Correct the holding rule, execution lag and asymmetry index; regenerate all downstream results

[Tofik (plut777)]

Proposed pull request

Title

Correct the holding rule, execution lag and asymmetry index; regenerate all downstream results

---

Summary

The published code did not implement the strategy the published paper describes.
Three defects are corrected here. The largest of them meant that

the published strategy held a position in 25 of 504 weeks.

It closed any open position the moment its entry signal stopped firing, which is
not the exit rule §2.4 states. Corrected, it holds a position in 55 weeks.

Every headline figure in the paper — the +3.60% return, the 0.149 Sharpe ratio,
the factor regression with its 25-observation effective sample, the "immaterial"
transaction costs, the 19.2-pip break-even — described that five percent of the
sample. That is why the published null result had so little content: a strategy
that is almost never invested cannot demonstrate much in either direction.

The corrected strategy loses 6.64% gross over the decade, Sharpe −0.153,
across 15 holding episodes. The paper's conclusion is unchanged in direction and
considerably stronger in substance. Two findings are new, and both sharpen the
null rather than softening it:

• There is no break-even transaction cost. Not a larger one — none. A
  break-even presumes a gross profit to be consumed, and there is none.
• The strategy carries a substantial short-momentum exposure. It loads
  negatively and significantly on time-series momentum (β = −0.82, 95% CI
  [−1.26, −0.39], p = 0.00019 on in-position weeks), a loading that was
  insignificant before correction. Momentum rose over the exposed weeks and the
  strategy was short it, which accounts for roughly a quarter of the realized
  loss — so part of that loss reflects a known factor exposure rather than a
  failure specific to asymmetry. Momentum alone explains 12% of the variation in
  in-position returns, so this is a material exposure rather than the whole
  story.

The sample is unchanged: n = 504, 8 January 2016 to 29 August 2025.

---

How to read this PR

Changes are grouped so that each group can be accepted or rejected on its own:

• (a) Implementation defects — the paper said X, the code did Y, the code now
  does X. Three items. Nothing is in this group unless the published paper and
  the published code genuinely disagreed.
• (b) Methodological changes proposed — the paper and the code agreed, and
  this PR proposes something different. Three items, each reversible without
  disturbing (a).
• (c) Manuscript corrections — the code is defensible and the paper describes
  it wrongly.
• (d) Prose corrected without a wrong figure.
• (e) Provenance footnotes restored.

docs/CORRECTION_CHANGELOG.md has the full detail.
analysis/before_after_results.csv gives every changed figure with its published
value, its corrected value, and which category produced the change.

---

(a) Implementation defects corrected

	Paper (4d21c69)	Published code	Now
a1	"Exit: signal reversal OR 4-week maximum"	The hold branch was unreachable — its guard was always true — so positions closed as soon as the entry signal stopped firing	Holds through quiet weeks; reverses on the opposing signal; expires after four returns
a2	Entry one period after the Friday signal	Signals lagged inside the loop, then the position shifted again: two lags, while benchmarks used one	One lag everywhere — headline, benchmarks, walk-forward, factors, costs, snooping
a3	Equation 5: mean squared deviations about the overall mean	pos.var()/neg.var() — re-centres each subgroup, uses n−1, and returns a neutral-looking 1.0 where the statistic is undefined	Equation 5 as printed; undefined cases return missing

a1 is the one that matters: 25 → 55 exposed weeks, and the dominant driver of
nearly every changed figure.

---

(b) Methodological changes proposed

These are judgement calls. The published paper and the published code agreed in
each case; this PR proposes departing from them.

b1. How to size a week in which a direction is held but no signal fires

Fixing a1 creates a state the published specification never had to describe,
because the published implementation could never reach it. The published rule was
"Rebalancing: Weekly (end of Friday close)" with Equation 10 evaluated at the
contemporaneous AI_t, and the published code did resize on every bar it held a
position — so paper and code agreed. Neither ever faced a held but unsignalled
week.

Proposed: evaluate the sizing equation weekly while a direction is held, as
the smaller of the two available extensions — it keeps the published rebalancing
frequency and the contemporaneous subscript, and changes no published sentence.
Freezing the notional at entry is the alternative; it is computed in the same run
and reported.

	weekly (proposed)	frozen (alternative)
Gross return	−6.64%	−7.57%
Sharpe	−0.153	−0.173
Max drawdown	−12.56%	−14.29%
In-position weeks	55	55
Holding episodes	15	15
Turnover	52.00	49.15

Entries, exits, direction and exposure are identical. No conclusion depends on
the choice. The argument against the proposal is in the changelog rather than
omitted.

b2. "Trades" reported as holding episodes and execution legs

The published paper defined trades as "position-change events divided by two" and
the code implemented exactly that — but the label said "completed round trips",
which that formula does not compute. For the momentum benchmark it reported 27
round trips for 54 directional holdings and 107 executions.

