Consensus, moved a fraction of the way toward the forecast
The customer’s question is never “what will revenue be?” — they already have consensus. It is “where is consensus wrong?” This page builds the number that answers it, and shows every step with real figures.
Ported from docs/anchoring.qmd and docs/anchoring_signal.py in the buy-side consensus repository, from one company-quarter of scalars to the panel API. That reference ends in a self-check with real numbers, and the self-check is a golden test here, so this page and the published research cannot drift apart.
Four inputs per company-quarter, each read as of the moment the number is published: the value whose known_at is the latest one strictly before that instant.
| Input | Cap |
|---|---|
| model | at most 21 days old |
| consensus | at most 60 days old |
| consensus 30 days earlier | at most 60 days old |
| first reported actual | evaluation only, never an input |
AS_OF = pd.Timestamp("2026-01-20", tz="UTC")
LOOKBACK = pd.Timedelta(days=30)
estimates = pfc.validate_estimates(pf.example_panel())
estimates| entity | period | target | period_end | source | value | known_at | |
|---|---|---|---|---|---|---|---|
| 0 | ZS | 2026Q1 | revenue | 2026-01-31 00:00:00+00:00 | consensus | 790.0 | 2025-12-01 00:00:00+00:00 |
| 1 | ZS | 2026Q1 | revenue | 2026-01-31 00:00:00+00:00 | consensus | 798.8 | 2026-01-15 00:00:00+00:00 |
| 2 | ZS | 2026Q1 | revenue | 2026-01-31 00:00:00+00:00 | model | 845.3 | 2026-01-12 00:00:00+00:00 |
Two consensus prints, one model run. The older consensus is what the 30-day revision measures against.
anchored = pfc.latest_before(estimates, AS_OF)
subjects = pfc.age_at(pfc.pivot_sources(anchored), AS_OF)
revisions = pfc.consensus_revision(estimates, AS_OF, lookback=LOOKBACK)
subjects = subjects.merge(revisions, on=pfc.subject_index(subjects), how="left")
subjects[["entity", "consensus", "model", "consensus_revision", "model_age", "consensus_age"]]| entity | consensus | model | consensus_revision | model_age | consensus_age | |
|---|---|---|---|---|---|---|
| 0 | ZS | 798.8 | 845.3 | 0.011139 | 8 days | 5 days |
Five steps, every one explicit: anchor, reshape, age, measure the revision, join it on. A method never reaches past this pipeline to the raw panel.
All three are relative quantities, so companies of any size are comparable.
\[ g = \frac{\text{model}}{\text{consensus}} - 1 \qquad\text{the gap: what the data says consensus is missing} \]
\[ r = \frac{\text{consensus}_t}{\text{consensus}_{t-30}} - 1 \qquad\text{the revision: what analysts have already started to do} \]
\[ s = \frac{\text{actual}}{\text{consensus}} - 1 \qquad\text{the surprise: the target, known only afterwards} \]
The revision is two anchored reads of the same quantity, thirty days apart, which is why it lives in history and not in the method. A missing prior consensus comes back missing, never as a revision of zero — those are different facts.
The published estimate is a forecast of the surprise from the gap and the revision:
\[ \hat s = a + b_g\, g + b_r\, r \]
Fitted by ordinary least squares on reports before a cut-off date, then never refitted inside the evaluation period. The library ships the fitted sets as data:
pd.DataFrame(
[
pfc.STUDY_2025_01.model_dump(mode="json"),
pfc.CORE_2025_01.model_dump(mode="json"),
]
).set_index("version").T| version | study-2025-01 | core-2025-01 |
|---|---|---|
| customary_beat | 0.0112 | 0.0089 |
| gap_weight | 0.129 | 0.0442 |
| revision_weight | 1.28 | 1.2348 |
| maximum_absolute_gap | 0.25 | 0.25 |
| maximum_prediction_age | P21D | P21D |
| maximum_consensus_age | P60D | P60D |
| fitted_through | 2024-12-31 | 2024-12-31 |
This is the step that surprises people. Let \(\theta\) be the part of the surprise that is genuinely knowable in advance. The gap is a noisy reading of it, and the surprise is \(\theta\) plus what nobody could have known:
\[ g = \theta + \eta, \qquad s = \theta + \epsilon \]
\[ b_g = \frac{\operatorname{Cov}(s, g)}{\operatorname{Var}(g)} = \frac{\operatorname{Var}(\theta)}{\operatorname{Var}(\theta) + \operatorname{Var}(\eta)} \]
A signal-to-total-variance ratio, always between 0 and 1. A weight of 0.129 does not mean the model is usually wrong. It means the gap’s noise variance is about seven times the variance of its predictive part.
