A factor with a 0.90 Sharpe ratio that breaks even at 7 basis points

# 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 Jegadeesh (1990), "Evidence of predictable behavior of security
# returns", Journal of Finance 45(3), 881-898, read from the Wiley abstract
# page. The full text was not fetched: two hosts returned 403 and 425.
# What the abstract page supports:
#   - the effect: significant negative first-order serial correlation in
#     monthly stock returns
#   - ten portfolios formed on one-month-ahead forecasts, extreme decile
#     spread of 2.49% a month over 1934-1987
#
# Nothing else here is his. In particular:
#   - French's ST_Rev factor is not Jegadeesh's portfolio. It is a
#     value-weighted long-short on the 30th and 70th NYSE percentiles of the
#     prior month's return, crossed with the NYSE size median. Terciles, not
#     deciles. The note reports on French's factor and says so.
#   - the split date is mine. Journal of Finance 45(3) is a 1990 issue but
#     the issue month was not verified, so the cutoff is the end of the
#     publication year rather than an invented month.
#   - turnover_legs, the cost grid, hac_lags and "success" are mine.
#
# The strategy replaces both legs every month, so the honest question is not
# only whether the gross premium shrank but at what cost level it dies. Both
# are preregistered.

PREREG = {
    "hypothesis": (
        "Ken French's short-term reversal factor earned a positive average "
        "monthly return before Jegadeesh was published, its average in the "
        "period after publication is lower, and the round-trip cost at which "
        "the strategy breaks even in that later period is below 25 basis "
        "points, which would mean it is no longer investable."
    ),
    "universe": (
        "Ken French's F-F_ST_Reversal_Factor, a value-weighted long-short "
        "built from six portfolios: NYSE, AMEX and NASDAQ stocks split at "
        "the NYSE size median and at the 30th and 70th NYSE percentiles of "
        "the prior month's return. Rebuilt monthly. Built from CRSP, so no "
        "survivorship bias in universe selection. The factor is gross of "
        "trading costs, which is the whole reason for the cost grid below."
    ),
    "start":     "1926-02-28",
    "end":       "2026-06-30",
    "holdout":   "1991-01-31 onwards, touched once in the last cell of Results",
    "rebalance": "monthly, both legs replaced in full",
    "params": {
        "pre_pub_end":   "1990-12-31",   # end of Jegadeesh's publication year
        "turnover_legs": 2.0,            # long and short both replaced each month
        "cost_grid_bps": [0, 10, 25, 50, 100],
        "hac_lags":      6,
        "decade_panel":  True,
    },
    "success": (
        "All three must hold for the decay claim to stand. (a) Over "
        "1926-02 to 1990-12 the factor has a positive gross mean monthly "
        "return with |t| > 2 under Newey-West standard errors. (b) In the "
        "holdout the gross mean is lower than the pre-publication mean. "
        "(c) In the holdout the breakeven round-trip cost is under 25 basis "
        "points. A decade panel is reported either way, so the reader sees "
        "when the change happened rather than only that a two-way split "
        "differs."
    ),
}

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"]

st = data.to_month_end(data.famafrench("F-F_ST_Reversal_Factor", AS_OF))
ff = data.to_month_end(data.famafrench("F-F_Research_Data_Factors", AS_OF))

st = st.loc[PREREG["start"]:PREREG["end"]]
ff = ff.loc[PREREG["start"]:PREREG["end"]]
rev = st["ST_Rev"]

PRE = slice(None, P["pre_pub_end"])
OUT = slice("1991-01-01", None)

print(f"reversal factor  {len(rev):6,} rows  {rev.index.min().date()} -> {rev.index.max().date()}")
print(f"research factors {len(ff):6,} rows  {ff.index.min().date()} -> {ff.index.max().date()}")
print(f"pre-publication {len(rev.loc[PRE]):,} months     holdout {len(rev.loc[OUT]):,} months")
print(f"missing values: {int(rev.isna().sum())}")

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

def net_of(x, cost_bps):
    return x - P["turnover_legs"] * cost_bps / 100.0

def breakeven_bps(x):
    """Round-trip cost, in basis points, at which the mean net return is zero."""
    return 100.0 * x.mean() / P["turnover_legs"]

# Criterion (a): was the gross premium there before publication?

print("Ken French short-term reversal factor, gross of costs\n")
print(f"{'period':40} {'n':>5} {'mean%':>8} {'t':>7} {'Sharpe':>8}")
for label, sl in [("pre-publication  1926-02 to 1990-12", PRE),
                  ("full sample      1926-02 to 2026-06", slice(None))]:
    n, mu, t, sr = mean_t(rev.loc[sl])
    print(f"{label:40} {n:>5} {mu:+8.3f} {t:+7.2f} {sr:+8.3f}")

n_p, mu_p, t_p, sr_p = mean_t(rev.loc[PRE])
print(f"\nbreakeven round-trip cost, pre-publication: {breakeven_bps(rev.loc[PRE]):.1f} bps")

