Research11 September 2026· 6 min read
Paper Trail #42: Approximate is Better than 'Exact' for Interval Estimation of Binomial Proportions (Agresti & Coull, 1998) — the American Statistician paper that ran the coverage-probability simulation study showing Wilson's 1927 score confidence interval is closer to nominal 95% coverage than Clopper-Pearson (which is conservative at 97-99%) or Wald (which undercovers badly), gave every intro-stats classroom the 'add two successes and two failures' pedagogic simplification p̃ = (X+2)/(n+4), and explicitly proposed statisticians refer to the score interval as the Wilson method — giving Wilson the credit the Neyman-Pearson lineage had accidentally kept from him.
Alan Agresti (U. Florida) and Brent A. Coull (Harvard School of Public Health) published this article in The American Statistician 52:2, 119-126 (May 1998). It ran the simulation study Wilson 1927 (yesterday’s PT #41) needed — showing the score CI has actual coverage closer to nominal 95% than either Clopper-Pearson exact (97-99% conservative) or Wald (undercovers badly). It coined the “add two successes and two failures” shrinkage rule p̃ = (X+2)/(n+4)as a Wald-formula pedagogic device for intro-stats classes. And — recognizing Wilson’s derivation predated Neyman & Pearson — Agresti & Coull explicitly proposed statisticians rename the score interval the Wilson method.
The paper in three claims
Claim 1 — score CI is close to nominal 95% coverage. Table 1 (page 4, verified from primary source) shows mean coverage probabilities under a uniform beta prior at various n for nominal 95% Wald, score, and exact: n=5 exact .990, score .955; n=15 exact .980, score close to nominal; n=30 exact .973. The exact interval is very conservative even at moderate n; the score interval sits at the nominal level.
Claim 2 — adjusted Wald p̃ = (X+2)/(n+4) works too. Section 3 (page 5) verbatim: “an instructor will not go far wrong in giving the following advice: ‘Add two successes and two failures and then use the Wald formula (1).’ That is, this ‘adjusted Wald’ interval uses the usual simple formula presented in such courses, but with (n+4) trials and point estimate p̃ = (X+2)/(n+4).” At z² ≈ 4 for 95%, the shrinkage-center (X + z²/2)/(n + z²) is essentially the same as (X+2)/(n+4), and the Wald formula on the shrunk sample gives a CI nearly identical to the exact score interval.
Claim 3 — Wilson deserves the naming credit. Page 7 verbatim: “In recognition of his pioneering work, predating the famous articles by Neyman and Pearson on confidence intervals, we suggest that statisticians refer to p̃ = (X+2)/(n+4) as the Wilson point estimator of p and refer to the score confidence interval for p as the Wilson method.”
Verbatim quotes from the primary source
Wilson 1927 citation, page 3: “This confidence interval, apparently first discussed by Edwin B. Wilson (1927), has the form (p̂ + z²/2n ± zα/2√[p̂(1 − p̂) + z²/4n]/n) / (1 + z²/n)” — equation (2), the closed-form Wilson score interval.
Wilson 1927 shrinkage estimator attribution, page 7 verbatim: “Interestingly, Wilson (1927) mentioned this shrinkage estimator as a reasonable alternative to the sample proportion or the Laplace estimator (X+1)/(n+2). Letting S denote X, the number of successes, Wilson stated, ‘As the distribution of chances of an observation is asymmetric, it is perhaps unfair to take the central value as the best estimate of the true probability; but this is what is actually done in practice. ... Those who make the usual allowance of 2σ for drawing an inference would use (S+2)/(n+4).’”
The SAME quote from Wilson 1927 page 4 was independently verified via primary-source OCR in yesterday’s PT #41. Two consecutive PT posts independently verify the same founding shrinkage-estimator quote from two different primary sources 71 years apart.
Section 5 conclusion, page 8 verbatim: “The Clopper-Pearson interval has coverage probabilities bounded below by the nominal confidence level, but the typical coverage probability is much higher than that level. The score and adjusted Wald intervals can have coverage probabilities lower than the nominal confidence level, yet the typical coverage probability is close to that level. In forming a 95% confidence interval, is it better to use an approach that guarantees that the actual coverage probabilities are at least .95 yet typically achieves coverage probabilities of about .98 or .99, or an approach giving narrower intervals for which the actual coverage probability could be less than .95 but is usually quite close to .95? For most applications, we would prefer the latter.”
Cross-links and the small-sample-inference thread
This is the third day of a tight 3-paper arc. PT #40 (Hanley & Lippman-Hand 1983 Rule of Three, 2026-09-09) opened it with the k=0 one-sided upper bound. PT #41 (Wilson 1927 Probable Inference, 2026-09-10) derived the two-sided score interval that generalizes Rule of Three to any k, and gave the shrinkage estimator (S+2)/(n+4) 71 years before Agresti & Coull rediscovered it. Today’s PT #42 closes the arc: Agresti & Coull ran the simulation study Wilson 1927 needed for practical adoption AND proposed the Wilson naming attribution. The arc pairs cleanly with Stats #40 → Stats #41 → today’s Stats #42 Wilson score derivation applied to today’s NZDCAD 2/11 sample as the running worked example.
Verification note
Full 9-page PDF fetched from https://math.unm.edu/~james/Agresti1998.pdf (University of New Mexico Math Department course mirror, 881 KB, text-native — no OCR required) and text-extracted via pymupdf on 2026-09-11. Verified authorship page 2, journal citation page 1, equation (2) score interval formula page 3, adjusted-Wald rule page 5, Wilson shrinkage-estimator citation page 7, attribution proposal page 7, conclusion page 8, references page 9. NOT verified: exact numeric contents of Figures 1-5 (PDF-embedded raster coverage-probability plots that pymupdf can’t cleanly extract as tabular data). Verified only that the figures exist and their captions match the surrounding text claims. 32nd PT of 42 with full primary-source access.
Keep reading
NZ Employment Change q/q on NZDCAD: small_miss n=11 shows 2 of 11 UP at EVERY window from 5 minutes through 4 hours — the SAME 9-of-11 DOWN count holds at 5m, 15m, 30m, 1h, and 4h. Third leg of the NZ Employment cross-family after AUDNZD antipodal (2026-09-08) and NZDJPY domestic (2026-09-10), and the FIRST leg whose small_miss unanimity persists unbroken all the way to 4h — NZDJPY started deeper at 5m 0/11 up but decayed to 5/11 up (45.5%) by 4h.63 non-contaminated NZ Employment Change q/q releases on NZDCAD (15m sample). Small_miss n=11 shows 2 of 11 UP (18.2%) at every window from 5 minutes through 4 hours — the same count of 9 DOWN and 2 UP holds at 5m, 15m, 30m, 1h, and 4h. Median walk -9.90 / -14.60 / -9.50 / -12.10 / -10.90 pips through the same five windows. Applied to today's Stats #42 Wilson score interval, the 95% two-sided CI on the true up-rate is [5.1%, 47.7%] — coin-flip cleanly OUTSIDE the upper bound. Yesterday's Clopper-Pearson (Stats #41) on the same 2/11 sample gives [2.3%, 51.8%] — fails to reject fair-coin. Wilson tightens the CP upper bound by 4.1pp, exactly enough to flip the decision. Third leg of the NZ Employment cross-family, and the FIRST persistent-through-4h reading — NZDJPY yesterday was tighter at 5m (0/11 up) but decayed to 45.5% up by 4h.Tuesday 07:00 UTC is the LOUDEST 07:00 UTC cell of the week across all 28 liquid FX pairs — median rank 25/237, top-50 for 26 of 28 pairs, top-100 for all 28. Beats Wed 07:00 UTC by 13 rank positions on median and every central-bank decision cell except BoC. Isolates the 'European-morning pre-London ramp baseline' the 2026-09-09 SNB post identified qualitatively.28 fresh /api/v1/calm-zones/scan pulls on 2026-09-11. Tuesday 07:00 UTC ranks in the top-50 loudest half-hours for 26 of 28 liquid FX pairs, top-30 for 20 of 28, and top-100 for all 28. Median rank across 28 pairs is 25 — 13 rank positions louder than Wed 07:00 UTC (median 38), 26 louder than Mon 07:00 UTC (51), and louder than every central-bank rate-decision cell except BoC Wed 14:00. EURJPY leads the pair-family pattern at rank 8 (only top-10 cell); JPY-crosses cluster inside top-20 (EURJPY 8, AUDJPY 13, GBPJPY 13, CHFJPY 16, NZDJPY 20). CAD-crosses trail (GBPCAD 57 quietest, USDCAD 51, CADCHF 50). Mechanism: Tokyo late-session carry-unwind meets London fixing pre-open bid — a European-morning JPY-cross lift that quantifies what the SNB Thu 07:30 UTC post (2026-09-09) attributed to 'pre-London ramp baseline'.Statistics for Traders #42: The Wilson score confidence interval — invert the score test rather than the Wald test, and the resulting closed form (Wilson 1927 Section 2) is TIGHTER than yesterday's Clopper-Pearson exact interval on every unanimity sample the last three days have generated. Applied to today's slot 1 NZDCAD small_miss 2 of 11 UP: Wilson 95% CI on up-rate = [5.1%, 47.7%] cleanly rejects fair-coin where Clopper-Pearson's [2.4%, 51.8%] does not.For n Bernoulli trials with k successes, the Wilson score interval is (p̂ + z²/(2n) ± z · sqrt(p̂q̂/n + z²/(4n²))) / (1 + z²/n). Derived by inverting the score test (Wilson 1927 Section 2, primary source verified in yesterday's PT #41). Cross-comparison of four methods on today's slot 1 NZDCAD 2-of-11 UP sample: Rule of Three (n/a, k≠0), Clopper-Pearson [2.4%, 51.8%], Agresti-Coull [4.0%, 48.8%], Wilson [5.1%, 47.7%]. Wilson is TIGHTEST and the ONLY method whose upper bound clears 50%, exactly flipping the fair-coin decision from 'inside' (CP) to 'outside' (Wilson). Same pattern on the CHFJPY 4/4 unanimity sample from 2026-09-10 slot 1: Wilson [51.0%, 100%] rejects 50%, CP [39.8%, 100%] does not. Wilson's advantage comes at a coverage-spike cost near p=0 and p=1; today's PT #42 (Agresti & Coull 1998) documents this trade-off and recommends Wilson anyway.Japan National Core CPI y/y on USDJPY: the 15-minute and 1-hour readings are muted (big_beat 57-63% up, median move under 3 pips), but by 4 hours the big_beat bucket (n=16) has flipped to just 25% UP — 12 of 16 DOWN, median -6.25 pips. Wilson 95% CI on up-rate [10.2%, 49.5%] rejects fair-coin. The hawkish-BoJ JPY-strengthening interpretation only LOCKS IN at 4h, not at 15m — the delayed-response story the 2026-08-05 muted-at-15m deferral missed.This event was DEFERRED on 2026-08-05 with the note 'muted response across all buckets at 15m'. The fresh angle: the 15m-through-1h muted story is correct but incomplete. At 4 hours after release, the big_beat bucket (n=16, non_contaminated) shows 25% UP — 12 of 16 DOWN, median -6.25 pips. Applied to today's Stats #42 Wilson score interval, the 95% CI on the true up-rate is [10.2%, 49.5%] — cleanly rejects fair-coin. The hawkish-BoJ JPY-strengthening interpretation of a Japan CPI BEAT arrives with a 3-hour delay: 15m big_beat is 12/21 up (57.1%, no signal), 30m 8/21 (38.1%, hint), 1h 10/16 (62.5%, reverts), 4h 4/16 (25%, hawkish lock-in), EOD 4/12 (33.3%, persists). Miss-side at 4h is near-coin-flip (54-57% up) — the signal is beat-side-only because the BoJ is at the effective lower bound and a soft CPI can't move the policy path much lower than it already is.Japan Prelim GDP q/q on CHFJPY: 4/4 big-miss DOWN at 1h ONLY — same delayed lock-in as yesterday's EURJPY, and the SHALLOWEST 1h magnitude (-6.45p) in the whole JPY GDP cross-family. Seventh and FINAL pair, closes the 7-pair family with a two-tier structure.64 non-contaminated Japan Prelim GDP q/q releases on CHFJPY. Big_miss median walks -4.25p → -5.80p → -6.45p through 1h, deepens monotonically, and locks into full 4/4 DOWN unanimity ONLY at 1h — the same delayed pattern EURJPY showed yesterday. The 1h magnitude -6.45p is the SHALLOWEST in the entire 7-pair family (half of GBPJPY's -13.45p), because CHF competes with JPY for safe-haven flow more strongly than any other base currency in the family. 4h reverts to 2/4 down (median -1.55p) — the deepest 4h flip of any Tier 2 pair. Seventh and final pair; closes the family with a clean 5-Tier-1 / 2-Tier-2 split.Thursday 14:30 UTC — the 'post-jobless-claims settle' — is the 4th-loudest half-hour of the whole week: top-10 for ALL 28 liquid FX pairs, top-5 for 16 of 28, and #1 for 2 pairs (AUDCHF and GBPCHF). Median rank #5 across 28 pairs. Natural Thursday mirror of the Fri 14:30 UTC post-NFP settle cell.Fresh /api/v1/calm-zones/scan pulls across all 28 liquid FX pairs on 2026-09-10. Thursday 14:30 UTC lands top-10 for every pair (28/28), top-5 for 16 of 28, and is #1 for 2 pairs (AUDCHF and GBPCHF). Median rank across pairs is #5 — the 4th-loudest weekday half-hour in the whole trading week, behind only Thu 13:30, Fri 14:30, and Fri 13:30 UTC. The mechanism is the same as Fri 14:30's post-NFP settle: Thu 13:30 UTC absorbs the US jobless-claims / PPI / retail-sales release surprise, and 14:30 UTC exactly clocks the US cash-equities open (09:30 ET) — the 30-minute window catches pre-open positioning spillover and the actual opening auction. Together with Thu 13:30 UTC (2026-09-07 post) and Thu 14:00 UTC, this forms a contiguous 90-minute top-10 block that Thursdays uniquely share with Fridays.Statistics for Traders #41: The Clopper-Pearson exact binomial confidence interval — the two-sided generalization of yesterday's Rule of Three. Applied to today's slot 1 CHFJPY 4-of-4 DOWN at 1h: 95% two-sided CI on the true down-rate is [39.76%, 100%]. Coin-flip (50%) lies INSIDE the interval — 4/4 unanimity is NOT enough at 95% to reject a fair-coin null on n=4. It would take n=6 unanimity for Clopper-Pearson two-sided to clear the 50% threshold.For n Bernoulli trials with k observed successes, the Clopper-Pearson (1934) exact binomial confidence interval is [BetaInv(α/2; k, n-k+1), BetaInv(1-α/2; k+1, n-k)]. For the unanimity edge cases (k=0 or k=n) it admits a clean closed form: p_L = (α/2)^(1/n) at k=n, p_U = 1 - (α/2)^(1/n) at k=0. Yesterday's Rule of Three is the one-sided k=0 approximation. Applied to today's slot 1 CHFJPY 4/4 DOWN at 1h: 95% two-sided CI on the true down-rate is [39.76%, 100%]. Coin-flip stays inside. Applied to yesterday's GBPJPY 0/4 UP at 15m: [0, 60.24%]. Coin-flip also inside. Even 4-of-4 unanimity fails to reject fair-coin at 95% two-sided. Compare against Wilson score (tightest, from today's PT #41 Wilson 1927), Agresti-Coull, and yesterday's Rule of Three.Paper Trail #41: Probable Inference, the Law of Succession, and Statistical Inference (Wilson, 1927) — the 4-page JASA paper that derived the modern 'Wilson score interval' 60 years before it got that name, AND worked out the exact 95% upper bound λ²/(n+λ²) for observing zero successes in n trials — 56 years before Hanley & Lippman-Hand named the Rule of Three (PT #40 yesterday). At n=4, Wilson gives 48.99%; the Rule of Three gives 75%; Clopper-Pearson exact gives 52.71%.Edwin B. Wilson (Harvard School of Public Health), 'Probable Inference, the Law of Succession, and Statistical Inference,' Journal of the American Statistical Association 22(158):209-212, June 1927. 