rng = np.random.default_rng(20260922)
size = 4000
theta = rng.normal(0, 0.012, size)
reports = pd.DataFrame(
{
"gap": theta + rng.normal(0, 0.012 * np.sqrt(6.75), size),
"surprise": theta + rng.normal(0, 0.020, size),
}
)
slope = np.cov(reports.surprise, reports.gap)[0, 1] / reports.gap.var()
reports["quintile"] = pd.qcut(reports.gap, 5, labels=[1, 2, 3, 4, 5])
figure, axes = plt.subplots(1, 2, figsize=(11, 4))
sns.regplot(
data=reports, x="gap", y="surprise", ax=axes[0], ci=None,
scatter_kws={"s": 5, "alpha": 0.15, "color": pf.ACCENT, "edgecolor": "none"},
line_kws={"color": pf.WARM, "label": f"fitted slope {slope:.3f}"},
)
grid = np.linspace(reports.gap.min(), reports.gap.max(), 50)
axes[0].plot(grid, grid, color=pf.GREY, ls="--", lw=1.2, label="publishing the model")
axes[0].set(xlabel="gap $g$", ylabel="surprise $s$", title="One point per report")
axes[0].legend()
sns.barplot(
data=reports.assign(beat=reports.surprise > 0),
x="quintile", y="beat", ax=axes[1], color=pf.ACCENT, errorbar=None,
)
axes[1].axhline(0.5, color=pf.WARM, lw=1.2, ls="--", label="coin flip")
axes[1].set(
xlabel="gap quintile", ylabel="beat rate",
title="Share that beat consensus, by gap quintile",
)
axes[1].legend()
figure.tight_layout()
A coefficient above one looks wrong and is not. Analysts revise toward the truth but stop short, so the observed revision is a partial adjustment. The regression recovers the structural weight divided by the share analysts complete. A weight of 1.28 implies they complete roughly three-quarters of the move before the report.
Do not publish the expected surprise as a level on its own. Multiply consensus by it:
\[ \hat y = c \times (1 + \hat s) \]
Substituting the gap shows what anchoring really is:
\[ \hat y = \underbrace{c\,(1 + a + b_r r)}_{\text{consensus, corrected}} + \underbrace{b_g\,(m - c)}_{\text{a fraction of the disagreement}} \]
method = pfc.AnchoredEstimate(forecast_source="model")
published = method.fit(subjects).apply(subjects)
row = published.iloc[0]
pd.DataFrame(
[
{"field": name, "value": f"{row[name]:+.4%}"}
for name in [*pfc.CONTRIBUTION_COLUMNS, pfc.EXPECTED_SURPRISE_COLUMN]
]
+ [
{"field": pfc.ANCHORED_LEVEL_COLUMN, "value": f"{row.anchored_level:,.2f}"},
{"field": pfc.PARAMETERS_VERSION_COLUMN, "value": row.parameters_version},
]
)| field | value | |
|---|---|---|
| 0 | contribution_customary_beat | +1.1200% |
| 1 | contribution_gap | +0.7509% |
| 2 | contribution_revision | +1.4258% |
| 3 | expected_surprise | +3.2968% |
| 4 | anchored_level | 825.13 |
| 5 | parameters_version | study-2025-01 |
The three contributions sum to the expected surprise. That is what makes the number attributable: a customer sees which part of the adjustment is alternative data and which is consensus dynamics, and each data partner sees its own contribution.