Proposed: report holding episodes and execution legs separately, with
resizing and turnover, from dated ledgers. Headline: 17 published "trades" → 15
episodes and 61 legs. The underlying returns are untouched by this item.

b3. Statistics from a single episode are not reported as performance

The corrected walk-forward opens one out-of-sample episode in eight test
years. A Sharpe ratio, a hit rate and an annualized return computed from one
episode are not estimates of anything — the published 60% hit rate meant three
weeks, and one episode would mean one up week and one down week.

Proposed: decline to print them. The rule is enforced in code, applied
wherever such statistics arise rather than table by table, and logged when it
fires. Suppressed values stay in full_pipeline_results.json so the decision is
checkable. Withheld figures are removed with the reason given, never replaced by
an unexplained placeholder.

The walk-forward table now reports what the procedure did — training window,
selected threshold, episodes opened. The activity count is the finding, and
it is a stronger one than any return from a single episode because it does not
depend on how that episode happened to turn out.

---

(c) Manuscript corrections

The paper mis-stated its own code in four places: the fast-alpha equation showed
a price difference where the code uses a percentage return (the printed version
divides yen by a percentage volatility and is dimensionally incoherent); the
position-size formula carried an unreachable 0.5 floor and a "no leverage" claim
when the real range is [1, 2] gross-notional units; hedge alpha was printed with
a time-varying rate differential that exists nowhere in the repository, the code
using a fixed −2% constant; and the tail-alpha window was described in weeks
where the code uses trading days.

Two disagreements were resolved in favour of the code, against the working
rule that the code gets fixed to match the paper. Both are flagged so they can be
overruled:

• Monday-open execution. The paper specifies it; the code uses the Friday
  close. The Friday close is kept — but a false justification is removed. An
  earlier draft of this correction claimed Monday opening prices are absent from
  the dataset. They are present; the daily bars carry an Open column. The
  Friday-close proxy is a choice, and the paper now says so. Implementing
  Monday-open execution is on the backlog.
• The EVT section is presented in the paper as characterising tail-alpha
  exceedances; the code fits absolute weekly returns. The section is relabelled
  as a weekly-return diagnostic. The rule says the code should have been changed
  instead; refitting is on the backlog, and the relabelling should not be
  mistaken for the fix.

---

(d) Prose corrected without a wrong figure

The manuscript sweep changed 38 figures across 21 locations. But a
figure-by-figure sweep does not catch a sentence whose argument depends on a
result that no longer holds, and those matter more.

The published paper argued that a modest gross edge survived measurement and was
not eliminated by costs. Every sentence resting on that architecture is wrong
under the corrected numbers regardless of its digits. Examples, none containing
an incorrect figure: the robustness section described a backtest "statistically
indistinguishable from zero" (defensible on the interval, but it presents a
losing strategy as a null one) and asked whether costs "erode strategy returns"
(presupposing returns to erode); the drawdown paragraph called the figure "only
modestly smaller" than buy-and-hold's, presenting as mitigating what is damning —
four-fifths of a permanently invested position's drawdown, incurred while exposed
in 55 of 504 weeks.

The break-even statement is the clearest case. The published paper reported a
break-even round-trip cost of 19.2 pips and read it as reassurance. That figure
was meaningful only while the gross return was positive. It is not that the
corrected break-even is larger, or harder to estimate: it does not exist, and
the paper now says so in the cost section, the abstract and the conclusion. It is
a cleaner statement of the null than the cost table it replaces.

One qualification is added rather than removed: costs remain small in magnitude
(0.38pp at two pips), but the model charges spread strictly in proportion to
notional with no per-order component, while the corrected specification
generates 31 resizings averaging 0.19 units — exactly the population a per-ticket
charge would fall hardest on. The reported drag is a lower bound.

---

(e) Provenance footnotes restored

4d21c69 carried nine table notes recording the paper's own earlier corrections.
Seven had been deleted during the drafting of this branch; all seven are
restored. Two survived — and keeping two of nine is not an editorial decision,
it is what happens when notes get dropped while the prose around them is
rewritten.