4 pages. FULL PRIMARY SOURCE VERIFIED via WebFetch of McGill Biostatistics mirror + tesseract OCR on 2026-09-10 (image-only PDF, 9,282 characters recovered across 5 pages). Wilson opens by rejecting the naive p̂ ± λσ̂ formulation as 'elliptical', then derives the score interval as the quadratic-in-p solution to (p̂ - p)² = λ²pq/n — the exact modern Wilson score interval with center (p̂ + λ²/(2n))/(1 + λ²/n) and half-width √(p̂q̂/n + λ²/(4n²))/(1 + λ²/n). Wilson's Section on 'total failure' (p̂ = 0) worked out the upper bound λ²/(n+λ²) for the true rate — the same problem Hanley & Lippman-Hand 1983 (PT #40 yesterday) later renamed the Rule of Three, with a tighter formula. At today's slot 1 CHFJPY 4/4 sample n=4, Wilson score gives the tightest 95% CI of any method.NZ Employment Change q/q on NZDJPY: small_miss n=11 shows 0 of 11 UP at 5 minutes — 100% DOWN unanimity that cleanly rejects fair-coin at 95% (Clopper-Pearson two-sided CI on up-rate = [0%, 28.5%]). Second leg of the NZ Employment cross-family after AUDNZD antipodal (2026-09-08), delivering DEEPER mid-bucket unanimity on a domestic JPY-cross rather than tighter tail-bucket unanimity on the antipodal cross.63 non-contaminated NZ Employment Change q/q releases on NZDJPY (15m sample). At 5 minutes, the small_miss bucket is 0 of 11 UP (100% DOWN, median -8.60p) — a mid-bucket unanimity large enough to reject a fair-coin null at 95% two-sided (Clopper-Pearson CI on true up-rate = [0%, 28.5%]). Unanimity relaxes to 2/11 up (18.2%) at 15m, tightens back to 1/11 up (9.1%) at 30m and 1h, then softens to 5/11 up (45.5%) at 4h. Full 5-bucket 15m walk: -19.70 / -13.70 / -2.90 / +22.45 / +9.50 pips (pct-up 0.0 / 18.2 / 46.7 / 68.8 / 60.0). Second leg of the NZ Employment cross-family after AUDNZD antipodal (2026-09-08) — delivering DEEPER mid-bucket unanimity because JPY carries the flow direction cleanly on the NZ-data-only 22:45 UTC release; AUDNZD delivered TIGHTER bilateral tail unanimity because AUD is a passive Wellington-morning bystander. Different mechanics, complementary clean signals.Japan Prelim GDP q/q on GBPJPY: all 4 big-miss prints sent GBPJPY DOWN at 15m, 30m, AND 1h — TRIPLE-window big-miss unanimity and the DEEPEST 1h reading in the JPY Prelim GDP cross-family (-13.45p). Fifth pair in the family and the first whose 1h magnitude peaks above every sibling.64 non-contaminated Japan Prelim GDP q/q releases on GBPJPY. All 4 big-miss prints (2014-02-16, 2014-11-16, 2020-02-16, 2021-11-14) sent GBPJPY DOWN at 15m, 30m, AND 1h — triple-window big-miss unanimity on the same 4-print membership as the USDJPY/AUDJPY/NZDJPY/CADJPY siblings. Median deepens monotonically -6.25p → -7.55p → -13.45p through 1h, the DEEPEST 1h reading in the entire JPY Prelim GDP cross-family (edging USDJPY/AUDJPY -13.25p, well ahead of CHFJPY -6.45p). At 4h one print flips positive to +27.6p max and the median softens to -4.80p (3/4 still down). Bucket-boundary sign inversion holds: small_miss (n=16) is 68.75% UP at 15m (textbook JPY-weakens-on-soft-Japan-data), big_miss flips to 100% DOWN. GBP's high-beta risk-currency behavior makes GBPJPY the hardest-falling JPY cross at the 1-hour mark.SNB Monetary Policy Assessment slot Thursday 07:30 UTC is the THIRD-loudest central-bank decision slot in the calendar — median rank 48 across 28 pairs (28/28 in top-100, 17/28 in top-50). CHF-cross best at #26, worst GBPCAD at #79. Despite SNB firing only 4x/year — the LOWEST direct-firing density of any CB — it outranks FOMC/RBNZ/RBA/BoJ by 60-150 rank positions.The SNB Monetary Policy Assessment slot Thursday 07:30 UTC ranks TOP-100 for all 28 liquid FX pairs (28/28 = 100%), top-50 for 17/28, top-30 for 3/28 — median rank #48. CHF-cross best is CHFJPY/EURCHF tied at #26; worst is GBPCAD #79. Non-CHF median rank is 50 vs CHF median 32 — an 18-position direct-fire lift on CHF pairs. But that lift is modest: for 5 of 7 CHF pairs the 08:00 UTC London-open cell is LOUDER than the SNB 07:30 UTC decision cell. European-morning pre-London-ramp baseline carries the loudness, not SNB direct fire. Closes the 7-CB rank arc: BoC 13 < BoE 42.5 < SNB 48 < FOMC 108 < RBNZ 140 < RBA 194.5 ≈ BoJ 195. SNB fires only 4x/year (~7.7% Thursday direct density, lowest of any CB), yet outranks FOMC/RBNZ/RBA/BoJ by 60-150 positions — neighbouring-cell baseline dominates direct-fire density.Statistics for Traders #40: The Rule of Three — for n Bernoulli trials with 0 successes, the 95% upper confidence bound on the true success rate is approximately 3/n. Direct application to today's slot 1 (GBPJPY × Japan Prelim GDP: 0-of-4 UP at 15m) gives a 95% upper CI of 52.7% — the 4-of-4 unanimity is CONSISTENT WITH a true up-rate as high as 1-in-2. Opens a new small-sample-inference thread.For n Bernoulli trials with x=0 successes, the one-sided 95% upper confidence bound on the true success probability is approximately 3/n — derived by solving (1-p_U)^n = 0.05 → p_U = 1 - 0.05^(1/n) ≈ 3/n. Directly applied to today's slot 1 (GBPJPY × Japan Prelim GDP big-miss 0-of-4 UP at 15m): the exact 95% upper CI is 52.7%, so the 4-of-4 unanimity is consistent with a true up-rate as high as one-in-two. Rule of Three gives 3/4 = 0.75, safely conservative. This is why every slot-1 tail-unanimity post carries the 'small-sample tail-unanimity finding, not wide-sample effect-size claim' verification caveat. Opens a new small-sample-inference thread after Stats #34-#39 closed the 6-post multivariate-classifier arc.Paper Trail #40: If Nothing Goes Wrong, Is Everything All Right? Interpreting Zero Numerators (Hanley & Lippman-Hand, JAMA 1983) — the paper that named the 'rule of three' for small-sample zero-count inference and gave every clinician (and every trader looking at a tail-unanimity) the maximum-long-run-risk formula behind today's Stats #40.The 1983 JAMA paper by McGill epidemiologists James Hanley and Abby Lippman-Hand that named the 'rule of three' (upper 95% CI ≈ 3/n for x=0 successes in n Bernoulli trials) and turned it into a standard clinical-inference tool for the zero-numerator small-sample corner case — the same case that today's slot 1 GBPJPY 0-of-4 big-miss unanimity lands on. FULL primary source verified 2026-09-09 via WebFetch + zlib PDF-stream decompression from McGill Biostatistics mirror (4 pages, 15.4 KB, text-native). Verified authorship, three main-points enumeration verbatim, 5%-credibility-limit convention verbatim, Table 1 (P(0 in 167) at 7 trial rates from 1/10,000 to 1/25) verbatim, Table 2 (Rule of Three upper bounds at 0/10, 0/20, 0/30, 0/50, 0/100, 0/1000) verbatim including asterisked exact formula '(1 - maximum rate)^n = 0.05' and daggered rule-of-three column, and the closing quote urging authors to 'consider the maximum risk with which their findings are compatible.' PT #40 opens a new small-sample-inference thread and directly pairs with today's Stats #40.Japan Prelim GDP q/q on EURJPY: 4/4 big-miss DOWN at 1h ONLY — the 15m and 30m unanimity is BROKEN by one print (25% up). EURJPY has the SLOWEST safe-haven lock-in in the JPY GDP cross-family because EUR is safe-haven-adjacent. Sixth pair in the family and the first to break the 15m unanimity.64 non-contaminated Japan Prelim GDP q/q releases on EURJPY. Big-miss median walk -6.85p → -7.15p → -10.60p through 1h (deepens monotonically), but the 15m and 30m windows are only 3/4 DOWN (25% up) — the 2014-11-16 recession-confirmation print flips positive at 15m (+2.20p) before finally rolling over at 1h. Full 4/4 unanimity locks in ONLY at 1h, then reverts to 2/4 at 4h. Sixth pair in the JPY GDP cross-family and the FIRST to break the 15m unanimity — EUR is safe-haven-adjacent, so the initial JPY safe-haven bid competes with EUR-own safe-haven demand, delaying the sign-flip lock-in by 45 minutes vs the five high-beta-base siblings.Japan Prelim GDP q/q on CADJPY: all 4 big-miss prints sent CADJPY DOWN at 15m, 30m, AND 1h — TRIPLE-window big-miss unanimity (12 of 12 zero-flip miss-side moves) — but the aggregate REVERTS at 4h to a 2/4 mixed up-rate. Fourth pair in the JPY Prelim GDP cross-family, and the first whose safe-haven flip fades at 4h.61 non-contaminated Japan Prelim GDP q/q releases on CADJPY. All 4 big-miss prints (2014-02-16, 2014-11-16, 2020-02-16, 2021-11-14) sent CADJPY DOWN at 15m, 30m, AND 1h — triple-window big-miss unanimity on the same 4-print membership as the USDJPY/AUDJPY/NZDJPY siblings. Median deepens through 1h (-3.90p → -7.70p → -8.55p) then REVERTS to -1.05p at 4h (2/4 flippers). Fourth pair in the JPY Prelim GDP cross-family, and the first whose safe-haven flip fades at 4h — CAD's commodity-currency oil-beta reattaches once the initial JPY bid is absorbed. Bucket-boundary sign inversion holds: small_miss (n=16) is 68.75% UP at 15m (textbook JPY-weakens-on-soft-Japan-data), big_miss flips to 100% DOWN.RBNZ Official Cash Rate decision slot Wednesday 02:00 UTC is the THIRD-tier dead central-bank slot in the calendar — median rank 140/240 across 28 pairs, 5 of 28 pairs crack top-100 (best AUDNZD at #55). Louder than yesterday's BoJ Wed 03:00 UTC and last week's RBA Tue 03:30 UTC because it fires 30-60 minutes EARLIER, catching the tail of Tokyo pre-lunch flow before the lunch vacuum closes in.The RBNZ has fired its Official Cash Rate decisions at Wed 02:00 UTC (14:00 NZST) since 2016. Across all 28 liquid FX pairs the cell ranks between #55 (AUDNZD) and #192 (CADCHF) — median 139.5, mean 143.0. Zero of 28 pairs crack top-50; 5 of 28 crack top-100 (AUDNZD 55, AUDJPY 86, NZDJPY 87, NZDUSD 92, AUDUSD 92 — the AUD/NZD family). The 32-rank gap between NZD-cross median (118) and non-NZD median (~150) is the direct-fire signature: RBNZ meetings DO lift the cell for the pairs being repriced, but not by enough to break top-50 even for the flagship AUDNZD. RBNZ inserts BETWEEN FOMC (108) and the tied RBA/BoJ pair (195) in the 6-CB rank ordering. Mechanism: Wed 02:00 UTC is the LAST bin of Tokyo pre-lunch peak flow (Wed 01:30 UTC is the actual peak — AUDNZD ranks that cell at #9); by 02:30 UTC Tokyo lunch shuts down volatility and RBA/BoJ inherit the vacuum baseline.Statistics for Traders #39: Multinomial logistic regression on the same UK Core CPI × GBPCHF 6-window response panel Stats #34/#35/#36/#37/#38 used. LOO-CV accuracy 87/196 = 44.39% (best variant C=10 standardized) — BEATS LDA 84/196 = 42.86% (+1.53pp) and QDA 79/196 = 40.31% (+4.08pp). But McNemar's exact test on LDA vs logit LOO (b=1, c=4, exact 2-sided p=0.375) is NOT significant — practical dead heat between the two linear classifiers. Standardized coefficients confirm Stats #35's canonical direction: the 1-minute window dominates (biggest coefficient magnitudes on 1m across all 5 classes); 4h and 5m contribute essentially nothing.196 UK Core CPI × GBPCHF releases, K=5 bucket classes, d=6 response windows — the same panel Stats #34-38 used. Multinomial logistic regression (the DISCRIMINATIVE baseline vs LDA/QDA which are generative) reaches 87/196 = 44.39% LOO accuracy at its best variant (C=10, features standardized), beating LDA (84/196 = 42.86%) by +1.53pp and QDA (79/196 = 40.31%) by +4.08pp. But McNemar's exact test on the LDA vs logit LOO predictions (b=1, c=4, exact 2-sided p=0.375) says the LDA→logit gain is not statistically significant — practical dead heat. The +1.53pp comes entirely from small_miss (+2 correct) and in_line (+2), offset by -1 on big_beat. Multinomial logit hits the same 0/13 big_miss recall wall LDA and QDA both do — the log-prior handicap Stats #36 documented applies here identically. Standardized coefficients across the 5 classes concentrate mass on the 1-minute window (magnitudes 1.0-1.3) — the discriminative-classifier version of Stats #35's canonical direction, arrived at through a different objective function.Paper Trail #39: Presidential Address — Asset Price Dynamics with Slow-Moving Capital (Duffie, 2010). The AFA Presidential Address that generalized the limits-to-arbitrage literature into a single 'sharp reaction + gradual reversal' framework spanning fractions-of-a-second (limit-order books) to multi-year (catastrophe insurance) time scales. Cites PT #36 Gromb-Vayanos 2002 and PT #34 Brunnermeier-Pedersen 2009 directly in the same sentence as 'dynamic asset pricing theories based on intermediated movement of capital.' Introduces the inattentive-investor model in Section IV with closed-form equilibrium price S_t = c · Y_t under Gaussian AR cash flows and constant absolute risk aversion.Darrell Duffie's 2010 AFA Presidential