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05707f0 f784e93 05707f0 f784e93 05707f0 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 | """Point-in-time predictors for next-month factor returns.
Every feature dated month t is a function of returns observed in months <= t only.
The target is the return realised in month t+1. `tests/test_no_leakage.py` checks
this by perturbing future returns and confirming no feature changes.
"""
from __future__ import annotations
import numpy as np
import pandas as pd
FEATURES = [
"own_r1", # last month's factor return
"own_m3", # trailing 3-month mean
"own_m12", # trailing 12-month mean (factor momentum)
"own_m36", # trailing 36-month mean (slow-moving premium proxy)
"own_v12", # trailing 12-month volatility
"cty_m12", # same country, average 12-month mean across all factors
"dm_m12", # same factor, average 12-month mean across developed markets
]
def _regional_terms(R: pd.DataFrame, m12: pd.DataFrame, reg: pd.DataFrame) -> tuple[pd.DataFrame, pd.DataFrame]:
"""dm_m12 and the pooled regional mean when region membership can change over time.
reg has R's shape and holds each series' region in each month. The DM average at t
uses the series classified DM at t; the pooled mean for region g at t averages every
past country-month that was in g when it was observed, and a series uses the pooled
mean of the region it belongs to at t.
"""
factors = R.columns.get_level_values("factor")
dm = m12.where(reg == "DM").T.groupby(level="factor").mean().T
dm_m12 = dm.reindex(columns=factors).set_axis(R.columns, axis=1)
pooled = pd.DataFrame(np.nan, index=R.index, columns=R.columns)
for g in pd.unique(reg.to_numpy().ravel()):
if not isinstance(g, str):
continue
member = reg == g
sub = R.where(member)
s = sub.T.groupby(level="factor").sum(min_count=1).T.fillna(0).cumsum()
n = sub.notna().T.groupby(level="factor").sum().T.cumsum()
pm = (s / n.where(n > 0)).reindex(columns=factors).set_axis(R.columns, axis=1)
pooled = pooled.where(~member, pm)
return dm_m12, pooled
def build_features(panel: pd.DataFrame, hist_min: int = 24, kappa: float = 120.0) -> pd.DataFrame:
"""Long table: month, country, factor, region, FEATURES, hist_mean, shrink_mean, target, target_month."""
wide = panel.pivot_table(index="month", columns=["country", "factor"], values="ret")
full = pd.period_range(wide.index.min(), wide.index.max(), freq="M")
R = wide.reindex(full) # explicit gaps stay NaN; rolling windows do not skip them
feats: dict[str, pd.DataFrame] = {
"own_r1": R,
"own_m3": R.rolling(3, min_periods=3).mean(),
"own_m12": R.rolling(12, min_periods=12).mean(),
"own_m36": R.rolling(36, min_periods=24).mean(),
"own_v12": R.rolling(12, min_periods=12).std(),
}
m12 = feats["own_m12"]
cty = m12.T.groupby(level="country").mean().T # month x country
feats["cty_m12"] = cty.reindex(columns=m12.columns.get_level_values("country")).set_axis(m12.columns, axis=1)
hist_mean = R.expanding(min_periods=hist_min).mean()
n_own = R.notna().cumsum()
# Shrinkage benchmark: each series' own expanding mean pulled toward the
# expanding mean of the same factor pooled over all countries in its region,
# with weight n / (n + kappa). Beating the own historical mean can reflect
# nothing more than this kind of cross-sectional pooling; beating the shrunk
# mean is evidence of timing.
region = panel.drop_duplicates("country").set_index("country")["region"]
time_varying = bool((panel.groupby("country")["region"].nunique() > 1).any())
reg = None
if time_varying:
# month x country region, carried across months without data, then spread to series
reg_c = (panel.drop_duplicates(["month", "country"]).pivot(index="month", columns="country", values="region")
.reindex(full).ffill().bfill())
reg = reg_c.reindex(columns=R.columns.get_level_values("country")).set_axis(R.columns, axis=1)
feats["dm_m12"], pooled = _regional_terms(R, m12, reg)
else:
dm_cols = [c for c in m12.columns if region.get(c[0]) == "DM"]
if dm_cols:
dm = m12[dm_cols].T.groupby(level="factor").mean().T # month x factor
feats["dm_m12"] = dm.reindex(columns=m12.columns.get_level_values("factor")).set_axis(m12.columns, axis=1)
else:
feats["dm_m12"] = pd.DataFrame(np.nan, index=m12.index, columns=m12.columns)
pooled = pd.DataFrame(np.nan, index=R.index, columns=R.columns)
for g in region.dropna().unique():
cols = [c for c in R.columns if region.get(c[0]) == g]
sub = R[cols]
s = sub.T.groupby(level="factor").sum(min_count=1).T.fillna(0).cumsum()
n = sub.notna().T.groupby(level="factor").sum().T.cumsum()
pm = (s / n.where(n > 0)).reindex(columns=sub.columns.get_level_values("factor"))
pooled[cols] = pm.to_numpy()
shrink_mean = (n_own * hist_mean + kappa * pooled) / (n_own + kappa)
shrink_mean = shrink_mean.where(hist_mean.notna())
# Empirical Bayes adaptive shrinkage: kappa_t = clip(within_var / between_var, 12, 600)
within_var = R.expanding(min_periods=hist_min).var().clip(lower=1e-8)
between_var = ((hist_mean - pooled) ** 2).expanding(min_periods=hist_min).mean().clip(lower=1e-6)
eb_kappa = (within_var / between_var).clip(lower=12.0, upper=600.0)
eb_shrink_mean = (n_own * hist_mean + eb_kappa * pooled) / (n_own + eb_kappa)
eb_shrink_mean = eb_shrink_mean.where(hist_mean.notna())
target = R.shift(-1)
def stack(frame: pd.DataFrame, name: str) -> pd.Series:
s = frame.stack(["country", "factor"], future_stack=True)
s.name = name
return s
out = pd.concat(
[stack(feats[k], k) for k in FEATURES]
+ [
stack(hist_mean, "hist_mean"),
stack(shrink_mean, "shrink_mean"),
stack(eb_shrink_mean, "eb_shrink_mean"),
stack(target, "target"),
],
axis=1,
)
out.index.names = ["month", "country", "factor"]
out = out.reset_index()
out["region"] = stack(reg, "region").to_numpy() if time_varying else out["country"].map(region)
out["target_month"] = out["month"] + 1
return out
def model_ready(features: pd.DataFrame, extra: tuple[str, ...] = ()) -> pd.DataFrame:
"""Rows with a realised target, a benchmark and every feature (and extra column) observed."""
need = FEATURES + list(extra) + ["hist_mean", "shrink_mean", "target"]
return features.dropna(subset=need).reset_index(drop=True)
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