One deserves singling out. The data-snooping note recorded that the published
RC = 2.14 (p = 0.042) was not reproducible from any specification of the stated
candidate universe. That is the paper's most quotable statistic — the one number
in it that reported a significant result. Deleting the note deleted the record
that it was already known to be unreliable.

Each note is restored verbatim, with current values appended as a following
sentence rather than woven into the original. These notes are a dated record of
what was wrong and when; editing them to match today's numbers would destroy what
makes them worth keeping.

That preservation was enforced mechanically, not by eye: every one of the nine
original sentences is checked to appear in the current source as an exact
substring. The check earned its place — a first attempt inserted the words "then
reported" inside the factor-attribution sentence, a two-word rewrite of the
historical record that reading would not have caught. The claim of verbatim
restoration is worth something only because a machine enforced it.

---

Result changes

Full table with per-item attribution in analysis/before_after_results.csv.

Metric	Published (4d21c69)	Corrected
In-position weeks	25 of 504	55 of 504
Cumulative gross return	+3.60%	−6.64%
Sharpe	0.149	−0.153
Maximum drawdown	−7.96%	−12.56%
Holding episodes / execution legs	17 "trades"	15 / 61
Break-even round-trip cost	19.2 pips	does not exist
Retail-wide net return	+3.22%	−7.02%
Momentum loading (in-position)	−0.247, t = −0.51	−0.823, t = −3.73
Factor intercept (full sample)	+0.00008	−0.00012
In-position factor sample	25 weeks	55 weeks
Walk-forward pooled return / episodes	+2.46%, 3 trades	+2.74%, 1 episode
Walk-forward Sharpe / hit rate	0.419 / 60.0%	withheld — one episode
Low-VIX / high-VIX return	+2.38% / +2.67%	−5.08% / −1.65%
GBP/USD cross-market	+17.18%	−13.32%
SPY cross-market	+11.66%	+14.20%
GLD cross-market	−30.26%	−15.44%
Tail-alpha AI	0.17	0.03
Coverage-alpha AI	3.45	2.22

The GBP/USD sign flip is a finding, not a rounding. The published paper reads
+17.18% on GBP/USD as evidence that FX offers more favourable conditions for the
strategy than equities or gold. Corrected, it is −13.32%, and the flip is
attributable to the implementation fixes, not to the sizing proposal: with the
implementation fixes and the frozen-notional alternative the figure is −14.11%.
Rejecting (b1) does not restore the published reading. The cross-market section's
claim about FX conditions no longer has a basis.

For the same reason, the widened cross-market spread is traceable: the
cross_market code block is byte-identical to the version this branch started
from, and rerunning it under the frozen alternative reproduces the intermediate
figures exactly. The movement is the sizing default alone; the input skewness
statistics are unchanged in all four markets.

---

Verification

• 14 deterministic unit tests, all passing, covering the AI edge cases, the dated
  timing convention, entry, hold, expiry, reversal, simultaneous signals,
  no-signal periods, both sizing modes, resize cost accounting and reversal
  accounting.
• The complete pipeline runs online and reruns identically with --offline.
• Seven of the eight input files reproduce byte-for-byte on an independent
  download (see Data below).
• Every figure in the manuscript was machine-checked against
  analysis/full_pipeline_results.json.
• The nine original provenance sentences are machine-checked for verbatim
  presence.
• After every rerun: n = 504 spanning 2016-01-08 to 2025-08-29; the factor
  intercept matches the strategy's own mean weekly return
  (−0.00011964 against −0.00012029); the low- and high-VIX returns compound to
  the full-sample return (−6.640684% against −6.640684%).

The PDF was rebuilt and inspected

paper/alpha-asymmetry.pdf is rebuilt from the corrected source. It compiles
clean: 27 pages, zero overfull boxes, zero underfull boxes, no undefined
references or citations, bibliography resolved against references.bib.

Both figures were regenerated from the current pipeline and compared
byte-for-byte against the committed versions. backtest_results.png is drawn
from the corrected return series. alpha_asymmetry_analysis.png is unchanged
since before the sizing change, which is correct: it shows the alpha
distributions, which do not depend on the strategy.

The PDF's own text was extracted and checked. The corrected figures are present;
none of the superseded ones appear anywhere.