Address, published in Journal of Finance Vol. LXV No. 4 (August 2010) pp. 1237-1267. The paper synthesizes the entire limits-to-arbitrage / slow-moving-capital literature under one general perspective — 'asset prices can move away from fundamental values if capital is not perfectly mobile' — and introduces a new closed-form inattentive-investor model in Section IV that produces the canonical 'sharp reaction + gradual reversal' price path from a supply shock. Three motivating examples span the full time-scale range: S&P 500 index deletions (60-day reversal, 61 events 1990-2002 with 8% announcement drop + 6% additional to effective date, cited from Chen-Noronha-Singhal 2004), limit-order-book price impacts (seconds), and catastrophe insurance premiums after natural disasters (multi-year, cited from Enz 2001). Directly cites PT #36 Gromb-Vayanos 2002 and PT #34 Brunnermeier-Pedersen 2009 in the same sentence. Verified via WebFetch + pymupdf on 2026-09-08 from Duffie's personal website mirror (31 pages, 470 KB, text-native).NZ Employment Change q/q on AUDNZD: pct-up walk STRICTLY MONOTONIC across every window from 1m through 15m — 100 / 81.8 / 63.3 / 31.2 / 25.0% at 15m — and the 5-bucket median walk deepens +43.60 / +19.40 / +7.70 / -29.90 / -18.30 pips. First-ever anchor for NZ Employment on any pair, opens the NZ Employment cross-family arc. AUDNZD picked for the same antipodal-pair mechanic yesterday's nz-cpi-audnzd-antipodal used: AUD leg is a Wellington-morning bystander at the 22:45 UTC release, giving the CLEANEST NZ-macro repricing signal in the whole cross-family.62 non-contaminated NZ Employment Change q/q releases on AUDNZD. pct-up walk STRICTLY MONOTONIC across every window from 1m through 15m — at 15m the walk is 100 / 81.8 / 63.3 / 31.2 / 25.0% (big_miss down to big_beat), and the median walk is +43.60 / +19.40 / +7.70 / -29.90 / -18.30 pips. Small_miss n=11 (the largest tail bucket): 9 of 11 UP at 15m (81.8%), median +19.4p. Big_miss n=1 (single 2013-02-06 print, actual -1.0 vs consensus +0.4, z=-2.52): +43.60p at 15m and +37 to +48p at every other window. Big_beat n=4: 3 of 4 DOWN, median -18.3p. First-ever anchor for NZ Employment on any pair, opens the NZ Employment cross-family arc; second post in the AUDNZD × NZ-macro family after yesterday's nz-cpi-audnzd-antipodal, using the same antipodal-pair mechanic (AUD leg is a Wellington-morning bystander at 22:45 UTC release).Japan Prelim GDP q/q on NZDJPY: all 4 big-miss prints sent NZDJPY DOWN at 15m, 30m, 1h, AND 4h — QUADRUPLE-window big-miss unanimity, and the median deepens MONOTONICALLY through every window (-8.25 → -10.25 → -11.70 → -12.85 pips) — the first pair in the JPY Prelim GDP family whose big-miss magnitude keeps growing all the way to 4 hours instead of peaking early and fading. Third pair in the JPY Prelim GDP cross-family.63 non-contaminated Japan Prelim GDP q/q releases on NZDJPY. All 4 big-miss prints (2014-02-16, 2014-11-16, 2020-02-16, 2021-11-14) sent NZDJPY DOWN at 15m, 30m, 1h, AND 4h — safe-haven JPY bid overwhelms the currency-fundamentals response, and the median deepens MONOTONICALLY through every window (-8.25p → -10.25p → -11.70p → -12.85p). Third pair in the JPY Prelim GDP cross-family after USDJPY (peak at 15m) and AUDJPY (peak at 1h, fades by 4h); NZDJPY is the FIRST pair whose magnitude keeps growing all the way to 4 hours. Bucket-boundary sign inversion holds: small_miss (n=16) is 66.7% UP at 15m (textbook JPY-weakens-on-soft-Japan-data), big_miss flips to 100% DOWN.Thursday 13:30 UTC — the cell that outranks every central-bank-decision slot in the calendar. #1 loudest weekday half-hour for 9 of 28 liquid FX pairs, top-5 for 25 of 28, top-10 for 27 of 28. Beats Thursday 12:30 UTC (the US initial-jobless-claims release cell) on ALL 28 pairs. Median rank across the 28 pairs is #2 of ~237 weekday cells.Thursday 13:30 UTC is the loudest weekday half-hour cell for 9 of 28 liquid FX pairs (EURCHF, EURGBP, EURJPY, EURUSD, GBPUSD, NZDCHF, NZDUSD, USDCHF, USDJPY — the EUR-heavy majors) and lands in the top-5 for 25 of 28 pairs, top-10 for 27 of 28. Median rank across all 28: #2. It BEATS Thursday 12:30 UTC (the US initial-jobless-claims release cell) on every single pair. Three mechanisms overlap in this cell: US 08:30 ET macro-cluster follow-through, ECB press-conference commentary (on ECB Thursdays), and peak London/NY overlap liquidity. Outranks every central-bank rate-decision cell (BoC Wed 14:00, BoE Thu 12:00, FOMC Wed 18:00, BoJ Wed 03:00, RBA Tue 03:30) by a wide margin — despite not holding a rate decision itself.Statistics for Traders #38: QDA on the same UK Core CPI × GBPCHF 6-window response panel Stats #34/#35/#36/#37 used. QDA UNDERPERFORMS LDA on LOO: 79/196 = 40.31% vs LDA's 84/196 = 42.86% (-2.55pp), despite QDA fitting 57.14% in-sample vs LDA's 49.49%. Bias-variance overfitting — QDA's 2.65× extra parameters (135 vs 51) can't be reliably estimated from small tail-bucket samples (n=13 / n=15). Regularized QDA (reg_param=0.20) recovers to LDA-parity 42.35% — confirming the pooled covariance already has essentially all the discriminant information.196-release UK Core CPI × GBPCHF panel, same as Stats #34/#35/#36/#37. QDA gives each of the 5 bucket classes its own 6×6 covariance matrix (vs LDA's single pooled Σ). QDA fits 57.14% in-sample — 7.65pp better than LDA. But LOO drops to 40.31% — 2.55pp WORSE than LDA. QDA has 2.65× LDA's free parameters (135 vs 51); the tail-bucket sample sizes (n=13 big_miss, n=15 big_beat) are far below the classical 10-observations-per-parameter threshold for reliable covariance estimation. QDA gains big_beat recall (+13.34pp) but loses more on small_beat (-11.32pp). Regularized QDA (reg_param=0.20) recovers to 42.35%, essentially matching LDA — a tell that the pooled Σ already captures all the discriminant information. Cross-verified vs sklearn 1.9.0 QuadraticDiscriminantAnalysis with 100% agreement.Paper Trail #38: Risk in Dynamic Arbitrage — the Price Effects of Convergence Trading (Kondor, 2009) — the paper that dynamically extended yesterday's PT #36 arc by showing convergence-trade arbitrageurs can lose money EVEN ON A FUNDAMENTALLY RISKLESS TRADE, because the equilibrium gap between two identical assets must widen over time to keep the arbitrageurs indifferent to when they deploy capital. Smith Breeden First Prize for the Best Paper in Asset Pricing 2009.The Journal of Finance Smith Breeden First Prize 2009. Kondor builds an equilibrium model of convergence trading between two IDENTICAL assets in segmented markets, with a random exponentially-distributed window closure and a unit mass of risk-neutral arbitrageurs with limited capital. Main result: arbitrageurs' activity generates LOSSES with positive probability even though the trade is FUNDAMENTALLY RISKLESS. Proposition 4: the realized return conditional on window length t̃ is monotonically decreasing in t̃, so the distribution is NEGATIVELY SKEWED (large losses in small-probability states, small gains in large-probability states) — consistent with the empirical hedge-fund-return literature. Cites PT #33 SV 1997 and PT #36 GV 2002 directly. The dynamic extension of the two-period frames used in the earlier limits-of-arbitrage papers.New Zealand CPI q/q on AUDNZD: all 3 big-miss prints sent AUDNZD UP at EVERY window from 1m through 4h — 17 of 17 sextuple-window miss-side unanimity, AND all 6 big-beat prints sent it DOWN at 1m (double-tail unanimity), AND the 5-bucket pct-up walk is STRICTLY monotonic 100 / 87.5 / 40 / 21.4 / 0. First XXXNZD (NZD-quote) pair in the NZ CPI cross-family — the antipodal-pair mechanic gives the cleanest NZ CPI signal in the family so far.59 non-contaminated NZ CPI q/q releases on AUDNZD. All 3 big-miss prints (2012-01-18, 2016-01-19, 2018-01-24) sent AUDNZD UP at EVERY window from 1m through 4h — 17 of 17 sextuple-window miss-side unanimity. AND all 6 big-beat prints sent it DOWN at 1m (double-tail unanimity). AND the 5-bucket pct-up walk at 15m is STRICTLY monotonic: 100 / 87.5 / 40 / 21.4 / 0. Big-miss median deepens monotonically through 4h (+85p → +102p → +120p → +123p). Fifth pair in the NZ CPI cross-family after NZDUSD/NZDJPY/NZDCAD/NZDCHF, and the FIRST XXXNZD (NZD-quote) pair — the antipodal-pair mechanic gives the cleanest NZ CPI signal in the whole family.New Zealand CPI q/q on NZDCHF: all 3 big-miss prints sent the QUIETEST NZD-cross DOWN at EVERY window from 1m through 4h — 18 of 18 sextuple-window miss-side unanimity, and the median walk deepens -25 / -33 / -51 / -45 / -44 / -46 pips (5.9× the pair's typical range) instead of decaying. Fourth pair in the NZ CPI cross-family, third sextuple-window big-miss unanimity in a row.63 non-contaminated New Zealand CPI q/q releases on NZDCHF. Big_miss (n=3) is 3/3 DOWN at 1m, 5m, 15m, 30m, 1h, AND 4h — sextuple-window miss-side unanimity on the same 3-print membership. Median deepens -25.3 → -33.0 → -50.6 → -44.5 → -43.5 → -46.2 pips through 4h (5.9× the pair's typical 30-min range of 7.8p). At 15m the full 5-bucket median walk is monotonic (-50.6 / -26.4 / +2.2 / +13.0 / +15.7 pips) and small_beat (n=16) is 16 of 16 UP at 1m AND 5m. Fourth pair in the NZ CPI cross-family after nzd-cpi-nzdusd-tails (2026-08-06), nzd-cpi-nzdjpy-monotonic (2026-09-04), and yesterday's nzd-cpi-nzdcad-sextuple-miss (2026-09-05).BoJ decision window Wednesday 02:30-04:00 UTC ties Tuesday 03:30 RBA as the DEADEST central-bank slot in the calendar — Wed 03:00 UTC canonical centroid has median rank 195/237 across 28 pairs (essentially the same 194.5 the RBA slot posted yesterday). Zero of 28 pairs crack top-100 at Wed 03:00; even taking the BEST of the four candidate BoJ bins per pair still leaves 0/28 in top-100. Best rank AUDNZD at 117 (Wed 02:30 bin).Bank of Japan monetary policy statements land between 11:45 and 13:00 JST (Wed 02:45-04:00 UTC), inside the Tokyo-lunch global vacuum. At the canonical mid-window Wed 03:00 UTC slot, median rank across all 28 liquid FX pairs is 195/237 — essentially TIED with the RBA Tue 03:30 UTC slot (194.5) covered 2 days ago. Zero of 28 pairs crack top-100; best rank AUDNZD at 131. Widening to the full announce window Wed 02:30/03:00/03:30/04:00 UTC, best-of-window per pair still yields 0/28 in top-100; the earliest 02:30 bin captures the best rank for every one of the 28 pairs. Closes the 5-CB rank arc: BoC 13, BoE 42.5, FOMC 108, RBA 194.5, BoJ 195.Statistics for Traders #37: Pairwise Mahalanobis distance D_M between bucket centroids on the same UK Core CPI × GBPCHF 6-window panel Stats #34/#35/#36 used. D_M(big_miss, small_miss) = 0.895 in 6-window multivariate — vs univariate 15m Cohen's d = 0.011, an 82× amplification because big_miss and small_miss have essentially IDENTICAL 15m medians but completely different trajectories (big_miss peaks-then-decays, small_miss amplifies monotonically). D_M(big_miss, big_beat) = 2.185 vs univariate 15m d = 1.898 (1.15× amplification, and 95.4% captured by Stats #35's top canonical axis).Pairwise Mahalanobis distance D_M = √((μ_i-μ_j)^T Σ_pooled^{-1} (μ_i-μ_j)) worked end-to-end on the 196-release UK Core CPI × GBPCHF 6-window panel Stats #34-#36 used. D_M is the multivariate generalization of Cohen's d — measures bucket-centroid separation in pooled-within-SD units across all 6 windows jointly. Tail-to-tail D_M(big_miss, big_beat) = 2.185 (vs univariate 15m d = 1.898, 1.15× amplification; 95.4% captured by Stats #35's top canonical axis). Adjacent D_M(big_miss, small_miss) = 0.895 vs univariate d = 0.011 — an 82× amplification because big_miss and small_miss have essentially identical 15m centroids but completely different 6-window trajectories.Paper Trail #37: Betting Against Beta (Frazzini & Pedersen, 2014) — the paper that turned yesterday's PT #36 arc of funding-liquidity theory into a cross-sectional asset-pricing implication: high beta = low alpha because leverage-constrained investors bid up high-beta assets. Proposition 1 gives α = ψ(1 − β) verbatim; US-equity BAB factor Sharpe 0.78 over 86 years (1926-2012), roughly TWICE the value-effect Sharpe over the same period.Andrea Frazzini (AQR) and Lasse Heje Pedersen (NYU/CBS/CEPR/NBER) (2014) 'Betting Against Beta' — JFE 111(1):1-25, DOI 10.1016/j.jfineco.2013.10.005. Extends yesterday's PT #34 Brunnermeier-Pedersen funding-liquidity theory into a cross-sectional asset-pricing model: constrained investors bid up high-beta assets, flattening the security market line and creating a hedge-portfolio anomaly. Proposition 1 verbatim: α^s = ψ(1 − β^s) — alpha DECREASES in beta whenever the funding constraint ψ > 0. Empirical test: Table 3 US equities 1926-2012 shows CAPM alphas walking 0.52 / 0.48 / 0.42 / 0.39 / 0.34 / 0.34 / 0.22 / 0.21 / 0.10 / 0.10 pp/month across 10 beta-sorted deciles (declining almost monotonically). BAB factor (long leveraged low-beta, short de-leveraged high-beta) earns 0.73% monthly CAPM alpha, 0.55% 4-factor alpha (t=5.59), Sharpe 0.78. Same effect replicates on 19 international equity markets, US Treasury bonds, and US corporate credit (Treasury BAB Sharpe 0.81).Japan Prelim GDP q/q on AUDJPY: all 4 big-miss prints sent AUDJPY DOWN at 15m, 30m, 1h, AND 4h — QUADRUPLE-window big-miss unanimity, and the SAME bucket-boundary sign inversion yesterday's USDJPY sibling documented HOLDS on AUDJPY too (small_miss goes OTHER way 68.75% up at 15m — JPY weakens as expected on soft Japan data; big_miss flips to safe-haven JPY-STRENGTHENS response). Second pair in the JPY Prelim GDP cross-family.67 non-contaminated Japan Prelim GDP q/q releases on AUDJPY. All 4 big-miss prints (2014-02-16, 2014-11-16, 2020-02-16, 2021-11-14) sent AUDJPY DOWN at 15m, 30m, 1h, AND 4h — safe-haven JPY bid overwhelms the currency-fundamentals response. Bucket-boundary sign inversion: small_miss (n=16) is 68.75% UP at 15m (textbook JPY-weakens-on-soft-Japan-data), big_miss flips to 100% DOWN (safe-haven flow dominates). Same threshold-boundary pattern as yesterday's jpy-prelim-gdp-usdjpy-safe-haven (2026-09-05). Second pair in the JPY Prelim GDP cross-family — AUDJPY takes 10+ minutes vs USDJPY's 1 minute to establish direction because AUD leg is thinly traded during Wellington/Sydney overnight when JP GDP releases at 23:50 UTC ≈ 08:50 JST.New Zealand CPI q/q on NZDCAD: all 3 big-miss prints sent NZDCAD DOWN at EVERY window from 1m through 4h — 18 of 18 sextuple-window miss-side unanimity, and the median walk deepens monotonically -64 / -72 / -80 / -88 / -100 pips through 1h. Third pair in the NZ CPI cross-family, deepest miss-side magnitudes yet.63 non-contaminated NZ CPI q/q releases on NZDCAD. Big-miss (n=3) is 3 of 3 DOWN at every window from 1m through 4h — 18 of 18 down moves across 6 windows, no flips. Median walk deepens -64.0 → -72.0 → -80.5 → -88.0 → -99.7 pips through 1h before softening back to -93.5p at 4h. Big-beat (n=6) hits double unanimity at 5m and 15m (6/6 up) but breaks at 30m (2 flips, both driven by 2021-07-15 print firing on a CAD-side energy-price headwind day). Third pair after NZDUSD (2026-08-06) and NZDJPY (2026-09-04) — NZDCAD's miss-side persistence is the tightest in the family, and 1h peak magnitude -99.7p is 27% deeper than NZDJPY's 4h peak.Wednesday 14:00 UTC — the Bank of Canada rate-decision slot — cracks the top-20 loudest weekday half-hours of 26 of 28 liquid FX pairs, median rank #13. Every one of the 28 pairs has it inside the top-30 (28/28 = 100%). Loudest central-bank decision slot in the calendar — BoC is the only major CB whose decision fires INSIDE the natural US-morning loud window rather than fighting a dead cell.Wed 14:00 UTC — the BoC rate-decision slot — ranks in the top-20 loudest weekday half-hours of 26 of 28 liquid FX pairs, median rank #13, mean 13.9. USDCAD (the pair most directly affected) sits at #14; EURUSD at #8; every single one of the 28 pairs has it inside the top-30 (100%). Contrast this week's other CB-slot posts: Thu 12:00 UTC BoE cracked top-20 for just 1 pair (median #42), Wed 18:00 UTC FOMC 0 pairs top-20 (median #108), Tue 03:30 UTC RBA 0 pairs top-100 (median #194). BoC is the only major central-bank decision slot that fires INSIDE the natural US-morning loud window (14:00 UTC = 10:00 ET) rather than fighting a dead cell; every other major CB is either 30 min before, 5 hours after, or in the Tokyo lunch vacuum.Statistics for Traders #36: LDA (linear discriminant analysis) posterior-probability classifier on the same UK Core CPI × GBPCHF 6-window response panel Stats #34/#35 used. LOO accuracy 42.86% (84/196), +6.13 pp over Stats #35's 1D nearest-centroid (36.73%), but big_miss recall is ZERO (0/13) — LDA collapses the tail buckets into their adjacent mid-buckets because the small tail priors (6.6% / 7.7%) can't compete with the log-prior intercept from the mid-bucket centroids.Direct next-step extension of Stats #35 (1D canonical discriminant direction, 36.7% LOO nearest-centroid) — full 5-class Fisher LDA classifier on the 6-window UK Core CPI × GBPCHF response panel (n=196). Full-sample accuracy 49.49% (97/196), LOO-CV 42.86% (84/196), vs 31.63% majority-class baseline. Big_miss recall is ZERO (0/13) — every true-big-miss prints get predicted as small_miss (8×), in_line (2×), small_beat (2×), or big_beat (1×). Root cause: small tail priors (6.6% and 7.7%) get crushed by the log-prior intercept penalty (~1.4 nat handicap vs adjacent mid-bucket priors 27%). Cross-verified vs sklearn.discriminant_analysis.LinearDiscriminantAnalysis to full agreement. Closes yesterday's queued LDA follow-up item on Stats #35.Paper Trail #36: Equilibrium and Welfare in Markets with Financially Constrained Arbitrageurs (Gromb & Vayanos, 2002) — the paper that added the WELFARE layer on top of the arbitrageur-capital constraint of PT #33 SV 1997, showing that arbitrageurs' positions can fail to be socially optimal (Prop 3) and characterizing when they take too much vs too little risk (Prop 4-5). Closes the 4-paper limits-to-arbitrage arc PT #32/#33/#34/#35 with the welfare-theoretic tier.The paper that formalized WELFARE analysis on top of the arbitrageur-capital constraint mechanism PT #33 Shleifer-Vishny 1997 introduced. Multi-period model with 3 agent types (arbitrageurs + segmented A-investors + B-investors) and no-cross-margining constraint on 2 collateral accounts. Main result (Proposition 3): the arbitrageurs' period-0 position may fail to be socially optimal — sometimes too much risk, sometimes too little. Certainty case (Prop 4): Ψ_i > 0 always, planner cannot Pareto-improve. Uncertainty case (Prop 5): sign flips with calendar-time interval Θ and liquidity parameter s. Closes 4-paper limits-to-arbitrage arc PT #32/#33/#34/#35 with the welfare-theoretic tier — GV 2002 sits chronologically between SV 1997 and BP 2009 but was covered last because it's the pure-theory welfare layer.Japan Prelim GDP q/q on USDJPY: all 4 big-miss prints sent USDJPY DOWN at 15m, 30m, 1h, AND 4h — JPY STRENGTHENS on bad Japan-GDP news, the SAFE-HAVEN PARADOX. But SMALL-miss prints go the OTHER way — 62.5% send USDJPY UP through 30m (textbook JPY-weakens-on-softer-Japan-data). Bucket-boundary sign inversion: below big-miss threshold, safe-haven flow flips the sign; above it, currency fundamentals hold. First-ever USDJPY × JPY Prelim GDP anchor.63 non-contaminated Japan Prelim GDP q/q releases on USDJPY. Big-miss (n=4) is 4 of 4 DOWN at 15m/30m/1h/4h — quadruple-window safe-haven unanimity where BAD Japan-GDP news STRENGTHENS the yen (median walk deepens -6.4 → -10.15 → -13.25 → -11 pips through 4h). BUT small-miss (n=16) goes the OTHER way — 62.5% send USDJPY UP through 30m (textbook JPY-weakens-on-Japan-fundamentals). This is a THRESHOLD effect: only surprises large enough to trigger risk-off flow generate the safe-haven bid. 2014-11-16 (Japan recession confirmed) is the pedagogic gem: fake-out +26.7p at 1m, full flip to -78.7p at 4h. Cross-JPY-family: 5 of 7 JPY-crosses post 100% big-miss safe-haven unanimity — only EURJPY and CHFJPY (safe-haven-vs-safe-haven pairs) break the unanimity by one print. First-ever USDJPY × Japan Prelim GDP anchor.New Zealand CPI q/q on NZDJPY: 3 of 3 big-miss prints DOWN AND 6 of 6 big-beat prints UP at 15 minutes — DOUBLE tail unanimity, and the full 5-bucket median walk is near-monotonic (-66.6 / -22.0 / +4.8 / +17.5 / +20.0 pips). First-ever NZDJPY × NZ CPI anchor, second pair in the NZ CPI cross-family.63 non-contaminated New Zealand CPI q/q releases on NZDJPY. At 15 minutes: big_miss (n=3) is 3/3 DOWN (100%) AND big_beat (n=6) is 6/6 UP (100%). The 15m median walk (-66.6 / -22.0 / +4.8 / +17.45 / +20.0 pips) and pct-up walk (0 / 17.6 / 57.1 / 93.8 / 100.0%) are near-monotonic across all 5 surprise buckets. The double unanimity HOLDS at 1m, 15m, AND 1h; miss side deepens to -78p at 4h while beat side softens to +16p. First-ever NZDJPY × NZ CPI News Impact anchor, second pair after nzd-cpi-nzdusd-tails (2026-08-06).Tuesday 03:30 UTC — the RBA Cash Rate decision slot — doesn't crack the top-100 loudest weekday half-hours of ANY of the 28 liquid FX pairs. Even AUDUSD has it at only rank 138/240. Median rank across pairs is 194.5 (81st percentile of QUIETNESS). Deadest central-bank slot in the whole calendar.Tue 03:30 UTC (RBA Cash Rate slot, 11x/year) ranks 120-226 across all 28 liquid FX pairs — 0 pairs crack top-100. Best-ranked is AUDJPY at rank 120/240; AUDUSD itself is at rank 138. Median rank across pairs is 194.5 — the RBA slot sits at the 81st percentile of QUIETNESS. Compare to yesterday's Thu 12:00 BoE (median rank 42, 19/28 top-50) and Tue's Wed 18:00 FOMC (median rank 108, 9/28 top-100). 27/28 pairs have RBA quieter than FOMC; 28/28 have RBA quieter than BoE. Direct density is higher than both (RBA 21%, BoE 15%, FOMC 15%) — the neighbor-cell floor explains the ranks.Statistics for Traders #35: Canonical discriminant direction on yesterday's Stats #34 MANOVA panel — Roy's largest root (λ_1 = 0.528, 81% of trace) is dominated by the 1-minute window (standardized loading +0.058) with a smaller counter-weight at 30 min (+0.030); all other windows load near zero. The multivariate discriminant COLLAPSES onto the 1-minute move.Direct follow-up to Stats #34 MANOVA on the same 196-release UK Core CPI × GBPCHF 6-window panel. Canonical discriminant on Roy's largest root (λ_1 = 0.528, 81% of Hotelling-Lawley trace) has standardized loadings 1m +0.058 / 5m -0.004 / 15m -0.018 / 30m +0.030 / 1h -0.004 / 4h -0.002 — the 1-minute window carries almost all the discriminant weight. Structure coefficients tell a different story (0.98 / 0.88 / 0.85 / 0.88 / 0.73 / 0.48) — every window individually correlates highly, but suppression drops most of them to zero-loading in the multivariate combination. Group centroids on the canonical axis (big_miss -0.73, small_miss -0.91, in_line +0.03, small_beat +0.65, big_beat +1.36) span 2.08 SD units tail-to-tail — 38% larger than yesterday's Stats #30 Cohen's d of 1.51 on the sibling GBPUSD sample. Leave-one-out nearest-centroid classifier hits 36.7% accuracy vs 20% uniform baseline (1.84x chance).Paper Trail #35: Liquidity and Leverage (Adrian & Shin, 2010) — the paper that empirically validated yesterday's PT #34 Brunnermeier-Pedersen funding-liquidity theory on US broker-dealer balance-sheet data: leverage growth regressed on asset growth hits R²=62% across 5 major investment banks 1993-2008, and dealer repo growth forecasts VIX volatility risk premium at R²=41% one week ahead.Adrian & Shin (2010) 'Liquidity and Leverage', Journal of Financial Intermediation 19(3):418-437. NY Fed Staff Report #328 (May 2008, revised Dec 2010). Full primary source verified via WebFetch + pymupdf on 2026-09-04 (39 pages, 57,767 chars). Documents strongly procyclical marked-to-market leverage on 5 US investment banks 1993-2008 (Bear Stearns, Goldman, Lehman, Merrill, Morgan Stanley). Table 3 leverage panel regression: change_in_leverage ~ total_asset_growth coefficient +0.83 (p=0.00), R²=62% with 5-bank fixed effects. Table 5: dealer repo growth forecasts VIX innovation R²(adj) = 9.0%, and forecasts volatility risk premium at R²(adj) = 41.0% one week ahead. Directly cites PT #33 Shleifer-Vishny 1997 and PT #34 Brunnermeier-Pedersen 'margin spiral' terminology. Empirical validation tier of the 4-paper limits-to-arbitrage arc PT #32/#33/#34/#35.AU Trimmed Mean CPI q/q on AUDJPY: all 5 big-miss prints sent AUDJPY DOWN AND all 4 big-beat prints sent it UP — DOUBLE tail unanimity that HOLDS at 1m, 5m, 15m, 30m, AND 1h. Quintuple-window persistence beats yesterday's AUDCHF sibling (4-window). First-ever AUDJPY × Trimmed Mean CPI anchor, third pair in the Trimmed Mean CPI cross-family.67 non-contaminated Australia Trimmed Mean CPI q/q releases on AUDJPY. At 1m / 5m / 15m / 30m AND 1h: big_miss (n=5) is 5/5 DOWN (100%) AND big_beat (n=4) is 4/4 UP (100%) — quintuple-window DOUBLE tail unanimity. Beats yesterday's AUDCHF sibling by one full window (AUDCHF broke at 1h on the 2020-07-29 COVID print; on AUDJPY that print held its down direction as JPY safe-haven bid reinforced AUD selling). 15m median walk -24.0 / -26.75 / -1.2 / +32.7 / +13.2 pips; small_miss > big_miss AND small_beat > big_beat inversions come from COVID-era prints. Third pair after AUDUSD (2026-08-04) and AUDCHF (2026-09-03) — AUDJPY wins the persistence crown.UK Core CPI on GBPCHF: 14 of 15 big-beat prints sent GBPCHF up at 15m (93.3%) — and the 93.3% up-rate HOLDS at 5m, 15m, 30m, AND 1h. First-ever GBPCHF × UK Core CPI anchor, seventh and final leg closing the 7-pair GBP-cross family.198 non-contaminated UK Core CPI y/y releases 2010-01-19 through 2026-06-17 on GBPCHF. Big-beat 14/15 up (93.3%) at every window from 5 minutes through 1 hour — quadruple-window persistence on the same 15-print membership. The one counter-directional print is 2017-06-13 (UK hung-parliament week), the same print that flipped on GBPCAD and GBPJPY. Miss side is the family's messiest (only 66.7% down at 15m) with 5 boundary-z / COVID counter-directional prints. Seventh and final leg of the GBP-cross family — full 7-pair coverage now complete.Thursday 12:00 UTC — the BoE decision slot — cracks the top-50 loudest weekday half-hours of 19 of 28 liquid FX pairs (median rank 42), and EURGBP has it at rank 20. Yesterday's Wed 18:00 FOMC slot cracked top-50 for just 1 pair. Same 8-per-year cadence, opposite loudness — neighboring-slot bleed is the mechanism.Thu 12:00 UTC (BoE Bank Rate slot) ranks 20-83 across all 28 liquid FX pairs — 19 of 28 crack top-50, with EURGBP the only pair in top-20 (rank 20/237). Wed 18:00 UTC (FOMC slot, DST) ranks 46-168 — 0 pairs top-20, 1 pair top-50 (USDCAD at 46). Both slots fire the same 8x/year. The 62-position mean rank gap is explained by neighboring-slot bleed: BoE 12:00 UTC sits 30 min before the US 12:30 UTC macro window opens; FOMC Wed 18:00 UTC sits in a 5h dead zone between the last US macro (14:30) and Tokyo open (00:00). Direct sibling to yesterday's Wed 18:00 FOMC-blank post.Statistics for Traders #34: MANOVA on today's slot-1 UK Core CPI × GBPCHF 6-window response panel — Wilks' Λ = 0.5810 (Rao's F = 4.56 on df = (24, 650), p = 9.7×10⁻¹²), all four multivariate test statistics reject H₀ at p < 10⁻⁹, natural next step after Stats #24 one-way ANOVA and Stats #29 two-way factorial ANOVAMANOVA extends Stats #24's one-way ANOVA from a scalar response (move_pips at one window) to a p-dimensional response vector (move_pips at all 6 windows). Worked end-to-end on today's slot-1 sample. Panel: n=196 releases intersected across 1m/5m/15m/30m/1h/4h; response = signed move_pips vector; factor = 5 surprise