Is the accruals anomaly dead? Testing Sloan thirty years on

# Frozen before any data is loaded. Every cell below reads from PREREG,
# so no value is typed twice and the plan cannot drift from the code.
#
# Provenance of every parameter.
#
# From Sloan (1996), The Accounting Review 71(3), 289-315, read out of the
# JSTOR scan:
#   - the sort variable: accruals, scaled by average total assets
#   - ten portfolios, low accrual minus high accrual as the hedge portfolio
#   - his sample is Compustat NYSE and AMEX firm-years, 1962 through 1991
#   - returns are measured starting four months after fiscal year end
#
# From Green, Hand & Soliman (2011), Management Science 57(5), 797-816,
# abstract read on the INFORMS page:
#   - the claim under test: the hedge returns to Sloan's accruals anomaly
#     have decayed "to the point that they are, on average, no longer
#     reliably positive"
#
# Mine, not theirs, and named as mine:
#   - the three period boundaries. Both are publication dates, which are
#     facts, rather than either paper's sample end, which would put the
#     boundary at a date the market could not have known.
#   - cost_bps, hac_lags, and the decision rule in "success".
#
# French's AC/B is not Sloan's accrual measure. His is the change in
# operating working capital per split-adjusted share from t-2 to t-1 over
# book equity per share at t-1; Sloan's is balance-sheet accruals over
# average total assets. Decay is therefore measured within this one series
# across time and never against Sloan's printed hedge return.

PREREG = {
    "hypothesis": (
        "The low-minus-high accrual decile spread on Ken French's "
        "accrual-sorted portfolios earned a positive average monthly return "
        "before Sloan was published, and its average in the period after "
        "Green, Hand and Soliman declared the anomaly gone is lower and no "
        "longer reliably different from zero."
    ),
    "universe": (
        "Ken French Portfolios_Formed_on_AC, value-weighted deciles built "
        "from NYSE, AMEX and NASDAQ common stocks on CRSP, formed each June "
        "on AC/B. Equal-weighted deciles are the preregistered robustness "
        "cut, because Sloan's result was equal-weighted. Built from CRSP, so "
        "no survivorship bias enters through universe selection."
    ),
    "start":     "1963-07-31",
    "end":       "2026-06-30",
    "holdout":   "2011-05-31 onwards, touched once in the last cell of Results",
    "rebalance": "annual, French forms the portfolios at the end of June",
    "params": {
        "n_deciles":        10,
        "pre_pub_end":      "1996-06-30",   # month before Sloan, TAR 71(3), July 1996
        "interim_end":      "2011-04-30",   # month before Green/Hand/Soliman, MS 57(5), May 2011
        "cost_bps":         20,
        "hac_lags":         12,
        "min_months":       60,
    },
    "success": (
        "Both must hold for the decay claim to replicate. (a) Over "
        "1963-07 to 1996-06 the value-weighted low-minus-high spread has a "
        "positive mean monthly return with |t| > 2 under Newey-West standard "
        "errors, net of 20bp round-trip costs. (b) In the holdout the net "
        "mean is below the pre-publication mean and its |t| is under 2. "
        "If (a) fails, the note reports that the anomaly was never present "
        "in this series and the decay question does not arise."
    ),
}

import sys
import warnings

# Library import notices are not findings, and they would otherwise be
# published as output. Silenced before the imports that raise them.
warnings.filterwarnings("ignore")

import numpy as np
import pandas as pd
import statsmodels.api as sm
import matplotlib.pyplot as plt

sys.path.append("..")
from lib import style, data

style.use()
SEED = 0
np.random.seed(SEED)

