-15",
          "2025-07-16",
          "2025-07-17",
          "2025-07-18",
          "2025-07-19",
          "2025-07-20",
          "2025-07-21",
          "2025-07-22",
          "2025-07-23",
          "2025-07-24",
          "2025-07-25",
          "2025-07-26",
          "2025-07-27",
          "2025-07-28",
          "2025-07-29",
          "2025-07-30",
          "2025-07-31",
          "2025-08-01",
          "2025-08-02",
          "2025-08-03",
          "2025-08-04",
          "2025-08-05",
          "2025-08-06",
          "2025-08-07",
          "2025-08-08",
          "2025-08-09",
          "2025-08-10",
          "2025-08-11",
          "2025-08-12",
          "2025-08-13",
          "2025-08-14",
          "2025-08-15",
          "2025-08-16",
          "2025-08-17",
          "2025-08-18",
          "2025-08-19",
          "2025-08-20",
          "2025-08-21",
          "2025-08-22",
          "2025-08-23",
          "2025-08-24",
          "2025-08-25",
          "2025-08-26",
          "2025-08-27",
          "2025-08-28",
          "2025-08-29",
          "2025-08-30",
          "2025-08-31",
          "2025-09-01",
          "2025-09-02",
          "2025-09-03",
          "2025-09-04",
          "2025-09-05",
          "2025-09-06",
          "2025-09-07",
          "2025-09-08",
          "2025-09-09",
          "2025-09-10",
          "2025-09-11",
          "2025-09-12",
          "2025-09-13",
          "2025-09-14",
          "2025-09-15",
          "2025-09-16",
          "2025-09-17",
          "2025-09-18",
          "2025-09-19",
          "2025-09-20",
          "2025-09-21",
          "2025-09-22",
          "2025-09-23",
          "2025-09-24",
          "2025-09-25",
          "2025-09-26",
          "2025-09-27",
          "2025-09-28",
          "2025-09-29",
          "2025-09-30",
          "2025-10-01",
          "2025-10-02",
          "2025-10-03",
          "2025-10-04",
          "2025-10-05",
          "2025-10-06",
          "2025-10-07",
          "2025-10-08",
          "2025-10-09",
          "2025-10-10",
          "2025-10-11",
          "2025-10-12",
          "2025-10-13",
          "2025-10-14",
          "2025-10-15",
          "2025-10-16",
          "2025-10-17",
          "2025-10-18",
          "2025-10-19",
          "2025-10-20",
          "2025-10-21",
          "2025-10-22",
          "2025-10-23",
          "2025-10-24",
          "2025-10-25",
          "2025-10-26",
          "2025-10-27",
          "2025-10-28",
          "2025-10-29",
          "2025-10-30",
          "2025-10-31",
          "2025-11-01",
          "2025-11-02",
          "2025-11-03",
          "2025-11-04",
          "2025-11-05",
          "2025-11-06",
          "2025-11-07",
          "2025-11-08",
          "2025-11-09",
          "2025-11-10",
          "2025-11-11",
          "2025-11-12",
          "2025-11-13",
          "2025-11-14",
          "2025-11-15",
          "2025-11-16",
          "2025-11-17",
          "2025-11-18",
          "2025-11-19",
          "2025-11-20",
          "2025-11-21",
          "2025-11-22",
          "2025-11-23",
          "2025-11-24",
          "2025-11-25",
          "2025-11-26",
          "2025-11-27",
          "2025-11-28",
          "2025-11-29",
          "2025-11-30",
          "2025-12-01",
          "2025-12-02",
          "2025-12-03",
          "2025-12-04",
          "2025-12-05",
          "2025-12-06",
          "2025-12-07",
          "2025-12-08",
          "2025-12-09",
          "2025-12-10",
          "2025-12-11",
          "2025-12-12",
          "2025-12-13",
          "2025-12-14",
          "2025-12-15",
          "2025-12-16",
          "2025-12-17",
          "2025-12-18",
          "2025-12-19",
          "2025-12-20",
          "2025-12-21",
          "2025-12-22",
          "2025-12-23",
          "2025-12-24",
          "2025-12-25",
          "2025-12-26",
          "2025-12-27",
          "2025-12-28",
          "2025-12-29",
          "2025-12-30",
          "2025-12-31",
          "2026-01-01",
          "2026-01-02",
          "2026-01-03",
          "2026-01-04",
          "2026-01-05",
          "2026-01-06",
          "2026-01-07",
          "2026-01-08",
          "2026-01-09",
          "2026-01-10",
          "2026-01-11",
          "2026-01-12",
          "2026-01-13",
          "2026-01-14",
          "2026-01-15",
          "2026-01-16",
          "2026-01-17",
          "2026-01-18",
          "2026-01-19",
          "2026-01-20",
          "2026-01-21",
          "2026-01-22",
          "2026-01-23",
          "2026-01-24",
          "2026-01-25",
          "2026-01-26",
          "2026-01-27",
          "2026-01-28",
          "2026-01-29",
          "2026-01-30",
          "2026-01-31",
          "2026-02-01",
          "2026-02-02",
          "2026-02-03",
          "2026-02-04",
          "2026-02-05",
          "2026-02-06",
          "2026-02-07",
          "2026-02-08",
          "2026-02-09",
          "2026-02-10",