A note on this section, because it is the third time this document has made a
claim about its own provenance. The draft this branch started from asserted
that the PDF had been compiled and visually inspected when it had not. That was
removed and replaced with a statement that no LaTeX toolchain was available and
the PDF was stale. That statement was true when written and later stopped being
true, when a self-contained engine was installed and the paper compiled. A
document asserting something about itself that has since become false is the
failure this pull request exists to correct, so the sequence is recorded rather
than tidied away, and the build was deliberately left until last so that the
claim and the artefact became true at the same moment.

Version, DOI and supersession — decisions for you

The manuscript now carries \paperver 3.1.0, incremented from the 3.0.0 you set
in f04ae08 for the July manuscript. Three things need your decision:

The version identifiers in this repository disagree with each other, and did
before this branch. paper/alpha-asymmetry.tex carried 3.0.0 for the July
manuscript; CITATION.cff called the same work 2.1.0-dev; the last deposited
version is v2.0.1 (10.5281/zenodo.20635291). Neither 3.0.0 nor 2.1.0-dev
was ever deposited. CITATION.cff is set to 3.1.0-dev to follow the number
printed on the paper, with the disagreement documented in the file. Reconciling
them properly is yours.

Depositing mints a new Zenodo version DOI, which cannot be known in advance.
\paperdoi is therefore left as the concept DOI 10.5281/zenodo.18638784, which
resolves to the newest version. After deposit, record the new version DOI in
CITATION.cff and CLAUDE.md. The SSRN record (SSRN:6147567) is separate and
needs its own revision; Zenodo does not propagate to it.

We recommend posting a correction notice against the superseded record, not
merely depositing a new version. The headline result changes sign: +3.60% to
−6.64%. A reader who lands on v2.0.1 through a citation or a search result has no
way to know it has been superseded, and the specific claim they would take away —
that the strategy earns a small positive gross return — is wrong rather than
imprecise. Depositing a new version alone leaves that reader uninformed. This is
your call as author and it carries reputational weight either way, but asked
directly: we would post the notice.

---

Data, and a decision for you

The raw CSVs are not committed, and analysis/cache/ remains gitignored.
analysis/data_access.py gives the reason: Yahoo Finance data may be subject to
redistribution terms. Publishing eight files of vendor data in a public
repository is a licensing decision for the repository owner, not one an outside
contributor should make inside a correctness PR — so it is raised here for you
to decide rather than taken.

What is provided instead: analysis/fetch_data.py downloads the inputs and
verifies each file's SHA-256 against the committed manifest, so a fresh clone can
obtain the data and confirm it is the same data.

Seven of eight hashes reproduce byte-for-byte. Six of the eight series are FX
spot rates or index levels, which carry no corporate-action adjustment and
structurally cannot drift; GLD paid no distribution over the window. SPY, a
distributing ETF fetched with auto_adjust=True, has its entire history rescaled
by every new distribution — the only file in the set that could differ, and it
did. That is the expected outcome rather than a near miss. The difference moves
five values in the SPY cross-market row in their fifth or sixth significant
figure, each rounding to the same printed number, and nothing else in the
pipeline.

---

Reproduction

python3.12 -m venv .venv
.venv/bin/python -m pip install -r requirements.txt
.venv/bin/python -m pytest -q
.venv/bin/python analysis/fetch_data.py
.venv/bin/python analysis/full_pipeline.py --offline

---

Questions for you

1. The data licensing question above — commit the raw CSVs, or keep the
   fetch-and-verify approach?
2. (b1), the sizing proposal. Weekly evaluation or frozen at entry? Both are
   computed; no conclusion depends on it.
3. (b2) and (b3) — the trade-accounting redefinition and the refusal to
   report single-episode statistics. Both are reversible.
4. (c2), the two exceptions — keeping the Friday close despite the paper
   specifying Monday open, and relabelling the EVT section rather than refitting
   it. Either could be done properly instead.
5. The stale PDF. You have the toolchain.
6. Whether an approved EUR–JPY rate or forward series can be supplied, which
   would let hedge alpha stop being a constant multiplied by a correlation.

---

Provenance

This branch began from an unreviewed draft produced by an AI agent, committed
unmodified as 5135bac and labelled as such. That commit was audited rather
than adopted: its claims were checked against 4d21c69, its manuscript edits
were reviewed line by line, several were reversed, and every change that survives
is justified in this PR and in the changelog against the published paper. It
carries no authority and is kept in the history only so that the work done after
it is separately reviewable.

docs/REVIEW_NOTES.md is the working audit record from that process. It is not
part of the argument here.

No branch has been pushed, no pull request opened, and nothing merged.

🤖 Generated with Claude Code