buckets. Four multivariate test statistics: Wilks Λ = 0.581 (Rao's F = 4.56 on df=(24, 650), p = 9.7×10⁻¹²), Pillai V = 0.460, Hotelling-Lawley = 0.652, Roy's largest root = 0.528. All four reject H₀ at p < 10⁻⁹. Per-window univariate η² peaks at 33.1% at 1m, softens to 8.3% at 4h — the multivariate test pools cross-window covariance the one-at-a-time ANOVAs discard.Paper Trail #34: Market Liquidity and Funding Liquidity (Brunnermeier & Pedersen, 2009) — the paper that formalized the AMPLIFIER on top of yesterday's Shleifer-Vishny 1997 arbitrageur-capital constraint, deriving the two liquidity spirals (loss spiral + margin spiral) that turn small funding shocks into full liquidity crisesMarkus K. Brunnermeier (Princeton) and Lasse Heje Pedersen (NYU), Review of Financial Studies 22(6):2201-2238. Direct successor to yesterday's PT #33 (Shleifer-Vishny 1997) and PT #32 (DSSW 1990) — cites both explicitly on page 3. Where SV 1997 said arbitrageurs bail out AT THE WORST TIME, BP 2009 said this bail-out feeds back through TWO amplifying spirals: a LOSS SPIRAL (initial losses → reduced funding → further losses) and a MARGIN SPIRAL (higher price volatility → higher margins → forced deleveraging → higher volatility). The 6 propositions of the paper unify 5 stylized facts of market liquidity that had accumulated as separate empirical puzzles.AU Trimmed Mean CPI q/q on AUDCHF: all 5 big-miss prints sent AUDCHF DOWN AND all 4 big-beat prints sent it UP — DOUBLE tail unanimity that HOLDS at 1m, 5m, 15m, AND 30m. First-ever AUDCHF anchor for the RBA's preferred inflation gauge, second post in the Trimmed Mean CPI series.67 non-contaminated Australia Trimmed Mean CPI q/q releases 2010-01-27 through 2026-06-24 on AUDCHF. At 1m/5m/15m/30m: big_miss (n=5) is 5/5 DOWN (100%) AND big_beat (n=4) is 4/4 UP (100%) — quadruple-window DOUBLE tail unanimity. The 15m pct-up walk (0 / 17 / 52 / 80 / 100%) is perfectly monotonic across all 5 buckets. Median walk 15m: -28.0 / -19.4 / +0.3 / +19.0 / +11.1 pips. Coin-flip null probability of the double unanimity is 1/512 = 0.20%; quadruple-window replication adds multiplicative-under-independence bound (correlation-inflated). Second post in the Trimmed Mean CPI series after aud-trimmed-mean-cpi-audusd (2026-08-04).UK Core CPI on GBPJPY: 13 of 15 big-beat prints sent GBPJPY up at 15m (86.7%) — and at 5 minutes the big-beat bucket is 15 of 15 UP (100%). First-ever GBPJPY × UK Core CPI anchor, sixth cross-family leg with 5m unanimity.198 non-contaminated UK Core CPI y/y releases 2010-01-19 through 2026-06-17 on GBPJPY. At 5 minutes: 15 of 15 big-beat prints sent GBPJPY UP (100% unanimous, coin-flip null p = 0.003%) AND 13 of 15 big-miss prints sent it down (86.7%). At 15m: 13/15 big-beat up (86.7%). Big-beat median walk +22.2p at 5m holds +17-32p at every window from 1m through 4h; pct_up stays at 86.7% or higher at 1m/5m/15m/30m/1h. Miss side carries a small_miss > big_miss bucket-boundary artefact (same pattern as us-core-cpi-audusd 2026-08-23 and us-core-cpi-usdjpy 2026-08-31). SIXTH UK Core CPI cross-family leg — only GBPCHF remains.Wednesday 18:00 UTC — the FOMC-decision slot — doesn't crack the top-20 loudest weekday half-hours of any of the 28 liquid FX pairs. Best rank is USDCAD at #46; median rank across pairs is #108/237 (middle of the pack). Dilution by non-FOMC Wednesdays is the mechanism.8 FOMC decisions per year × ~15.7 years = ~126 releases get diluted into ~750 Wednesday half-hour observations per pair. Median weekly range of Wed 18:00 UTC cells is dominated by the 84% of non-FOMC Wednesdays — no scheduled US data at that hour, quiet pre-close. Result: 0 of 28 pairs have Wed 18:00 UTC in their top-20 loudest weekday cells. 0 of 28 in top-10. Only 1 pair (USDCAD, rank 46) in top-50. Median rank across pairs: 108 of 237 (45.6%ile — middle of the pack). Wed 19:00 UTC (the standard-time FOMC slot) is even weaker.Statistics for Traders #33: Sample co-kurtosis on today's slot-1 UK Core CPI × GBPJPY sample — Y has heavy marginal excess kurtosis (+1.36, z=+3.92) but excess co-kurtosis after correlation is kappa_{X²Y²} = -0.027 (essentially zero), and the mid-buckets carry the fat tails not the tail-bucketsFourth cumulant follow-up to yesterday's Stats #32 co-skewness. Same event class (UK Core CPI), different pair (GBPJPY not GBPCAD), same sample size (n=198). Marginal excess kurtosis γ_2(Y) = +1.36 (z=+3.92, strongly non-Gaussian). But excess co-kurtosis after removing the correlation component is kappa_{X²Y²} = -0.027 (essentially zero — the joint tails are Gaussian conditional on ρ). Bucket-conditional kurtosis reveals the FAT TAILS live in mid-buckets: in_line +1.14, small_miss +1.09; tail-buckets are near-Gaussian. Same 'outliers land where you don't expect' pattern as Stats #6. Practical: co-kurtosis does NOT add tradeable signal here, unlike Stats #32 co-skew which did.Paper Trail #33: The Limits of Arbitrage (Shleifer & Vishny, 1997) — the direct theoretical successor to yesterday's DSSW 1990 that added performance-based capital constraints and showed arbitrageurs bail out EXACTLY when mispricing is deepest, formalizing the 'markets can stay irrational longer than you can stay solvent' logicThe 1997 Journal of Finance paper that gave 'limits of arbitrage' its name. Direct successor to yesterday's PT #32 DSSW 1990: where DSSW modeled noise-trader-risk-as-priced-risk, SV 1997 added performance-based capital constraints on arbitrageurs (eq. 6: F_2 = F_1 - a·D_1·(1 - P_2/P_1)). Key mechanism: when noise-trader sentiment deepens further, arbitrageur loses money, INVESTORS WITHDRAW CAPITAL, and arbitrageur has LESS resources at PRECISELY THE MOMENT the mispricing is deepest. Numerical example (V=1, F_1=0.2, a=1.2, S_1=0.3, S_2=0.4) shows p_1 = 0.9 and p_2 = 0.7636 when sentiment worsens — arbitrageur bailing out amplifies the mispricing. Directly predicts persistence of specialist-market anomalies (momentum, PEAD, value-vs-glamour) and organizes the LTCM 1998 collapse a year later.AU Unemployment Rate on GBPAUD: 8 of 8 big-miss prints sent GBPAUD UP at 15 minutes (100% unanimous) — AND the 100% up-rate HOLDS at every window from 1 minute through 4 hours. First-ever GBPAUD × AU Unemployment anchor, DOUBLE the median magnitude of yesterday's EURAUD post.199 non-contaminated Australia Unemployment Rate releases 2010-01-14 through 2026-08-20 on GBPAUD. All 8 big-miss prints (higher-than-expected unemployment = AUD-weak) sent GBPAUD UP at 15 minutes (100% unanimous, p = 0.4%). The 100% up-rate HOLDS across every window from 1m through 4h — the same 8 prints held sign for the full 4-hour horizon over 15 years. Median big-miss walk +52.7 / +59.9 / +63.8 / +69.3 / +55.8 / +60.6p across 1m/5m/15m/30m/1h/4h. FOURTH cross-family leg, DOUBLE the magnitude of yesterday's aud-unemployment-euraud-100pct-miss (+40.2p 15m median).UK Core CPI on GBPCAD: 13 of 15 big-miss prints sent GBPCAD down at 15m (86.7%), 13 of 15 big-beat prints sent it up (86.7%) — and at 5 minutes the big-beat bucket is 15 of 15 UP (100%). First-ever GBPCAD × UK Core CPI anchor, fifth cross-family leg with 5m unanimity.198 non-contaminated UK Core CPI y/y releases 2010-01-19 through 2026-06-17 on GBPCAD. At 5 minutes: 15 of 15 big-beat prints sent GBPCAD UP (100% unanimous, coin-flip null p=0.003%). At 15m: 13/15 big-beat up (86.7%), 13/15 big-miss down (86.7%). Median walk PERFECTLY MONOTONIC across all 5 buckets: -18.9 / -13.6 / +0.5 / +6.0 / +20.0p. Pct-up walk PERFECTLY MONOTONIC: 13.3 / 28.3 / 51.6 / 71.7 / 86.7%. Beat side HOLDS +20-24p at every window from 5m through 4h. FIFTH UK Core CPI cross-family leg (after GBPUSD / EURGBP / GBPNZD / GBPAUD).All 7 USD-major pairs cluster their loudest 5 weekday half-hours inside Tue-Fri 12:30-14:30 UTC — 35 of 35 top-5 cells sit in the US-morning window (100%), closing the 7-day cross-family arc at 238 of 245 (97.1%) — and Fri 13:30 UTC (the NFP slot) is the loudest cell only for USDCADFresh /api/v1/calm-zones/scan for each of EURUSD, GBPUSD, USDJPY, USDCHF, AUDUSD, NZDUSD, USDCAD. All 7 pairs have all 5 of their top-5 loudest weekday half-hours inside the Tue-Fri 12:30-14:30 UTC US-morning window. Zero outliers. USD-majors join CHF-crosses and GBP-crosses as the third currency family with 100% concentration — the 7th and final cross-family generalisation post. Novel finding: Fri 13:30 UTC (the NFP release half-hour) is the LOUDEST cell only for USDCAD. Every other USD-major has Thu 13:30 UTC (weekly jobless claims) or Fri 14:00 UTC beating NFP. Highest family loudest/typical ratio yet: 1.95x. Zero FOMC-decision cells (Wed 18:00 UTC) in any pair's top-20 — same sparse-domestic-calendar averaging as JPY/CHF/AUD/NZD.Statistics for Traders #32: Sample co-skewness on today's slot-1 UK Core CPI × GBPCAD sample — the aggregate Harvey-Siddique β_SKD is only +0.09 (small), but the bucket-conditional skewness of move_pips is +1.14 in big_beat and +0.58 in big_miss — asymmetric fat tails IN THE DIRECTION OF THE SURPRISE that correlation and aggregate co-skew both missSample co-skewness worked end-to-end on today's slot-1 UK Core CPI × GBPCAD 15m sample (n=198). Correlation ρ(X,Y) = +0.508 explains 25.8% of Y variance linearly. Higher-moment cumulants: aggregate Harvey-Siddique β_SKD = γ_{X²Y} = +0.090 is small; γ_{XY²} = +0.015 is essentially zero. But bucket-conditional skewness of move_pips is +1.14 in big_beat (n=15), +0.58 in big_miss (n=15), +0.56 in small_beat, -0.73 in small_miss — asymmetric fat tails IN THE DIRECTION OF the pair's response, hidden by aggregate averaging. All numbers cross-verified via numpy 2.4.6 + scipy 1.17.1.Paper Trail #32: Noise Trader Risk in Financial Markets (De Long, Shleifer, Summers & Waldmann, 1990) — the foundational limits-to-arbitrage paper that showed noise-trader-generated risk can push prices persistently below fundamental values AND let noise traders earn higher expected returns than the arbitrageurs betting against themThe 1990 JPE paper that formalized 'noise trader risk' — the risk that noise traders' beliefs become MORE mispriced before reverting. Overlapping-generations model with CARA utility yields a pricing function (eq. 12) with a NEGATIVE noise-trader-risk term that persists even when noise traders are unbiased on average. Four effects (hold-more +, price-pressure -, Friedman -, create-space +) determine whether noise traders earn positive excess return; requires p* > 0. Directly organizes four anomalies: excess volatility (Shiller 1981), mean reversion (Fama-French 1988b), closed-end fund discounts (Malkiel 1977), and the Mehra-Prescott equity premium.AU Unemployment Rate on EURAUD: 8 of 8 big-miss prints sent EURAUD UP at 15 minutes (100% unanimous) — AND the 100% up-rate HOLDS at every window from 1 minute through 4 hours. First-ever EURAUD × AU Unemployment anchor.199 non-contaminated Australia Unemployment Rate releases 2010-01-14 through 2026-08-20 on EURAUD. Big-miss unanimity is the story: 8 of 8 big-miss prints sent EURAUD UP at 1m, 5m, 15m, 30m, 1h AND 4h — the same 8 prints hold sign across all 6 windows over 14 years of coverage. Median walk PERFECTLY MONOTONIC across all 5 buckets at 15m: +57.8 / +30.4 / +0.5 / -21.15 / -40.20p. Pct-up walk PERFECTLY MONOTONIC: 100.0 / 72.7 / 50.0 / 31.2 / 27.8%. Big-beat n=18 is 72.2% down at 15m; strip 4 COVID-era and small-magnitude counter-directional prints and 14/14 = 100% down.US Core CPI m/m on USDJPY: 42 of 54 small-miss prints sent USDJPY down at 15 minutes (77.8%), 25 of 40 small-beat prints sent it up (62.5%), and the miss-vs-beat directional gap holds cleanly through 1 hour on 198 non-contaminated releases — first-ever USDJPY × US Core CPI anchor198 non-contaminated US Core CPI m/m releases on USDJPY across 6 windows. At 15 minutes the miss side (n=71) is 22-24% up on both small-miss (n=54) and big-miss (n=17); the beat side (n=50) is 60-63% up on both small-beat (n=40) and big-beat (n=10). Same directional split holds through 1 hour. Bucket-boundary artefact on the tails: small-miss median (-8.6p) is DEEPER than big-miss (-6.5p) at every window through 1h — same inversion pattern as us-core-cpi-audusd-beat-monotonic (2026-08-23), the sister US Core CPI post 8 days ago. First-ever USDJPY × US Core CPI anchor.All 7 GBP-crosses cluster their loudest 5 weekday half-hours inside Tue-Fri 12:30-14:30 UTC — 35 of 35 top-5 cells sit in the US-morning window (100%), GBP-crosses join CHF-crosses as the 2nd currency family with 100% concentration, and Tuesday is entirely absent from any pair's top-5Fresh /api/v1/calm-zones/scan for each of GBPUSD, GBPJPY, GBPCHF, GBPCAD, GBPAUD, GBPNZD, EURGBP. All 7 pairs have all 5 of their top-5 loudest weekday half-hours inside the Tue-Fri 12:30-14:30 UTC US-morning window. Zero outliers. GBP-crosses become the second currency family with 100% concentration after CHF-crosses (2026-08-27) — the 6th and final major-family generalisation post extending JPY (33/35) → CHF (35/35) → AUD (33/35) → NZD (33/35) → EUR (34/35) → GBP today (35/35). Novel finding: GBP-crosses have ZERO Tuesdays in top-5 (matching CHF), and the 12:30 UTC slot hits 6 times (highest of any family). Only USD-majors remain for future cross-family coverage.Statistics for Traders #31: Rolling-window Politis-White b_opt on the same NFP × USDJPY series Stats #16 used — the whole-sample b_opt of 4.70 hides regime-dependent block lengths that span 1.38 to 20.29 across 10 rolling 100-release windows, and the 2012-2014 taper-tantrum window picks m̂=8 vs m̂=1 for the pre-2012 and post-2015 windowsThe queued 'is the block length stable across the sample?' question flagged in Stats #16 (2026-08-16, 15 days ago) — worked end-to-end via rolling-window Politis-White 2004 b_opt on the same 196-release NFP × USDJPY 15m |move_pips| series. Whole sample: b_opt = 4.70 (matches Stats #16's 4.98 within rounding). Rolling 100-window step-10 b_opt: spans 1.38 to 20.29 (14.7x range), with a clean 3-regime pattern: 2010-2011 starts ~1.5, 2012-2014 taper-tantrum starts ~19, 2015-2017 recovery starts ~10. The m̂ selector jumps from 1 to 8 back to 4 across the same regimes. b_opt is NOT stable, and the whole-sample number is a regime-weighted average that hides 10x variation.Paper Trail #31: Capital Investments and Stock Returns (Titman, Wei & Xie, 2004) — the direct primary source of the CMA investment factor in FF 2015 (PT #22), on a 58,880 firm-year sample the paper documents a CI-spread of 0.168% per month that is positive in 15 of 17 non-hostile-takeover years and NEGATIVE in every one of the 1984-1989 hostile-takeover yearsSheridan Titman, K.C. John Wei, Feixue Xie (2004), Journal of Financial and Quantitative Analysis 39(4) pp. 677-700. Sample: 58,880 industrial firm-years, Compustat + CRSP, Jul 1973–Jun 1996. CI = current year capex/sales divided by 3-year average. Long lowest-two-CI quintiles, short highest-two-CI quintiles = 0.168% per month excess return (p<0.01). 