AS_OF = "2026-08-28"          # as-of date of every cached pull in this note
P = PREREG["params"]
DECILES = ["Lo 10"] + [f"Dec {i}" for i in range(2, 10)] + ["Hi 10"]

dec = data.to_month_end(data.famafrench("Portfolios_Formed_on_AC", AS_OF, table=0))
ff  = data.to_month_end(data.famafrench("F-F_Research_Data_Factors", AS_OF))

m = dec[DECILES].join(ff[["Mkt-RF", "RF", "SMB", "HML"]], how="inner")
m = m.loc[PREREG["start"]:PREREG["end"]]
ex = m[DECILES].sub(m["RF"], axis=0)          # excess returns, percent per month

print(f"deciles  {len(dec):6,} rows  {dec.index.min().date()} -> {dec.index.max().date()}")
print(f"factors  {len(ff):6,} rows  {ff.index.min().date()} -> {ff.index.max().date()}")
print(f"merged   {len(m):6,} rows  {m.index.min().date()} -> {m.index.max().date()}")
print(f"missing values in the merged panel: {int(m.isna().sum().sum())}")

def hedge(table=0, cols=None, cost_bps=P["cost_bps"]):
    """Low-accrual minus high-accrual, with the annual round trip charged in
    July, the month after French rebuilds the portfolios."""
    cols = cols or DECILES
    d = data.to_month_end(data.famafrench("Portfolios_Formed_on_AC", AS_OF, table=table))
    mm = d[cols].join(ff[["Mkt-RF", "RF", "SMB", "HML"]], how="inner")
    mm = mm.loc[PREREG["start"]:PREREG["end"]]
    gross = mm[cols[0]] - mm[cols[-1]]
    charge = pd.Series(0.0, index=mm.index)
    charge[mm.index.month == 7] = 2 * cost_bps / 100.0   # out of one leg, into the other
    return gross - charge, mm

def mean_t(r, lags=P["hac_lags"]):
    """Mean and its Newey-West t-statistic against zero."""
    fit = sm.OLS(r.values, np.ones(len(r))).fit(cov_type="HAC", cov_kwds={"maxlags": lags})
    return len(r), r.mean(), float(fit.tvalues[0]), np.sqrt(12) * r.mean() / r.std()

spread, m = hedge()
PERIODS = [
    ("before Sloan        1963-07 to 1996-06", slice(None, P["pre_pub_end"])),
    ("between the papers  1996-07 to 2011-04", slice("1996-07-01", P["interim_end"])),
]

# Criterion (a): was the spread there before Sloan was published?

print("low-accrual minus high-accrual decile, value-weighted, net of costs\n")
print(f"{'period':40} {'n':>4} {'mean%':>8} {'t':>7} {'Sharpe':>8}")
for label, sl in PERIODS:
    n, mu, t, sr = mean_t(spread.loc[sl])
    print(f"{label:40} {n:>4} {mu:+8.3f} {t:+7.2f} {sr:+8.3f}")
n, mu, t, sr = mean_t(spread)
print(f"{'full sample         1963-07 to 2026-06':40} {n:>4} {mu:+8.3f} {t:+7.2f} {sr:+8.3f}")

fig, ax = plt.subplots(figsize=(8, 4.4))

pre  = ex.loc[:P["pre_pub_end"]].mean()
hold = ex.loc["2011-05-01":].mean()
x = np.arange(1, 11)

# Demeaned within each period. Raw means are not comparable across periods:
# the holdout is a bull market, which lifts all ten deciles together and would
# hide the only thing being compared, which is the slope.
ax.plot(x, pre - pre.mean(), color=style.ACCENT, lw=1.8, marker="o", ms=4,
        label="Before Sloan, 1963-07 to 1996-06")
ax.plot(x, hold - hold.mean(), color=style.SERIES[1], lw=1.2, marker="o", ms=4,
        label="Holdout, 2011-05 to 2026-06")
ax.axhline(0, color=style.MUTED, lw=0.7)
ax.set_xticks(x)
ax.set_xlabel("Accrual decile, 1 = lowest accruals")
ax.set_ylabel("Mean monthly excess return\nrelative to the period average, %")
ax.set_title("The accrual sort used to slope down. It no longer does.")
ax.legend(loc="lower left")
plt.show()

fig, ax = plt.subplots(figsize=(8, 4.2))

growth = (1 + spread / 100).cumprod()
ax.plot(growth.index, growth.values, color=style.ACCENT, lw=1.6)

# Linear, not log. The series spans about 6x, and a log axis over that range
# only buys a set of minor tick labels nobody reads.
for date, label, height in [("1996-07-31", "Sloan", 0.94),
                            ("2011-05-31", "Green, Hand and Soliman", 0.10)]:
    ax.axvline(pd.Timestamp(date), color=style.SERIES[1], lw=1.0, ls="--")
    ax.annotate(label, (pd.Timestamp(date), growth.max() * height),
                textcoords="offset points", xytext=(6, 0),
                fontsize=8.5, color=style.MUTED)
ax.set_ylabel("Growth of $1")
ax.set_title("Long low-accrual, short high-accrual, net of costs")
plt.show()

