French Revised-History Monthly-Return Configuration: Technical Protocol

This document retains the complete technical body of the v2 protocol accepted on 2026-10-13, including the signal, continuous ledger, costs, and statistical conventions. Only the teaching navigation and candidate-stage process language have been adapted. G02 and G04 have received technical acceptance; the source freeze is unchanged. Current permissions and execution status are summarized in the Capstone README. Monthly labels and historical clocks are specified in the Time and Label Contract; required outputs and interpretations are listed in the report guide. A basis point (bps) is $10^{-4}$ ; net asset value (NAV) is ledger net value; HAC means heteroskedasticity and autocorrelation consistent covariance estimation.

Question, assets, signal, and prior exposure

The bounded question is unchanged: under the fixed revised French ten-industry history, hypothetical monthly allocations, and all-in costs, does an equal-weighted long-only portfolio of the three industries with the highest compounded returns over the prior 11 months have a higher average net monthly return than the ten-industry monthly equal-weight benchmark? Slow industry-level information diffusion is a possible explanation to test; this design does not identify causation or establish a real-world tradable advantage. The primary direction is $H_1:\mu_d>0$ , against $H_0:\mu_d\le 0$ . A zero or negative result, an interval crossing zero, and a blocked gate have distinct interpretations. Negative results are retained, and a blocked study is not described as a zero market effect.

Asset order: NoDur, Durbl, Manuf, Enrgy, HiTec, Telcm, Shops, Hlth, Utils, Other. The primary signal is $\operatorname{score}_{i,t}=\prod_{m=t-12}^{t-2}(1+R_{i,m})-1$ , exactly 11 months, skipping the most recent month $t-1$ . Sort scores descending and break ties stably by ascending manifest index; the primary top 3 receive $1/3$ each. Every top- $k$ sensitivity assigns $1/k$ to each selected industry. Gross and net exposure are both 1; leverage is 1; positions are fully invested long-only, with no financing, shorting, or negative cash. Missing, non-finite, or discontinuous-month data are rejected and logged; the asset pool is not silently changed, zero-filled, or dropped. There is no model training, factor screening, fitted standardization, or parameter optimization.

P3 has exposed the full 1990-01 through 2026-08 ten-industry/equal-weight history and sensitivities. P1/P2 exposed three industries during 2010–2019, and P1 also showed descriptive results for 2020–2024. The full history was not blindly preregistered from scratch. The locked-reporting designation constrains future access and changes for this target; it does not make the sample a blind holdout. Any future target execution still requires G01 and G05. Public download availability does not establish authorization for the actual subject or use.

The one confirmed calendar and primary sample

Phase	Monthly interval, inclusive	Months	Use
Warm-up	1988-07..1989-12	18	Feature inputs; do not use these months to initialize account wealth
Development	1990-01..2004-08	176	Description and implementation/contract consistency; fixed rules, no tuning
Validation	2004-09..2015-08	132	Prespecified consistency/description; do not select a winner
Locked reporting	2015-09..2026-08	132	The sole primary mean-test sample, taken as 132 rows of the continuous ledger
Full evaluation	1990-01..2026-08	440	Full-period descriptions, figures, and ledger reconciliation; does not replace the primary 132-month test

The calendar arithmetic is $440=(2026-1990)\times12+(8-1)+1$ ; $\lfloor0.4\times440\rfloor=176$ , $\lfloor0.3\times440\rfloor=132$ , leaving 132 months. The three full-month segments are contiguous, non-overlapping, and each is at least 24 months; the evaluation window is at least 120 months. For the first evaluation month, 1990-01, L17/skip1 uses 1988-07..1989-11 and skips 1989-12; L11/skip1 uses 1989-01..1989-11; L5 uses 1989-07..1989-11; L11/skip2 uses 1988-12..1989-10. The general endpoints are $[t-\mathrm{skip}-L,\ t-\mathrm{skip}-1]$ , containing exactly $L$ months. Calendar arithmetic was checked in the accepted protocol's constructed checks without reading market-return values; this teaching adaptation did not rerun those checks.

Thirteen continuous paths and segment boundaries

The nine fixed strategies are: M0=L11/skip1/k3/c10; C0/C25/C50 vary only the all-in cost rate; L5/L17 vary only $L$ ; K2/K4 vary only $k$ ; S2 changes only skip to 2. The four equal-weight cost paths are EW0/EW10/EW25/EW50. There are 13 paths total and zero optimization trials. Do not form a Cartesian grid or add independently reset subwindows. The primary difference is $d_t=r_{M0,\mathrm{net},t}-r_{EW10,\mathrm{net},t}$ ; the other eight strategies and three benchmark cost differences are prespecified descriptive sensitivities. They do not expand the significance-selection family or replace M0.