5-year raw returns walk monotonically 81.53% → 114.50% → 132.85% → 145.64% → 153.77% across quintiles — firms that invest MOST subsequently earn LEAST. Effect vanishes during hostile-takeover era 1984-1989 (takeover pressure disciplines empire building) and strengthens with cash flow / falls with debt. Direct primary source of the CMA investment factor in FF 2015 (PT #22, 2026-08-22) and of the asset-growth anomaly that Cooper-Gulen-Schill 2008 (PT #26, 2026-08-26) extends. Full primary source verified via NBER working paper 9951.Australia CPI m/m on AUDUSD: at 5 minutes the big-miss bucket (n=4) is 0 of 4 up (100% down) AND the big-beat bucket (n=7) is 7 of 7 up (100%) — DOUBLE tail unanimity, and both bucket-tail readings hold monotonically through 1 hour67 non-contaminated releases of Australia's monthly ABS CPI series (started September 2022) on AUDUSD. At 5 minutes: 0 of 4 big-miss prints sent AUDUSD up (100% down), 7 of 7 big-beat prints sent it up (100% up) — DOUBLE bucket-tail unanimity. The miss side stays 0/4 at every window from 5 minutes through 4 hours; the beat side amplifies to +35.00p median at 4h. The 5-bucket walk at 15m is perfectly monotonic on both median AND pct-up. First-ever Australia CPI m/m News Impact anchor. Small-sample caveat: joint 4-and-7 unanimity clears p<0.01 under coin-flip null.US CPI m/m on GBPUSD: 12 of 13 big-miss prints sent GBPUSD up (92.3%), 11 of 15 big-beat prints sent it down at 15m — and by 4 hours the big-beat median FLIPS SIGN from -6.4p to +5.4p while the big-miss side holds +21.8p at 92.3% up196 non-contaminated US CPI m/m releases on GBPUSD, 15-minute window. Big-miss (n=13) 12 up 1 down (92.3%), big-beat (n=15) 11 down 4 up (26.7% up). Median walk +18.5 / +4.65 / +4.60 / -5.70 / -6.40 pips — near-monotonic. Pct-up walk 92.3 / 63.8 / 58.7 / 40.0 / 26.7% — near-monotonic. First-ever GBPUSD × US CPI m/m News Impact anchor. The asymmetric-persistence angle: miss side holds through 4 hours (+21.8p, 92.3% up), beat side FLIPS SIGN by 4 hours from -6.4p to +5.4p — same 4h beat-side reversal shape as the XAUUSD post 13 days ago (2026-08-17), only quieter.All 7 EUR-crosses cluster their loudest 5 weekday half-hours inside Tue-Fri 12:30-14:30 UTC — 34 of 35 top-5 cells sit in the US-morning window, and EUR-crosses are uniquely Wednesday-dominant (19 Wed / 13 Thu / 2 Tue / 0 Fri) with ZERO Fridays anywhere in the top-20Fifth cross-family Calm Zones post, closing the arc that ran JPY (2026-08-26), CHF (2026-08-27), AUD (2026-08-28), NZD (2026-08-29). 34 of 35 EUR-cross top-5 cells (97.1%) fall inside Tue-Fri 12:30-14:30 UTC — matching every other family. But EUR-crosses are unique on day-of-week: 19 of 34 in-window cells are Wednesday (vs 15 Fri and 13 Thu each for AUD/NZD families), and ZERO cells are Friday. The one outlier is EURNZD Mon 14:30 UTC — still a 14:30 UTC US-macro slot, just on Monday.Statistics for Traders #30: Cohen's d on today's slot-1 US CPI × GBPUSD sample — big_miss vs in_line is d = +1.13 (LARGE by Cohen 1988), big_beat vs in_line is only d = -0.56 (MEDIUM), and the miss-side effect is 2× the beat-side effect in effect-size languageCohen's d worked end-to-end on today's slot-1 US CPI m/m × GBPUSD 15m sample (n=196). Pairwise bucket-vs-in_line d values: big_miss +1.13, small_miss +0.45, small_beat -0.71, big_beat -0.56 — asymmetric even in standardized-mean-difference language (miss side ~2× the beat side). Tail-to-tail d = +1.51 (VERY LARGE). Small-sample Hedges' g corrections shrink d by 0.9-2.9%. Cohen 1988 conventions: |d| < 0.2 negligible, 0.2 small, 0.5 medium, 0.8 large — so miss-side is unambiguously large; beat-side sits at the medium/large boundary.Paper Trail #30: Discount Rates (Cochrane, 2011) — the AFA presidential address that shifted asset pricing's central question from 'test market efficiency' (Fama 1970) to 'why do discount rates vary?', named the 'zoo of new factors' problem, and showed that 100% of P/D-ratio variation is expected-return variation (β = 1.01, direct 15-year regression) rather than the expected-cashflow-variation the 1970s literature assumedJohn H. Cochrane's 2011 Journal of Finance presidential address (Vol. 66 No. 4 pp. 1047-1108) — the theoretical umbrella over the 4-factor vs 5-factor debate PT #22 flagged. Central claim: 'We thought returns were uncorrelated over time, so variation in price-dividend ratios was due to variation in expected cashflows. Now it seems all price-dividend variation corresponds to discount-rate variation.' Table 2 direct 15-year regression: β(returns) = 1.01, β(dividends) = -0.11 — 'What we expected to be 0 is 1; what we expected to be 1 is 0'. Explicit successor to PT #4 Fama 1970 EMH. Full primary source verified via WebFetch + pymupdf on 2026-08-30 (58 pages, 134,865 chars text-native). 22nd PT out of 30 with full primary-source access.AUD Employment Change on EURAUD: 22 of 26 big-beat prints sent EURAUD down (84.6%), median walk +30.4 / +38 / +1 / -28 / -57 pips — first-ever EURAUD News Impact anchor, and the SEVENTH AND FINAL cross closing the 7-pair AUD-Employment cross-family (AUDUSD / AUDJPY / AUDNZD / AUDCHF / AUDCAD / GBPAUD / EURAUD)199 non-contaminated AUD Employment Change releases on EURAUD, 15-minute window. Big-miss (n=9) 7 up 1 down 1 flat (77.8%), big-beat (n=26) 22 down 4 up (15.4% up). Median walk +30.4 / +38.0 / +1.0 / -28.05 / -56.9 pips — near-monotonic with the same small_miss > big_miss bucket-boundary artefact seen yesterday on GBPAUD. Big-beat side is the loudest of the entire AUD-Employment cross-family: median -56.9p at 15m holds through 4 hours at -55.6p. First-ever EURAUD News Impact anchor, and the seventh and final leg of the AUD-Employment cross-family.Canada CPI m/m on AUDCAD: 12 of 13 big-miss prints sent AUDCAD up (92.3%), 16 of 20 big-beat prints sent it down (80%), and the whole 5-bucket walk is monotonic on BOTH median AND pct-up — first-ever AUDCAD News Impact anchor, closes the 4-pair CAD-CPI cross-family195 non-contaminated Canada CPI m/m releases on AUDCAD, 15-minute window. Big-miss (n=13) 12 up 1 down (92.3%), big-beat (n=20) 16 down 4 up (80%). Median walk +10.4 / +8.2 / +0.5 / -7.35 / -13.45 pips — perfectly monotonic. Pct-up walk 92.3 / 73.9 / 50.0 / 31.3 / 20.0% — also perfectly monotonic. Both tails hold or amplify through 1 hour: big-miss median grows +10.4 → +19.7p (1.9× at 1h); big-beat holds -13.5 → -16.6p (1.2× at 1h). First-ever AUDCAD News Impact anchor, and the fourth CAD-CPI cross-family post — closes the CAD-CPI 4-cross family (CADJPY / EURCAD / USDCAD / AUDCAD).All 7 NZD-crosses cluster their loudest 5 weekday half-hours inside Tue-Fri 12:30-14:30 UTC — 33 of 35 top-5 cells sit in the US-macro window, and the 2 exceptions are both AUDNZD Wellington-morning cells (same outlier profile as the AUD-cross family)33 of 35 loudest-5 cells across NZDUSD, NZDJPY, NZDCHF, NZDCAD, AUDNZD, EURNZD and GBPNZD sit inside the Tue-Fri 12:30-14:30 UTC US-macro window. The 2 outliers are both AUDNZD: Wed 21:00 UTC (12.60p) and Fri 21:30 UTC (12.50p), Wellington-morning cells that also topped yesterday's AUD-cross family. Domestic-NZ slots (02:00 UTC RBNZ, 21:45 UTC NZ CPI, 22:45 UTC NZ Employment) contribute zero top-5 cells anywhere else in the family. Completes the 4-day JPY / CHF / AUD / NZD cross-family generalisation arc; 94.3% coverage matches the AUD family exactly.Statistics for Traders #29: Two-way ANOVA on today's slot-1 CAD CPI × AUDCAD (n=182 × 6 windows = 1092 obs) — bucket main effect F=59.7 (p=1.8×10⁻⁴⁵), window main effect F=0.13 (p=0.98), bucket × window interaction F=0.28 (p=0.999). The bucket-response shape is TIME-STABLE.Type-I two-way factorial ANOVA on the CAD CPI × AUDCAD bucket × window balanced-per-window panel (n=182 releases × 6 windows = 1092 observations). Bucket main effect: F(4, 1062) = 59.665, p = 1.75×10⁻⁴⁵ (η² = 18.26%). Window main effect: F(5, 1062) = 0.132, p = 0.98 (η² = 0.05%). Bucket × Window interaction: F(20, 1062) = 0.284, p = 0.999 (η² = 0.43%). The window main effect is null AND the interaction is null — meaning the 5-bucket surprise-response shape doesn't reshape across time windows. Bucket alone explains 18.26% of variance (matches Stats #24's 19.52% single-window ANOVA on the sibling USDCAD sample); the other 81% is within-bucket residual. Closes the queue item flagged in Stats #24 (2026-08-24) for a two-way generalisation. Cross-links today's Paper Trail #29 (Fisher 1918, the paper that coined 'variance' and 'analysis of variance').Paper Trail #29: The Correlation between Relatives on the Supposition of Mendelian Inheritance (Fisher, 1918) — the 108-year-old paper that coined the word 'variance', introduced the phrase 'analysis of variance', and gave every ANOVA (today's Stats #29 included) its founding partition-into-constituent-causes machineryR. A. Fisher's 1918 Transactions of the Royal Society of Edinburgh paper is the origin of the word 'variance' (verbatim: 'We shall term this quantity the Variance of the normal population to which it refers') and of the phrase 'analysis of variance' (Table of Contents § 21 heading). The paper reconciled Mendelian discrete inheritance with biometric continuous variation by showing many small-effect Mendelian factors produce approximate-normal continuous traits — but its longer-lasting contribution is the conceptual frame that a response's variability can be partitioned into fractions ascribable to independent constituent causes. That partition is the founding move of today's Stats #29 two-way ANOVA, and of every one-way / factorial / mixed-effects / R²-decomposition / path-analysis method that followed.UK Core CPI on GBPAUD: 14 of 15 big-beat prints sent GBPAUD up at 15m (93.3%), 13 of 15 big-miss prints sent it down (86.7%) — and at BOTH 5 minutes AND 30 minutes the big-beat bucket is 15 of 15 UP (100%). First-ever GBPAUD × UK Core CPI anchor.198 non-contaminated UK Core CPI y/y releases on GBPAUD, 15-minute window. Big-beat (n=15) 14 up 1 down (93.3%), big-miss (n=15) 13 down 2 up (86.7%). Median walk -23.0 / -15.3 / +3.05 / +8.1 / +21.0 pips — perfectly monotonic. Pct-up walk 13.3 / 24.5 / 54.8 / 73.6 / 93.3% — also perfectly monotonic. Double-window unanimity: at 5 minutes AND at 30 minutes the big-beat bucket is 15 of 15 UP (100%). The one down big-beat at 15m (2017-06-13) is UK-hung-parliament week and reverts back to up at 5m and 30m. Fourth UK Core CPI cross-family post — extends the ledger's tightest three-pair replication (GBPUSD 86.7% / EURGBP 86.7% / GBPNZD 86.7%) to a four-pair replication at 86.7-93.3%.Australia Employment Change on GBPAUD: 8 of 9 big-miss prints sent GBPAUD up (88.9%), 22 of 26 big-beat prints sent it down (84.6%), and the 88.9% miss-side up-rate HOLDS across every window from 1 minute through 1 hour — first-ever GBPAUD News Impact anchor, largest beat-side magnitude in the AUD-Employment cross-family199 non-contaminated Australia Employment Change releases on GBPAUD, 15-minute window. Big-miss (n=9) 8 up 1 down (88.9%), big-beat (n=26) 22 down 3 up 1 flat (84.6% strictly down). Median walk +39.7 / +45.6 / +0.3 / -33.4 / -67.2 pips — small bucket-boundary artefact at big_miss vs small_miss (medians swap because n=9 big_miss includes 2020-COVID-Q2 dampeners). Pct-up walk 88.9 / 87.2 / 50.6 / 22.9 / 11.5% — near-monotonic. Both tails PERSIST or AMPLIFY through 4h: miss side amplifies from +39.7p at 15m to +46.9p at 4h; beat side holds -60p through 1h. First-ever GBPAUD News Impact anchor and sixth AUD Employment cross-family post — with the largest big-beat magnitude in the family (-67p vs prior max AUDCAD +44p at 4h).All 7 AUD-crosses cluster their loudest 5 weekday half-hours inside Tue-Fri 12:30-14:30 UTC — 33 of 35 top-5 cells sit in the US-macro window, and the 2 exceptions are both AUDNZD Sydney/Wellington-morning cells (already flagged in the 2026-08-15 top-2 post)Fresh /api/v1/calm-zones/scan for each of AUDUSD, AUDJPY, AUDNZD, AUDCHF, AUDCAD, EURAUD, GBPAUD. Six of seven pairs have all 5 of their top-5 loudest weekday half-hours inside the Tue-Fri 12:30-14:30 UTC US-macro window (Thu jobless claims / ECB / BoE, Fri NFP / ISM, Wed EIA, Tue Consumer Confidence). Only AUDNZD has an exception: 3-of-5 in-window plus Wed 21:00 UTC (Sydney-morning, 12.60p) and Fri 21:30 UTC (Wellington-morning, 12.50p) — both already documented by audnzd-top2-outside-overlap (2026-08-15). Total: 33 of 35 top-5 cells (94.3%) in Tue-Fri 12:30-14:30 UTC. Zero domestic-AUD cells (RBA 03:30 UTC, AU CPI/Employment/GDP 00:30 UTC) appear in any pair's top-5 or top-20 — the AUD-cross family is US-macro-loudest, domestic-quiet, matching yesterday's CHF-cross family (35/35) and 2026-08-26 JPY-cross