          "2026-02-11",
          "2026-02-12",
          "2026-02-13",
          "2026-02-14",
          "2026-02-15",
          "2026-02-16",
          "2026-02-17",
          "2026-02-18",
          "2026-02-19",
          "2026-02-20",
          "2026-02-21",
          "2026-02-22",
          "2026-02-23",
          "2026-02-24",
          "2026-02-25",
          "2026-02-26",
          "2026-02-27",
          "2026-02-28",
          "2026-03-01",
          "2026-03-02",
          "2026-03-03",
          "2026-03-04",
          "2026-03-05",
          "2026-03-06",
          "2026-03-07",
          "2026-03-08",
          "2026-03-09",
          "2026-03-10",
          "2026-03-11",
          "2026-03-12",
          "2026-03-13",
          "2026-03-14",
          "2026-03-15",
          "2026-03-16",
          "2026-03-17",
          "2026-03-18",
          "2026-03-19",
          "2026-03-20",
          "2026-03-21",
          "2026-03-22",
          "2026-03-23",
          "2026-03-24",
          "2026-03-25",
          "2026-03-26",
          "2026-03-27",
          "2026-03-28",
          "2026-03-29",
          "2026-03-30",
          "2026-03-31",
          "2026-04-01",
          "2026-04-02"
        ],
        "beta_score_mean": [
          -0.001022449362339207,
          -0.034967012426097226,
          0.005457793583460768,
          0.006112878757956391,
          0,
          0,
          0.0005992332607859044,
          0.00179051383140127,
          0.0006032929000059247,
          -0.0007699107534815125,
          0.002768725642927585,
          0,
          0,
          0.003386683480536952,
          -0.0000853002814381459,
          -0.00014371646388657906,
          0.001638713390153296,
          -0.0027097130866503088,
          0,
          0,
          -0.003962471464050887,
          -0.000524642944324467,
          0.00004452152315144816,
          0,
          -0.000008034065828590811,
          0,
          0,
          -0.004195593110483151,
          -0.0021108871181636517,
          0.001245063334731494,
          0.002398817244411427,
          0.0032187570269196593,
          0,
          0,
          -0.011839001339389458,
          -0.000581080278654725,
          0.0012531953164130385,
          -0.0008991665638014072,
          -0.0009614083982468196,
          0,
          0,
          0.005858946414562722,
          0.002139414221061084,
          -0.004246191599002674,
          0.0020825747293669278,
          0.0009706711139043551,
          0,
          0,
          0.006985423445417157,
          0.0005908170903621516,
          0,
          -0.0012259965585897726,
          -0.0007679242629523663,
          0,
          0,
          -0.0012579297338781272,
          -0.0004761382053874725,
          0,
          0.006960058062875901,
          -0.0008688686672578864,
          0,
          0,
          0.005532462581572795,
          -0.002805901741561343,
          0.0007818553069650426,
          0,
          0.0021998881296997554,
          0,
          0,
          -0.002912532426907767,
          0.001769863062981837,
          -0.002071979042437559,
          -0.0006816111578181878,
          -0.001236357438808502,
          0,
          0,
          0,
          -0.00039630310622397805,
          0.0026282637853793406,
          -0.0012249765020323619,
          0.00019129395712860994,
          0,
          0,
          -0.01570275204003435,
          -0.005103730677513527,
          0.00044969615343980597,
          0.0031123841018564076,
          0.00007560696184748741,
          0,
          0,
          0.0020365224720104353,
          -0.003088875601370544,
          0.00014757212713771396,
          0.0011669972883600309,
          0.0016299578197274517,
          0,
          0,
          -0.004724739884634982,
          0.0006012834560689156,
          0.002331188610113006,
          -0.0009998132263073231,
          -0.002532420339365054,
          0,
          0,
          0,
          -0.002312844044955406,
          0.0027243089150550733,
          -0.001784896788450531,
          0.0074104866343026625,
          0,
          0,
          -0.0053365488586038625,
          0.003979664273495927,
          -0.0059808566991667355,
          0.0006962256523692793,
          0.002427535123318552,
          0,
          0,
          0.008493701908990677,
          0.0021659779066280213,
          -0.0010189421751206713,
          -0.0004740101374949335,
          0.006954890970089629,
          0,
          0,
          -0.021753137837647086,
          -0.00671183494781681,
          0.006121167661937782,
          -0.004408456505395774,
          -0.004170548926391207,
          0,
          0,
          0.0025991328276352616,
          0.002152591730979566,
          -0.003119806359085155,
          0.0022627006871508253,
          -0.0012875178187357046,
          0,
          0,
          -0.005832932321298815,
          0.0025953385962975534,
          -0.0008503001544963519,