# Criterion (b): the holdout. Evaluated once.

hold_r = spread.loc["2011-05-01":]
n_h, mu_h, t_h, sr_h = mean_t(hold_r)
n_p, mu_p, t_p, sr_p = mean_t(spread.loc[:P["pre_pub_end"]])

print(f"holdout 2011-05 to 2026-06, net of {P['cost_bps']}bp   n {n_h} months")
print(f"  mean    {mu_h:+.3f}% per month")
print(f"  t       {t_h:+.2f}")
print(f"  Sharpe  {sr_h:+.3f}")
print()
print(f"  before Sloan:  mean {mu_p:+.3f}%  t {t_p:+.2f}  Sharpe {sr_p:+.3f}")
print(f"  holdout:       mean {mu_h:+.3f}%  t {t_h:+.2f}  Sharpe {sr_h:+.3f}")
print(f"  the spread retains {100 * mu_h / mu_p:.0f}% of its pre-publication mean")

QUINTILES = ["Lo 20", "Qnt 2", "Qnt 3", "Qnt 4", "Hi 20"]
variants = [
    ("preregistered: VW deciles, 20bp", dict()),
    ("equal-weighted deciles",          dict(table=1)),
    ("quintiles instead of deciles",    dict(cols=QUINTILES)),
    ("cost 0bp",                        dict(cost_bps=0)),
    ("cost 100bp",                      dict(cost_bps=100)),
]

print(f"{'variant':34} {'pre n':>6} {'pre%':>7} {'pre t':>6}   "
      f"{'hold n':>6} {'hold%':>7} {'hold t':>7}")
for label, kw in variants:
    r, _ = hedge(**kw)
    a = mean_t(r.loc[:P["pre_pub_end"]])
    b = mean_t(r.loc["2011-05-01":])
    print(f"{label:34} {a[0]:>6} {a[1]:+7.3f} {a[2]:+6.2f}   "
          f"{b[0]:>6} {b[1]:+7.3f} {b[2]:+7.2f}")

# Subperiod behaviour, preregistered specification.

print("decade      n    mean%       t")
for start in range(1960, 2030, 10):
    s = spread.loc[f"{start}":f"{start + 9}"]
    if len(s) >= 24:
        _, mu, t, _ = mean_t(s)
        print(f"{start}s   {len(s):>3}  {mu:+7.3f}  {t:+6.2f}")

fig, ax = plt.subplots(figsize=(8, 3.9))

labels, means, counts = [], [], []
for start in range(1960, 2030, 10):
    s = spread.loc[f"{start}":f"{start + 9}"]
    if len(s) >= 24:
        labels.append(f"{start}s")
        means.append(s.mean())
        counts.append(len(s))

# The decades that clear t = 2 on their own are the loud ones. Everything
# else is context, including the positive-but-insignificant bars.
sig = [abs(mean_t(spread.loc[f"{lab[:4]}":f"{int(lab[:4]) + 9}"])[2]) > 2 for lab in labels]
colors = [style.ACCENT if s else style.SERIES[2] for s in sig]

ax.bar(labels, means, color=colors, width=0.62)
ax.axhline(0, color=style.MUTED, lw=0.7)
for i, (v, n) in enumerate(zip(means, counts)):
    ax.annotate(f"n={n}", (i, 0), textcoords="offset points",
                xytext=(0, -16 if v > 0 else 8), ha="center",
                fontsize=7.5, color=style.MUTED)
ax.set_ylabel("Mean monthly return, %")
ax.set_title("Decades reaching t > 2 on their own, in accent")
ax.tick_params(axis="x", pad=14)
plt.show()

print(f"python       {sys.version.split()[0]}")
print(f"pandas       {pd.__version__}")
print(f"numpy        {np.__version__}")
print(f"statsmodels  {sm.__version__}")
print(f"seed         {SEED}")
print(f"data as-of   {AS_OF}  (research/data/famafrench/{AS_OF}/)")