# Criteria (b) and (c): the holdout. Evaluated once.

n_h, mu_h, t_h, sr_h = mean_t(rev.loc[OUT])
be_h = breakeven_bps(rev.loc[OUT])

print(f"holdout 1991-01 to 2026-06, n {n_h} months\n")
print(f"  gross mean     {mu_h:+.3f}% per month")
print(f"  t              {t_h:+.2f}")
print(f"  gross Sharpe   {sr_h:+.3f}")
print(f"  breakeven cost {be_h:.1f} bps round trip")
print()
print(f"  pre-publication: mean {mu_p:+.3f}%  t {t_p:+.2f}  breakeven {breakeven_bps(rev.loc[PRE]):.1f} bps")
print(f"  holdout:         mean {mu_h:+.3f}%  t {t_h:+.2f}  breakeven {be_h:.1f} bps")
print(f"  the holdout retains {100 * mu_h / mu_p:.0f}% of the pre-publication mean")

fig, ax = plt.subplots(figsize=(8, 4.3))

for cost, colour, width, label in [
    (0,  style.ACCENT,    1.7, "Gross, no costs"),
    (10, style.SERIES[1], 1.2, "10bp round trip"),
    (25, style.SERIES[2], 1.2, "25bp round trip"),
]:
    g = (1 + net_of(rev, cost) / 100).cumprod()
    ax.plot(g.index, g.values, color=colour, lw=width, label=label)

ax.axvspan(pd.Timestamp("1991-01-31"), rev.index.max(),
           color=style.SUBTLE, alpha=0.14, lw=0)
ax.annotate("holdout", (pd.Timestamp("1993-06-30"), 0.6),
            fontsize=8.5, color=style.MUTED)
ax.set_yscale("log")
ax.set_ylabel("Growth of $1, log scale")
ax.set_title("Short-term reversal at three cost assumptions")
ax.legend(loc="upper left")
plt.show()

# The preregistered cost grid, both periods.

print(f"{'cost bps':>9} {'pre mean%':>11} {'pre t':>8}   {'hold mean%':>11} {'hold t':>8}")
for c in P["cost_grid_bps"]:
    a = mean_t(net_of(rev.loc[PRE], c))
    b = mean_t(net_of(rev.loc[OUT], c))
    print(f"{c:>9} {a[1]:+11.3f} {a[2]:+8.2f}   {b[1]:+11.3f} {b[2]:+8.2f}")

# The decade panel, and the breakeven cost in each.

print(f"{'decade':8} {'n':>4} {'mean%':>8} {'t':>7} {'breakeven bps':>14}")
for start in range(1920, 2030, 10):
    s = rev.loc[f"{start}":f"{start + 9}"]
    if len(s) >= 24:
        n, mu, t, _ = mean_t(s)
        print(f"{start}s   {n:>4} {mu:+8.3f} {t:+7.2f} {breakeven_bps(s):>14.1f}")

fig, ax = plt.subplots(figsize=(8, 4.0))

labels, bes = [], []
for start in range(1920, 2030, 10):
    s = rev.loc[f"{start}":f"{start + 9}"]
    if len(s) >= 24:
        labels.append(f"{start}s")
        bes.append(breakeven_bps(s))

# Accent marks the decades that clear the preregistered 25bp threshold. That
# threshold is the verdict, so it is the only thing the colour should encode.
colors = [style.ACCENT if b > 25 else style.SERIES[2] for b in bes]
ax.bar(labels, bes, color=colors, width=0.64)
ax.axhline(0, color=style.MUTED, lw=0.7)

# The 1920s and 2020s are part-decade stubs. Without the counts the chart
# would present 47 months and 120 months as equally solid.
for i, (lab, b) in enumerate(zip(labels, bes)):
    n = len(rev.loc[f"{lab[:4]}":f"{int(lab[:4]) + 9}"])
    ax.annotate(f"n={n}", (i, 0), textcoords="offset points",
                xytext=(0, -14 if b > 0 else 8), ha="center",
                fontsize=7.5, color=style.MUTED)
ax.axhline(25, color=style.SERIES[1], lw=1.1, ls="--")
ax.annotate("25bp, the preregistered threshold", (len(labels) - 0.4, 25),
            textcoords="offset points", xytext=(0, 6), ha="right",
            fontsize=8.5, color=style.MUTED)
ax.set_ylabel("Breakeven round-trip cost, bps")
ax.set_title("The cost at which reversal stops paying, by decade")
ax.tick_params(axis="x", pad=12)
plt.show()

# Does the factor just load on the market? Checked in both periods.

joined = pd.DataFrame({"rev": rev}).join(ff[["Mkt-RF", "SMB", "HML"]], how="inner")
print(f"{'period':18} {'alpha%':>8} {'t':>7} {'mkt beta':>10} {'n':>6}")
for label, sl in [("pre-publication", PRE), ("holdout", OUT)]:
    d = joined.loc[sl].dropna()
    fit = sm.OLS(d["rev"], sm.add_constant(d[["Mkt-RF", "SMB", "HML"]])).fit(
        cov_type="HAC", cov_kwds={"maxlags": P["hac_lags"]})
    print(f"{label:18} {fit.params['const']:+8.3f} {fit.tvalues['const']:+7.2f} "
          f"{fit.params['Mkt-RF']:+10.3f} {len(d):>6}")

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}/)")