          0.004072090525156618,
          0.0070628092679436896,
          0,
          0,
          0.0016773912034115021,
          -0.0032727124610079576,
          0.0002090285626605404,
          -0.017956209286768825,
          0.004903915955000145,
          0,
          0,
          -0.0020498421515564237,
          0.0011427467336074574,
          -0.001660740419004454,
          -0.00010442131156115214,
          0.001907180771054561,
          0,
          0,
          -0.0007774399615425187,
          -0.0002858814013633528,
          0.0011650564914627037,
          -0.0016194549805248614,
          0,
          0,
          0,
          -0.00036145926808440305,
          -0.002605171445197951,
          0.0013542326965708506,
          0.006975052627941928,
          0.004105164300064773,
          0,
          0,
          0.0006654135912593955,
          0.0003272890047257524,
          0.0003755038302589268,
          0.00033789309257292136,
          0.00313939178079445,
          0,
          0,
          -0.00006644155525343753,
          0.001214734628345058,
          -0.00022884896918651666,
          -0.0035722171625483957,
          0.0006736390038034533,
          0,
          0,
          -0.009364938720722823,
          0.009913233852699353,
          0.002637991378778197,
          -0.0012343260740272353,
          -0.001548422708221933,
          0,
          0,
          -0.0015215437667335878,
          0.0024777607146352154,
          0.007877724224548532,
          -0.001015277331558219,
          0.0017378741099011751,
          0,
          0,
          0,
          -0.0007315338418498368,
          0.0011546695410266886,
          -0.0018813490176129116,
          -0.0018864008625885183,
          0,
          0,
          0.001190797836640703,
          -0.0038179067254943476,
          0.0007418799918095507,
          0.003239541032814007,
          0.0011593989573485983,
          0,
          0,
          0.003914708148549798,
          0.00437941828049842,
          0.001728356892030821,
          0.0019804668219985436,
          0.006880142469930508,
          0,
          0,
          0.007199833143548445,
          -0.002466615745365744,
          0.00014003771679501795,
          0,
          0.0006107011225562792,
          0,
          0,
          0.0020360723093262446,
          0.001489798208751172,
          0.003261334076768411,
          0.003102696736011889,
          -0.005652466011916933,
          0,
          0,
          0.004775745106769539,
          -0.0015508867098316661,
          0.012770583040591468,
          0.002628433629610601,
          0,
          0,
          0,
          -0.000031577327113469374,
          -0.0032005727616263697,
          0.002161956495505013,
          -0.0022577855345032225,
          0.0009024968433394626,
          0,
          0,
          0.002947288241299336,
          0.0011601772876264909,
          0.0008912009173264449,
          0.001699900999270266,
          0.0031929590314879134,
          0,
          0,
          -0.0021585342813010945,
          -0.004797854517565725,
          0.0009607886732878766,
          0.006193962116419515,
          -0.0020779305440933745,
          0,
          0,
          0.006617828122966152,
          0.0013638457669588983,
          0.006388370675513031,
          0.0026959269480021295,
          -0.0005984090874179721,
          0,
          0,
          0.0008904016821254113,
          -0.001827644496138457,
          0.0011776058328234118,
          0.000610120396092987,
          0.006863265102489925,
          0,
          0,
          0.0022548128369242804,
          -0.00450605065772213,
          -0.002381030967947694,
          -0.0037076671278903155,
          0.001606246419976725,
          0,
          0,
          0.0010371961914945823,
          -0.003986310684124804,
          0.0021924825698499155,
          -0.004122412718611092,
          -0.006057836318432098,
          0,
          0,
          0.003781411118209452,
          0.0019831365038159164,
          0.0007456291756682064,
          0.002772673976131053,
          -0.0018552487035101248,
          0,
          0,
          0,
          0.0010069208843110833,
          0.0006284617582957302,
          -0.0021672900830196655,
          -0.0008081784168936945,
          0,
          0,
          0.00830478895975969,
          0.0007534733552913089,
          0.00906942722328512,
          -0.002063236567771123,
          0.0026936488199848503,
          0,
          0,
          0.0012694618480219354,
          -0.0026181966202042466,
          -0.000057935978354130986,
          0.00427135182852823,
          0.0015104221666739734,
          0,
          0,
          0.00495102322581872,
          -0.0031271035956252097,
          0.0034101917812222214,
          0.0014793159434547244,
          0.00017806917405517025,
          0,
          0,
          -0.0030735661999691287,
          0.007147580974951978,