family (33/35 with different exceptions).Statistics for Traders #28: Coefficient of partial determination on today's slot-1 AUD Employment × GBPAUD sample — surprise_z adds 2.08 pp of TOTAL R² over bucket assignment, or 3.18% of the RESIDUAL variance after bucket is removedCoefficient of partial determination = sr² / (1 - r_yz²) — the fraction of Y's residual variance (after removing Z) that X explains. On today's slot-1 AUD Employment × GBPAUD 15m sample (n=199): r(surprise_z, move_pips) = -0.593; r(surprise_z, bucket_ord) = +0.905; r(move_pips, bucket_ord) = -0.587. Semi-partial r_Y(X-Z) = -0.144, sr² = 0.0208 (2.08 pp of TOTAL variance). Coefficient of partial determination = 0.0208 / (1 - 0.345) = 0.0208 / 0.655 = 0.0318 (3.18% of RESIDUAL variance). Bucket assignment carries 34.5% of Y variance; of what's left, surprise_z picks up only 3%. Same story as Stats #23/#25 on a fresh sample — but expressed as a partition-fraction rather than a total-R² identity.Paper Trail #28: Value Investing (Piotroski, 2000) — the paper that turned 9 binary accounting signals into a 7.5% annual return improvement inside the high book-to-market portfolio, and gave the value strategy a fundamental-analysis filter that survives 25+ years of out-of-sample testsJoseph D. Piotroski (University of Chicago), 'Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers', Journal of Accounting Research 38 (Supplement, 2000): 1-41. Sample: 14,043 high book-to-market firm-year observations, 1976-1996. Nine binary accounting signals combined into F_SCORE (0-9): profitability (F_ROA, F_ΔROA, F_CFO, F_ACCRUAL), leverage/liquidity/source-of-funds (F_ΔLEVER, F_ΔLIQUID, EQ_OFFER), operating efficiency (F_ΔMARGIN, F_ΔTURN). Screening the high-BM portfolio for F_SCORE ≥ 5 lifts mean return from 5.9% to 13.4% (7.5 pp gain); a long-short high-vs-low F_SCORE hedge portfolio earns 23% annual return between 1976 and 1996. Twentieth PT with full primary-source access, verified via WebFetch + pymupdf on Piotroski's own University of Chicago GSB Selected Paper 84 reprint.Canada Unemployment Rate on CADJPY: 22 of 26 big-beat prints sent CADJPY up (84.6%), 7 of 10 big-miss prints sent it down (70%), median walk perfectly monotonic across all 5 buckets — first-ever CAD-Unemployment × CADJPY anchor, second post in the CAD-Unemployment cross-family198 non-contaminated Canada Unemployment Rate releases on CADJPY, 15-minute window. Median walk -19.7 / -13.5 / +6.0 / +20.1 / +32.6 pips — perfectly monotonic across all 5 buckets. Pct-up walk 30.0 / 33.3 / 60.9 / 76.7 / 84.6% — near-monotonic (small bucket-boundary artefact at big_miss 30.0 vs small_miss 33.3 on n=10 vs n=33). Big-beat n=26: 22 up, 4 down (all 4 down prints are small-magnitude beats within CADJPY's typical 9.9p noise band). Big-miss n=10: 7 down, 3 up (all 3 up prints have specific context: 2011-02 small miss, 2015-09 China-slowdown oil-crash, 2020-04 COVID Q1 risk-off dominating CAD signal). Multi-hour persistence: both tails hold their sign through 4h. First-ever CAD-Unemployment × CADJPY anchor; extends the CAD-Unemployment cross-family after cad-unemployment-usdcad-monotonic (2026-08-09).Canada Employment Change on GBPCAD: 8 of 9 big-miss prints sent GBPCAD up (88.9%), 22 of 23 big-beat prints sent it down (95.7%), and at 1 minute the big-miss bucket is 9 of 9 UP — first-ever GBPCAD News Impact anchor, largest magnitudes in the CAD-Employment cross-family196 non-contaminated Canada Employment Change releases on GBPCAD, 15-minute window. Median walk +85.1 / +26.5 / -0.85 / -44.8 / -66.9 pips across the 5 surprise buckets — perfectly monotonic on both median AND pct-up (88.9 / 72.7 / 48.9 / 18.6 / 4.3%). At 1 minute the big-miss bucket is 9 of 9 up — a unanimous initial reaction across every observed miss print since 2010. The one big-miss down print at 15m is April 2020's COVID Q1 catastrophe (act -1.01M vs cons -427k, z=-12.59). Asymmetric persistence: the beat side stays put through 1h (-66p median holds); the miss side amplifies to +85p at 15m and holds through 1h but collapses to +8.7p at 4h. First-ever GBPCAD News Impact anchor; extends the ledger's CAD-Employment cross-currency family to its fifth pair — and with the largest medians of the five.All 7 CHF-crosses cluster their loudest 5 weekday half-hours inside Tue-Fri 12:30-14:30 UTC — 35 of 35 top-5 cells sit in the US-macro window, and zero domestic-Swiss cells (06:30 CPI, 07:30 SNB) appear anywhere in the top-2035 of 35 loudest-5 cells across USDCHF, EURCHF, GBPCHF, AUDCHF, NZDCHF, CADCHF and CHFJPY sit inside the Tue-Fri 12:30-14:30 UTC US-macro window. Not one of them lands at 06:30 UTC (Swiss CPI m/m), 07:30 UTC (SNB Policy Rate), or 06:30 UTC (Swiss GDP) — the domestic Swiss calendar contributes zero cells to any CHF-cross top-5. Same finding CHFJPY showed alone on 2026-08-24, now confirmed across all seven CHF-crosses; cleaner than the parallel JPY-crosses cross-family finding (33 of 35 in the tighter Thu/Fri window).Statistics for Traders #27: Welch's ANOVA on today's slot-1 CAD Employment × GBPCAD sample — Welch F = 27.52 on df=(4, 41.02) vs classic F = 34.06 on df=(4, 191), Welch's Satterthwaite df collapses 4× under variance heterogeneity but both tests reject H0 by 11+ orders of magnitudeWelch's ANOVA is the unequal-variance alternative to the classic Fisher F-test. On today's slot-1 CAD Employment × GBPCAD 15m sample (n=196), variance ratio max/min = 2.007 and SD ratio 1.417 — inside Box (1954)'s 3× size-correctness threshold. Classic F = 34.06 on df=(4, 191), p ≈ 1.9e-21; Welch F = 27.52 on df=(4, 41.02), p ≈ 3.9e-11. Welch's Satterthwaite denominator df collapses from 191 to 41 (4× smaller) because it downweights n_i/var_i for the higher-variance tail buckets, but both tests reject H0 far beyond any conventional α. Levene W = 1.094 (p = 0.36), Brown-Forsythe W = 0.730 (p = 0.57): the variance-homogeneity assumption isn't actually violated here, so classic F is trustworthy on this sample and Welch is the size-safe insurance.Paper Trail #27: Do Stock Prices Fully Reflect Information in Accruals and Cash Flows? (Sloan, 1996) — the paper that showed accruals persist at 0.765 vs cash flows at 0.855, and that a hedge portfolio long-low-accrual and short-high-accrual earned 10.4% in year 1 (t=4.71) on 40,679 firm-yearsRichard G. Sloan (Wharton) showed in 1996 that current earnings' persistence into future earnings splits cleanly between the two components: the cash-flow component persists at 0.855 while the accrual component persists at only 0.765 — an F-test rejects equality. Stock prices act as if investors fixate on total earnings rather than the accrual/cash-flow split. A trading strategy that goes long the lowest accrual decile and short the highest, held for one year, earns a size-adjusted 10.4% (t=4.71) on 40,679 NYSE/AMEX firm-years from 1962-1991. The anomaly halves by year 2 (4.8%, t=3.15) and is no longer significant by year 3. Cross-referenced by both PT #25 (FF 2006) and PT #26 (CGS 2008) as the accruals-anomaly primary source they build on.UK Core CPI on GBPNZD: 13 of 15 big-beat prints sent GBPNZD up (86.7%), 14 of 15 big-miss prints sent it down (93.3%), and at both 5 minutes AND 1 hour the big-beat bucket is 15 of 15 UP — first-ever GBPNZD News Impact anchor198 non-contaminated UK Core CPI releases on GBPNZD, 15-minute window. Median walk -23.3 / -11.8 / +3.3 / +13.6 / +22.8 pips across the 5 surprise buckets — perfectly monotonic on both median AND pct-up (6.7 / 26.4 / 54.8 / 69.8 / 86.7%). At 5 minutes AND at 1 hour the big-beat bucket is 15 of 15 up — double-window unanimity across every observed big-beat print since 2010. Both tails amplify through the multi-hour arc: big-miss median deepens from -21p at 1m to -28p at 4h; big-beat grows from +22p at 1m to +38p at 30m. First-ever GBPNZD News Impact anchor; extends the UK Core CPI family to its third pair on the ledger's loudest liquid pair.Canada Employment Change on EURCAD: 22 of 23 big-beat prints sent EURCAD down (95.7%), 8 of 9 big-miss prints sent it up (88.9%), and at 1 minute the big-beat bucket is 23 of 23 DOWN — first-ever CAD-Employment × EURCAD anchor198 non-contaminated Canada Employment Change releases on EURCAD, 15-minute window. Median walk +58.0 / +18.3 / 0.0 / -37.2 / -61.9 pips across the 5 surprise buckets — perfectly monotonic on both median AND pct-up (88.9 / 81.8 / 50.0 / 14.0 / 4.3%). At 1 minute the big-beat bucket is 23 of 23 down — a unanimous initial reaction across every observed print since 2010. The one big-miss down print is April 2020's COVID Q1 catastrophe (actual -1.01M jobs vs consensus -427k, z=-12.59). Asymmetric persistence: the beat side stays put through 4 hours (-63p median holds); the miss side fully unwinds by 4h (median flips from +58p to -13p). First-ever CAD-Employment × EURCAD anchor; extends the ledger's CAD-Employment cross-currency family.All 7 JPY-crosses cluster their loudest half-hours in Thu/Fri 12:30-14:30 UTC — 33 of 35 top-5 cells sit inside that 5-cell US-morning window, and the 2 outliers are still US-morning macro (Tue 14:30 for NZDJPY, Wed 14:30 for CADJPY)Extending yesterday's CHFJPY finding to the entire JPY-cross family. Across all 7 pairs (USDJPY, EURJPY, GBPJPY, AUDJPY, NZDJPY, CADJPY, CHFJPY), 33 of the 35 top-5 loudest weekday half-hour cells sit inside a single 5-slot window: Thu/Fri 12:30-14:30 UTC. The 2 outliers (NZDJPY Tue 14:30, CADJPY Wed 14:30) are ALSO US-morning weekday macro cells — just on different weekdays. Widening the window to Tue-Fri 12:30-14:30 UTC captures all 35 of 35. Domestic hours (BoJ around 03:00 UTC, Japan National Core CPI at 23:30 UTC) appear in ZERO top-5 slots across any of the 7 pairs. JPY-cross loudness is a US-morning macro satellite regardless of the OTHER currency in the pair.Statistics for Traders #26: Levene, Brown-Forsythe, and Bartlett tests on today's slot-1 CAD Employment × EURCAD sample — SD ratio 1.49x LOOKS like variance heterogeneity, all three tests fail to reject at p = 0.53 / 0.57 / 0.34The CAD Employment Change × EURCAD 15m sample (n=198) has bucket standard deviations ranging from 32.2 pips (small_miss) to 47.8 pips (big_miss) — a 48.5% max-to-min SD spread that looks like heterogeneous variance by eye. All three formal variance-homogeneity tests disagree: classic Levene W = 0.79 (p = 0.53), Brown-Forsythe W = 0.73 (p = 0.57), Bartlett T = 4.50 (p = 0.34). None reject H₀ at any conventional α. The tests validate the equal-variance assumption for the ANOVA on this sample. Message: eyeball SD spread is a bad guide when the smallest bucket is n=9; the F(4, 193) 0.05 critical value is 2.42, well above what any of the three tests deliver.Paper Trail #26: Asset Growth and the Cross-Section of Stock Returns (Cooper, Gulen & Schill, 2008) — the paper that turned yesterday's PT #25 asset-growth slope (t = -3.87) into a decade of literature, and the direct source for the CMA factor in FF 2015 (PT #22)Yesterday's Paper Trail #25 (Fama-French 2006) put four t-statistics on the table: B/M near +3, profitability +2.55, positive accruals -6.82, and asset growth -3.87. Today's PT #26 is the paper that gave the asset-growth slope its dedicated treatment: Cooper, Gulen & Schill (2008) sorted CRSP/Compustat U.S. stocks into 10 deciles each year by the annual percentage change in total assets (AG_t = AT_t / AT_{t-1} - 1) and found low-asset-growth stocks systematically outperformed high-asset-growth stocks over July 1968 to June 2003 — the anomaly that Fama-French 2015 (PT #22) later packaged as the CMA factor. Primary source is JF paywalled; today's post cites verbatim from NBER 22894 (Green-Hand-Zhang 2017) and the Cooper-Gulen-Ion 2019 follow-up (two of the three original authors), which are the closest-to-primary secondary sources available.UK Unemployment Rate on GBPCHF: 18 of 23 big-beat prints sent GBPCHF up (78.3%), 6 of 8 big-miss down (75%), median and pct-up walks BOTH perfectly monotonic across all 5 buckets — first-ever GBPCHF News Impact anchor198 non-contaminated UK Unemployment Rate releases on GBPCHF, 15-minute window. Median walk -12.5 / -1.4 / +1.6 / +5.4 / +14.9 pips — perfectly monotonic across all five surprise buckets. Pct-up walk 25.0 / 40.6 / 55.7 / 61.7 / 78.3% — also perfectly monotonic. Both tails persist through 4 hours: big_miss median deepens from -12.5p at 15m to -16.7p at 4h (1.34x amplification); big_beat median holds at +11.6p through 4h. First-ever GBPCHF News Impact anchor in the ledger; 17 days from the sibling GBP-Unemployment × GBPUSD post (2026-08-09). Both big-miss up prints (2023-07-11, 2023-08-15) fall inside the mid-2023 BoE-hiking-cycle window where sterling repriced against unemployment misses.Canada Retail Sales m/m on CADJPY: 11 of 12 big-beat prints sent the pair up (91.7%), median walk perfectly monotonic across all 5 buckets, first-ever CAD-Retail × CADJPY anchor197 non-contaminated Canada Retail Sales m/m releases on CADJPY, 15-minute window. Median walk -13.7 / -12.25 / -0.95 / +6.5 / +16.3 pips — perfectly monotonic across all five surprise buckets. 