places = pd.DataFrame(
[
{"number": "consensus", "level": row.consensus},
{"number": "anchored", "level": row.anchored_level},
{"number": "model", "level": row.model},
]
)
figure, axis = plt.subplots(figsize=(9, 2.6))
axis.hlines(0, row.consensus - 8, row.model + 8, color=pf.GREY, lw=1.5, zorder=1)
sns.scatterplot(
data=places, x="level", y=0, hue="number", s=160, ax=axis, zorder=3,
palette=[pf.GREY, pf.ACCENT, pf.WARM],
)
for _, place in places.iterrows():
axis.annotate(f"{place.level:.1f}", (place.level, -0.42), ha="center", fontsize=9)
axis.annotate(
"", xy=(row.anchored_level, 0.14), xytext=(row.consensus, 0.14),
arrowprops={"arrowstyle": "->", "color": pf.ACCENT, "lw": 1.4},
)
axis.annotate(
f"{row.expected_surprise:.2%} of consensus",
((row.consensus + row.anchored_level) / 2, 0.2),
color=pf.ACCENT, ha="center", fontsize=9,
)
axis.set(ylim=(-0.8, 0.55), yticks=[], ylabel="", xlabel="revenue ($m)")
axis.set_title("Where the published number sits")
sns.despine(ax=axis, left=True)
figure.tight_layout()
The published number inherits the accuracy of consensus, and every bit of the alternative data sits in the difference.
A feed that fills a gap with consensus is publishing “no information” as if it were a forecast. A feed that drops the row silently makes the gap invisible. So the row stays, the numbers go missing, and the reason travels with it.
cases = pd.DataFrame(
{
"entity": ["fine", "no model", "stale model", "stale consensus", "wide gap"],
"period": ["2026Q1"] * 5,
"target": ["revenue"] * 5,
"period_end": pd.to_datetime(["2026-01-31"] * 5, utc=True),
"consensus": [798.8] * 5,
"model": [845.3, float("nan"), 845.3, 845.3, 1100.0],
"consensus_revision": [0.0] * 5,
"model_age": pd.to_timedelta([8, 8, 22, 8, 8], unit="D"),
"consensus_age": pd.to_timedelta([5, 5, 5, 61, 5], unit="D"),
}
)
method.fit(cases).apply(cases)[
[
"entity",
pfc.ELIGIBLE_COLUMN,
pfc.ELIGIBILITY_REASON_COLUMN,
pfc.EXPECTED_SURPRISE_COLUMN,
pfc.ANCHORED_LEVEL_COLUMN,
]
]| entity | eligible | eligibility_reason | expected_surprise | anchored_level | |
|---|---|---|---|---|---|
| 0 | fine | True | publishable | 0.018709 | 813.74506 |
| 1 | no model | False | missing_input | NaN | NaN |
| 2 | stale model | False | stale_prediction | NaN | NaN |
| 3 | stale consensus | False | stale_consensus | NaN | NaN |
| 4 | wide gap | False | gap_too_wide | NaN | NaN |
The check order is part of the contract: missing input, then stale model, then stale consensus, then wide gap. A subject that is both stale and wide-gapped reports the staleness, because that is the fault to fix.
A gap beyond 25% is almost always a mismatched fiscal period or a restatement rather than information, which is why it is a data break and not a very strong signal.
Fitted coefficients become constants shipped with the signal, re-estimated on a schedule and never tuned between releases. A consumer who backtests your history needs to know which coefficient set produced each published value.
pd.DataFrame(
[
{
"version": parameters.version,
"fitted_through": str(parameters.fitted_through),
"expected_surprise": f"{out.expected_surprise:+.4%}",
"anchored_level": f"{out.anchored_level:,.2f}",
}
for parameters in (pfc.STUDY_2025_01, pfc.CORE_2025_01)
for out in [
pfc.AnchoredEstimate(forecast_source="model", parameters=parameters)
.fit(subjects)
.apply(subjects)
.iloc[0]
]
]
)| version | fitted_through | expected_surprise | anchored_level | |
|---|---|---|---|---|
| 0 | study-2025-01 | 2024-12-31 | +3.2968% | 825.13 |
| 1 | core-2025-01 | 2024-12-31 | +2.5228% | 818.95 |
Same inputs, different published number, and the difference is explainable rather than mysterious. The record a run writes down carries both:
method.fit(subjects).to_dict(){'method': 'anchored.estimate',
'forecast_source': 'model',
'consensus_source': 'consensus',
'parameters_version': 'study-2025-01',
'fitted_through': '2024-12-31',
'parameters': {'customary_beat': 0.0112,
'gap_weight': 0.129,
'revision_weight': 1.28,
'maximum_absolute_gap': 0.25,
'maximum_prediction_age': 'P21D',
'maximum_consensus_age': 'P60D',
'version': 'study-2025-01',
'fitted_through': '2024-12-31'}}Plain values only. It serialises with nothing more than a JSON dump, and no pickle stands between a published number and its explanation.
Next: the Bayesian posterior, which reaches a similar number by a different route and carries an uncertainty band.