          0.003565102864217408,
          0.0012969378048557027,
          -0.001215111370884916,
          0,
          0,
          0.0038104378227430216,
          -0.0008142177679806068,
          -0.0005719024046683698,
          0.00016826539763516743,
          -0.0049147773932734125,
          0,
          0,
          0.0032812883390601066,
          -0.0023045570730692547,
          -0.003659944294176466,
          0.0017634009385476665,
          -0.0006230698043065332,
          0,
          0,
          0.002457386696971335,
          0.00034510435100319325,
          -0.0013662783571882814,
          0.005183625624255939,
          0.003983762674215667,
          0,
          0,
          0.0010570880213571982,
          0.00819536176456966,
          0.012055582005928907,
          0.005463294897725822,
          0.0017243724988653705,
          0,
          0,
          -0.006789286816773834,
          -0.002754233430325612,
          0.003372740089257943,
          -0.0023784489857543363,
          0.006610910373467066,
          0,
          0,
          0.009636625373672762,
          -0.0032582762639278566,
          -0.0015746935596709893,
          -0.5407261996880288,
          0.0022851234327482314,
          0,
          0,
          0.0007964607359543136,
          0.0005857654576134395,
          0.001378531148254959,
          -0.002942383744627662,
          -0.0008377831776810546,
          0,
          0,
          -0.00546548013533467,
          -0.008980379300109182,
          -0.0019398406680100286,
          0,
          -0.0009645985484871768,
          0,
          0,
          -0.008711616003839226,
          -0.0036825091922362053,
          0.001914168588389259,
          -0.0028222466941920286,
          -0.0018185362909512387,
          0,
          0,
          -0.0030964537372912392,
          -0.00001531977613715262,
          -0.0006202226062963596,
          0.0005931125042337672,
          -0.004820931100040575,
          0,
          0,
          0.0007704745863279474,
          -0.0010625710896264,
          -0.0038616273114329175,
          0.0009770287822233553,
          0.0054944151698793405,
          0,
          0,
          -0.01527286528009311,
          0.005506840187148528,
          -0.00191693291926402,
          0,
          -0.0012299706840144407,
          0,
          0,
          -0.0006161368826396857,
          -0.003298952062300407,
          0.0009587261764463659,
          0,
          0.00025440726337756694,
          0,
          0,
          0.0031782667084829684,
          0.0011950172257769018,
          0.0046511913973732045,
          -0.00546554122008668,
          -0.004780601441986097,
          0,
          0,
          0.001072112540063376,
          -0.0007440388704137411,
          0.002876768215326937,
          0.0016720341350930034,
          0.0045807034972685555,
          0,
          0,
          0,
          0.0010961200929107402,
          0.005946659319491544,
          0.0008731030403530736,
          0.0009395255936646064,
          0,
          0,
          -0.0012230698740775972,
          0.0011401190612600916,
          0.000815840511510242,
          -0.0020356465933481106,
          -0.003922011841713135,
          0,
          0,
          -0.007823934084948244,
          0.007966003914420516,
          -0.0037031899746525813,
          0.0015329773078135967,
          0.0057324782238385484,
          0,
          0,
          -0.00539037183467711,
          -0.0010219428620409155,
          0.00797933157269467,
          0.010357903961564639,
          -0.005450724395757624,
          0,
          0,
          0,
          -0.002002011270032242,
          0.0022181349839613396,
          0.000019126779027303836,
          0.0017602179538856355,
          0,
          0,
          0.0009169388645820922,
          -0.00008335039568091118,
          -0.00691239862745285,
          -0.007167934045320344,
          -0.004164497552935329,
          0,
          0,
          0.0023621481423393115,
          -0.0034887495815626663,
          -0.0034270386556019385,
          -0.008823746253332647,
          -0.0012040517884611623,
          0,
          0,
          -0.002380361390374513,
          0.0035641943857546753,
          0.0004131367821858871,
          0.004237529719273112,
          -0.0001326892030563387,
          0,
          0,
          -0.0006394082047770816,
          -0.003121037680771104,
          -0.0013567060721445428,
          -0.0013394237732059177,
          -0.0027294022136985278,
          0,
          0,
          -0.00045400298038809347,
          -0.0010842105390243629,
          0.0004769711680912165,
          -0.0026151320637816727,
          -0.0016890766477989409,
          0,
          0,
          -0.006784356020410576,
          0.004182723882272259,
          0.0032509771500262696,
          -0.001070940110750149,
          0
        ]
      },
      "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."
  ]
}