Each path invests normalized cash of 1 once at 1990-01, runs continuously through 2026-08, and liquidates fully in the final month. At 2004-09 and 2015-09, it directly carries forward the prior month's drifted holdings and NAV as they actually exist in the ledger. Here “actual holdings” means the actual state of the hypothetical ledger, not real-world trading. Segment boundaries do not liquidate, charge a new entry cost, reset positions, or reset NAV. Locked-reporting d uses the 132 rows from the two continuous paths over 2015-09..2026-08; its first denominator carries forward the actual ending NAV at 2015-08, and its final row includes the 2026-08 liquidation cost.

For display, a segment chart may divide by the segment's starting NAV so its first point equals 1. This changes display only; it cannot recompute trade amounts or costs or alter monthly net returns. A separate run that restarts cash at 1 on 2015-09 is a new path and is not authorized by this protocol. Each path's gross allocation return $R_{\mathrm{alloc},t}$ , calculated from the existing target and that month's returns, may be reported as a no-cost compounded descriptive series. It is a same-signal ledger series, not a new selection specification. The explicit 0 bps strategy/benchmark is already within the 13-path budget; a “gross chart” cannot add another parameter path.

Drift, self-financing, entry and terminal costs, and identities

Let $V_{\mathrm{pre},t}$ be the prior month's actual ending NAV, or initial cash 1 for the first month. Let $x_{i,t}$ be the amount held after drift and before allocation. All targets satisfy $w_{i,t}\ge 0$ and $\sum_i w_{i,t}=1$ ; post-cost NAV must solve the following equation. The supported domain requires $V_{\mathrm{pre}}>0$ , finite nonnegative drifted holdings, valid simple monthly returns no lower than $-1$ , and a positive ledger denominator for next-period normalization. A path that reaches zero must explicitly reject later weight/return division rather than insert a fabricated value. Finite cost rates must satisfy the fully invested long-only domain $0\le c<1$ . The solution conditions follow Chapter 29 in the current English reader; they do not change the agreed cost convention:

V_{post,t}=V_{pre,t}-c\sum_i|w_{i,t}V_{post,t}-x_{i,t}|,\quad F_t=c\sum_i|w_{i,t}V_{post,t}-x_{i,t}|.

The rate is $c=\mathrm{bps}/10000$ ; costs and $V$ share the same monetary unit. The sum of absolute purchases and sales is not divided by 2. After allocation, $x_{\mathrm{post},i,t}=w_{i,t}V_{\mathrm{post},t}$ , end-of-month holding value is $x_{\mathrm{end},i,t}=x_{\mathrm{post},i,t}(1+R_{i,t})$ , and drifted weights are $x_{\mathrm{end},i,t}/\sum_i x_{\mathrm{end},i,t}$ . In an ordinary month:

R_{alloc,t}=\sum_i w_{i,t}R_{i,t},\qquad r_{net,t}=\frac{V_{post,t}}{V_{pre,t}}(1+R_{alloc,t})-1.

At entry, $x_{i,1}=0$ , so $V_{\mathrm{post},1}=1/(1+c)$ ; the first-month return is measured against initial cash 1 and includes the entry cost. In the final month, realize the holding return and then liquidate fully:

V_{\mathrm{terminal}}=V_{\mathrm{end},T}(1-c),\qquad r_{\mathrm{net},T}=\frac{V_{\mathrm{post},T}}{V_{\mathrm{pre},T}}(1+R_{\mathrm{alloc},T})(1-c)-1.

Therefore,

\prod_{t=1}^{440}(1+r_{\mathrm{net},t})=\frac{V_{\mathrm{terminal}}}{V_{\mathrm{initial}}}.

The products across segments also multiply to the same total, without another entry cost. The product over the 132 reporting rows equals final cash divided by end-of-month NAV at 2015-08. It must not be described as the return of a strategy restarted with cash 1.

The 10 bps rate is an uncalibrated all-in linear-friction scenario, conceptually including commissions, spread, and similar costs; impact/capacity is unknown and unsupported components are not reported as measured zeros. At traded notional 200.10 and $c=0.001$ , all-in scenario friction is .20010. Do not charge an additional spread on top or treat the rate as an annual $0.1\%/12$ . The separate share example with a 5 bps half-spread embedded in fills and an explicit 10 bps commission is a different constructed setup, not a calibration of the primary 10 bps assumption. NAV-loss proportion $C$ and trade-rate $c$ have different definitions. The example $C=0.001$ and gross $r=0.02$ gives net $(1-C)(1+r)-1=0.01898$ ; this is a constructed unit example only.

Primary 132-month HAC mean inference

Let $d_t$ be the paired net monthly difference over the 132 continuous primary-ledger rows, in decimal per month; do not subtract RF again. Set $n=132$ , $k=1$ , and $X$ to a single column of ones; $\hat\mu=(1/n)\sum_{t=1}^n d_t$ and $u_t=d_t-\hat\mu$ . Fix $L=6$ as a count of complete calendar-month lags. All $\widehat\gamma_j$ use the common denominator $n$ :

\begin{aligned} \widehat\gamma_j&=\frac1n\sum_{t=j+1}^{n}u_tu_{t-j}, &&j=0,\ldots,6,\\ w_j&=1-\frac j7, &&j=1,\ldots,6,\\ \widehat\Omega&=\widehat\gamma_0+2\sum_{j=1}^{6}w_j\widehat\gamma_j. \end{aligned}

The weights for lags 1–6 are $6/7$ , $5/7$ , $4/7$ , $3/7$ , $2/7$ , and $1/7$ ; $\widehat\gamma_0$ uses $t=1,\ldots,n$ . The correction $q=n/(n-k)=132/131$ applies to the covariance:

\begin{aligned} \operatorname{Var}(\hat\mu)&=q\widehat\Omega/n=\widehat\Omega/(n-1),\\ \operatorname{SE}(\hat\mu)&=\sqrt{\widehat\Omega/(n-1)}. \end{aligned}

Do not replace the $\widehat\gamma_j$ denominator with $n-j$ , and do not multiply $\widehat\gamma_j$ or SE by $q$ a second time. For general $k$ , use

q(X'X)^{-1}S(X'X)^{-1};

with constant $X$ , $X'X=n$ and $S=n\widehat\Omega$ , yielding the expression above. At $L=0$ ,

\operatorname{Var}(\bar d)=\frac{\sum_t u_t^2}{n(n-1)}=\frac{s_d^2}{n};

the constructed check independently proves this. The full 440-month mean is descriptive only; do not use its n or degrees of freedom in place of the primary 132.

The statistic is $t_{\mathrm{stat}}=\hat\mu/\mathrm{SE}$ . The one-sided 5% positive-direction test and one-sided 95% lower bound are $\hat\mu-t_{0.95,131}\,\mathrm{SE}$ ; the two-sided 95% interval is $\hat\mu\pm t_{0.975,131}\,\mathrm{SE}$ . The $t(131)$ reference is an approximation and does not guarantee exact coverage under dependence or non-stationarity. If SE is zero/non-finite, months are missing, $n\le L$ , or parameters are not identified, report undefined / rejected explicitly with the reason. Do not fill months, silently reduce L, or set an undefined result to $p=0$ . Log numerical discrepancies; do not change the primary conclusion by choosing a different convention.

The local statsmodels constant-OLS mapping is maxlags=6, weights_func=weights_bartlett, use_correction=True, use_t=True. The original technical acceptance included constructed HAC and calendar/continuous-cost-contract checks. Those constructed checks are not research on the target market, and this reader adaptation did not rerun them.

For post-hoc FF3 attribution, subtract the same-month FF3 RF once from net total return; do not subtract RF again from published Mkt-RF, SMB, or HML. Keep months and currency aligned. Use an intercept and three factors, $k=4$ , with correction $n/(n-4)$ ; do not apply the primary $k=1$ correction. Do not change the course's existing attribution interface or insert invented factors into the primary paired difference to call it. The shared same-month RF already cancels in the primary mean difference, so do not subtract RF again there.

Fixed bootstrap, secondary reporting, and negative results

For the primary 132-row paired $d$ , use the circular block bootstrap with block length 12 months, 5,000 replications, and seed 20261012; lengths 6 and 24 are prespecified interval sensitivities only. Initialize one dedicated Python random.Random(seed) generator once before the replication loop. All 5,000 replications consume that same evolving state, without reseeding inside the loop. Draw each required block start uniformly using randrange(n), concatenate circular consecutive blocks until reaching $\lceil n/\mathrm{block}\rceil$ blocks, and truncate to $n$ ; compute each bootstrap mean. Compute percentile quantiles by linear interpolation at position $(B-1)p$ ; the one-sided lower bound uses $p=0.05$ , and the two-sided interval uses $0.025$ / $0.975$ . Report any disagreement with HAC; do not select the favorable interval or add another statistical selection family. This design is retained, and this batch did not run the target-sample bootstrap or a new selection.

CAGR, volatility, net-excess Sharpe, drawdown, costs, and weights are prespecified descriptive measures for a future authorized run. Development, validation, and the full 440 months do not replace the primary mean test and are not used for training or parameter selection. Keep the 10 bps/month illustrative net-advantage threshold separate from statistical significance. Preserve the original 18-item mapping for risk, industry concentration, tails, a uniform constructed shock, and FF3 attribution. With no trade prices/volume, stock IDs, or historical constituent versions, do not estimate real capacity or claim the absence of survivorship bias for the whole market. Do not invent PSR/DSR/PBO results to fill headings; where applicability is insufficient, mark not_applicable / not_evaluated. Retain all positive, zero, and negative results.