11 of 12 big-beat prints sent CADJPY up (91.7%); the one exception is 2016-01-22 during the oil-crash CAD-weakness regime. Pct-up walk 33.3 / 27.5 / 43.0 / 70.5 / 91.7 percent has one small-vs-big-miss inversion that traces to five outlier CAD-Retail miss prints where the JPY-cross moved against the CAD leg (including the COVID Q2 -26.4% actual with z=-20). First-ever CAD-Retail × CADJPY anchor in the ledger; the USDCAD sibling landed 2026-08-12.EURGBP is uniquely Thursday-dominant among all 28 liquid FX pairs — 4 of its 5 loudest weekday half-hours are Thursday (Thu 13:30, 14:30, 12:30, 14:00 UTC)Median EURGBP weekday cell prints 6.0 pips of range. Its 5 loudest half-hours: Thu 13:30 (11.45p), Thu 14:30 (11.10p), Fri 14:30 (11.10p), Thu 12:30 (11.00p), Thu 14:00 (10.85p). Four of those five are Thursday — the only non-Thursday is Fri 14:30 UTC (post-NFP). Widen to the top 20 and 8 are Thursday, 5 are Wednesday, 4 are Friday, 3 are Tuesday, 0 are Monday. No other liquid FX pair has more than 3 Thursdays in its top-5. The mechanism: ECB announcements (Thu 12:45 UTC), BoE announcements (Thu 12:00), weekly US jobless claims (Thu 12:30), and UK GDP/retail (Thu 07:00) all bleed into a single weekday, and EURGBP moves on both sides of every European-macro pair.Statistics for Traders #25: Semi-partial (part) correlation on today's slot-1 CAD Retail × CADJPY sample — raw surprise_z adds only 0.7 percentage points of R² over the 5-bucket assignment (0.02 pp if the COVID outlier drops)Semi-partial correlation is the sibling of Stats #23's partial correlation: partial removes Z from BOTH X and Y, semi-partial removes Z from X ONLY. Its key property: r_Y(X-Z)² = ΔR² added by X over Z when both predict Y. On today's slot-1 CAD Retail × CADJPY 15m sample (n=197), r(surprise_z, move_pips) is +0.21, r(surprise_z, bucket_ord) is +0.65, r(move_pips, bucket_ord) is +0.42. The semi-partial r_Y(X-Z_ord) = -0.082, squared 0.68 percent. Bucket_ord already explains 17.6% of move_pips variance; adding raw surprise_z pushes the two-predictor R² from 17.60% to 18.27% — a 0.68pp incremental gain that ties to the semi-partial exactly. Drop the 2020-06-19 COVID Q2 outlier (z=-20.42, +6.6p) and the semi-partial collapses further to +0.013 (0.02pp of R²). Buckets carry the signal — surprise magnitude beyond bucket adds essentially nothing.Paper Trail #25: Profitability, Investment and Average Returns (Fama & French, 2006) — the 'before' picture that Novy-Marx 2013 (yesterday's PT #24) later corrected by replacing earnings with gross profitsFama & French published this in the Journal of Financial Economics 82(3) in 2006. They derive a dividend-discount identity that predicts three things about expected returns: higher book-to-market → higher return, higher expected profitability → higher return, higher expected investment → LOWER return. Then they test all three on Fama-MacBeth cross-section regressions of NYSE/AMEX/Nasdaq firms 1963-2003 (financials excluded), and find every prediction confirmed: profitability slope t = 2.55, asset growth slope t = -3.87, accruals slope t = -6.82. The catch is that profitability is measured as earnings before extraordinary items (Compustat item IB) — the messy accounting number that Novy-Marx replaced seven years later with the much cleaner gross profits (Compustat item GP). FF06 is the 'before' picture that PT #24 corrected. Direct-predecessor lineage to yesterday's paper.AUD Employment on AUDCAD: 23 of 26 big-beat prints sent the pair up (88.5%), median walk perfectly monotonic on both median AND pct-up across all 5 buckets, first-ever AUDCAD News Impact anchor199 non-contaminated Australia Employment Change releases on AUDCAD, 15-minute window. Median walk -21.8 / -21.0 / +1.0 / +21.2 / +39.2 pips — perfectly monotonic. Pct-up walk 11.1 / 15.4 / 53.2 / 79.2 / 88.5 percent — also monotonic. 8 of 9 big-miss prints down (89%); 23 of 26 big-beat prints up (89%). Both tails amplify through 4h: big-miss deepens to -34.6p at 4h (1.6x); big-beat amplifies to +44.4p at 4h (1.13x). Completes the AUD Employment cross-currency-family: after JPY (2026-08-10), NZD (2026-08-17), and CHF (2026-08-22), the CAD cross is the fourth commodity-cross leg. First-ever AUD Employment × AUDCAD anchor.US GDP q/q on EURUSD: 71 releases with monotonic median AND pct-up walks at 15m — but the beat side REVERSES sign by 4 hours while the miss side holdsFirst-ever US GDP × EURUSD News Impact post in the ledger. 71 non-contaminated releases, 15-minute window. 5-bucket median walk +10.65 / +8.75 / +3.40 / -2.40 / -10.00p and pct-up 87.5 / 80.0 / 64.5 / 42.9 / 25.0 — perfectly monotonic on both metrics. 7 of 8 big-miss prints sent EURUSD up (only 2026-02-20 down). 6 of 8 big-beat prints sent it down. The story flips at 4h: the miss side still sits at +15.3p 87.5% up (persistent USD-weakness), while the big-beat median has REVERSED from -10.0p to +14.0p 62.5% up (intraday dollar strength fades and reverses). Miss holds; beat fades and flips.CHFJPY is a Swiss/Japanese pair whose loudest 5 weekday half-hours are ALL Thu/Fri 12:30-14:30 UTC — the US-morning macro windowMedian CHFJPY range across 236 weekday half-hour cells: 12.0 pips. The 5 loudest cells are Fri 14:30, Thu 13:30, Thu 14:30, Fri 13:30, Thu 14:00 — all inside the Thu/Fri 12:30-14:30 UTC US-morning macro window (NFP, jobless claims, ISM, retail sales). Widen to the loudest 20 and 9 still sit in that same window; the remaining 11 spread across London open (07:00-08:00 UTC) and the rest of the NY overlap. Neither Swiss macro hours (06:30 UTC for CPI, 07:30 UTC for SNB) nor Japanese hours (03:00 UTC BoJ, 23:30 UTC previous-day for JP CPI) appear in the top 20. In the aggregate, CHFJPY is a pure USD-flow satellite.Statistics for Traders #24: One-way ANOVA and R² on yesterday's Stats #23 sample — 19.52% of move_pips variance is between-bucket, F(4, 190) = 11.52, p = 2.14×10⁻⁸Yesterday's Stats #23 partial-correlation post reported 19.5% between-bucket / 80.5% within-bucket SS decomposition on the CAD CPI m/m × USDCAD 15m sample and stopped there. Today's Stats #24 formalizes the same decomposition as ANOVA: SS_total 169,211 pips², SS_between 33,031 (19.52%), SS_within 136,180 (80.48%), R² = 0.1952, F(4, 190) = 11.52 with p = 2.14×10⁻⁸ (highly significant), Cohen's f = 0.492 (large effect). Bias-corrected ω² = 0.1775 shrinks R² by about 2 percentage points to account for the k-1 degrees of freedom the bucket assignment spends. Same sample as Stats #23, same 19.52% between/within split, formalized into the standard ANOVA machinery.Paper Trail #24: The Other Side of Value (Novy-Marx, 2013) — the paper that showed gross profits / assets predicts the cross-section of stock returns roughly as well as book-to-market, and hedges value with correlation −0.57Robert Novy-Marx published this in the Journal of Financial Economics 108(1) in 2013 and it won that year's Fama-DFA Prize. He replaces the messy earnings-based profitability signal that Fama-French 2006 had used with a much cleaner numerator — gross profits (revenues minus cost of goods sold, Compustat item GP) divided by total assets — and shows the cross-sectional predictive power lands 'roughly the same' as book-to-market on the July 1963-December 2010 sample. The two strategies have correlation −0.57 in the all-cap universe and −0.58 in the large-cap universe, so a 50/50 mix reaches Sharpe 0.85 all-cap (t-statistic 5.87) and 0.44 large-cap-only, versus 0.34 for the market. This is the primary source for the RMW factor Fama & French later added to their 2015 five-factor model (PT #22 two days ago).Swiss CPI m/m on CHFJPY: big-miss median deepens 2.9× through 4 hours (from -9.2p at 15m to -26.6p at 4h) while big-beat median doubles (+5.7p to +13.1p) — both tails amplifyFirst-ever CHFJPY News Impact anchor in the ledger. 199 non-contaminated Swiss CPI m/m releases. At 15 minutes the median walk is monotonic (-9.15 / -4.55 / +0.60 / +3.10 / +5.70p) but the miss-side pct-up has a small inversion (big_miss 38.9% > small_miss 31.7%). Both tails amplify materially through the 1h and 4h windows: big_miss median goes -9.15 → -19.40 → -26.60p with pct-up collapsing to 13.3% (13 of 15 down), and big_beat median goes +5.70 → +11.50 → +13.10p with pct-up rising to 77.8% (7 of 9 up). The pct-up walk becomes strictly monotonic across all 5 buckets by 1h and stays monotonic at 4h.Canada CPI m/m on USDCAD: 12 of 13 big-miss prints sent USDCAD up (92.3%), 16 of 20 big-beat prints sent it down (80%), and the pct-up walk is perfectly monotonic across all 5 buckets195 non-contaminated Canada CPI m/m releases on USDCAD, 15-minute window. Miss side has 12 of 13 big-miss and 34 of 46 small-miss prints up; beat side has 16 of 20 big-beat prints down. Pct-up walks 92.3 / 73.9 / 52.4 / 37.5 / 20.0 percent — perfectly monotonic across all five surprise buckets. Beat side is also monotonic on median magnitude (small_beat -6.3p, big_beat -21.0p — a 3.3x amplification). Miss side has a tiny 0.15-pip inversion (small_miss +12.95p vs big_miss +12.80p) that sits well inside the n=13 CI. Fills a long-standing coverage gap — this is the first cad-cpi-usdcad standalone in the ledger, after two cross-pair siblings landed on CADJPY (2026-08-11) and EURCAD (2026-08-19).Tuesday 14:30 UTC is a top-10 loudest weekday half-hour for 26 of 28 liquid FX pairs — the third '10:00 ET US data' cluster after Wed EIA and Thu jobless claimsThe US 10:00 ET data slot on Tuesday — hosting a rotating menu of Consumer Confidence, S&P/Case-Shiller HPI, JOLTS, Chicago PMI, and Fed-regional-president speakers — ranks in the top-10 loudest weekday half-hour for 26 of 28 liquid FX pairs, and top-15 for all 28. The two outliers (EURJPY at 12, EURUSD at 14) are still tighter than most pairs' top-15 cells. No single Tuesday release dominates — the cluster is genuinely a menu effect, adding to Wed 14:30 UTC (EIA petroleum) and Thu 13:30 UTC (jobless claims / GDP) to complete a three-day / three-cell US 10:00 ET weekday volatility cluster.Statistics for Traders #23: Partial correlation on today's slot-1 CAD CPI × USDCAD sample — total r is −0.43, but controlling for the 5-bucket assignment collapses it to −0.05 (95% CI crosses zero)The Pearson r between surprise_z and 15m move_pips across 195 CAD CPI m/m × USDCAD releases is −0.43 — the correlation-language version of the 5-bucket monotonic walk (Stats #11 established the pattern on the mirror pair). Partial correlation formally decomposes it. Controlling for the 5-bucket surprise assignment (ordinal or full categorical), the partial r drops to −0.05 / −0.06 and both Fisher 95% CIs cross zero. The between-bucket r (weighted by n) is −0.97: nearly the full structure lives in the differences between bucket means, essentially none in within-bucket surprise magnitude. This closes the queue item flagged since Stats #11 introduced Pearson r 12 days ago and formalizes 'buckets carry the signal' as a partial-correlation identity.Paper Trail #23: Value and Momentum Everywhere (Asness, Moskowitz & Pedersen, 2013) — the paper that showed value and momentum work across 8 asset classes AND are negatively correlated within and across all of them, lifting the 50/50 combo Sharpe to 1.42The paper that generalized US-equity value and momentum into a global-8-asset-class value-and-momentum-everywhere framework. Asness, Moskowitz & Pedersen (2013), Journal of Finance 68(3):929-985, DOI 10.1111/jofi.12021. Sample January 1972 to July 2011 (39.5 years). Eight asset classes: US/UK/Europe/Japan individual stocks, country equity index futures, currencies, government bonds, commodity futures. Global-all-asset-classes P3-P1 Sharpe: value 0.73, momentum 0.67 — separately about the same as Fama-French SMB or HML. Combined 50/50 P3-P1 Sharpe: 1.42; factor version 1.59 — roughly 2x either component. The lift comes entirely from the −0.53 value-momentum correlation. And the paper's punchline: value returns correlate positively with each other across asset classes, momentum returns correlate positively across asset classes, but value and momentum are negatively correlated within AND across every asset class studied. Partly explained by opposite-sign exposure to global funding liquidity risk (Brunnermeier-Pedersen 2009), with the funding-risk channel strengthening after the 1998 LTCM crisis.US Core CPI m/m on AUDUSD: 8 of 10 big-beat prints sent AUDUSD down (80%), and the beat side is perfectly monotonic on both median and pct-up — but the miss side has a bucket-boundary inversion197 non-contaminated US Core CPI m/m releases on AUDUSD, 15-minute window. Beat side is textbook: small_beat median −9.40p / 25.6% up, big_beat median −12.20p / 20.0% up — monotonic on both metrics, amplifies through the 1h and 4h windows (big_beat median −18.75p at 4h, 10% up-rate). Miss side has a mechanical inversion: 11 of the 17 big-miss prints are the exact same 'actual 0.1% vs consensus 0.2%' shape that surprise_z bucketing forces into big_miss but which barely moves the market. Strip those 11 and the remaining 6 big_miss prints have median +16p and 5 of 6 up. The bucket boundary is doing more work than the underlying surprise magnitude, on the miss side. First-ever US Core CPI News Impact post in the ledger.US ISM Manufacturing on EURUSD: miss side is perfectly monotonic (+12 / +3.8 / +1.2 pips), but the beat side has a DOUBLE inversion — small_beat drops EURUSD further AND more consistently than big_beat does198 non-contaminated US ISM Manufacturing PMI releases on EURUSD, 15-minute window. Miss side walks +12.0 / +3.8 / +1.2 pip medians with 83% / 71% / 54% up-rates — perfectly monotonic on both metrics. Beat side has a rare double inversion: small_beat median magnitude (−8.4p) is bigger than big_beat (−7.0p), AND small_beat down-rate (80.5%) is higher than big_beat (66.7%). At 1 hour the miss side amplifies (big_miss +12.0 → +22.1p, +84%) while the beat side fades to zero. First-ever US ISM Mfg × EURUSD anchor in the ledger.The CHF cross of every commodity currency is its family's quietest — CADCHF 7.25p, NZDCHF 7.78p, AUDCHF 8.12p all win the typical-weekday-cell crown across all three 7-pair CAD/NZD/AUD familiesScan all 21 commodity-currency crosses (CAD × 7 + NZD × 7 + AUD × 7) for typical weekday half-hour range and rank each family: the CHF cross wins every time. CADCHF 7.25p vs runner-up AUDCAD 8.80p (21% gap). NZDCHF 7.78p vs NZDUSD 8.10p (4% gap). AUDCHF 8.12p vs AUDUSD 8.55p (5% gap). None of the three CHF-crosses peaks on its own domestic macro hour — CADCHF/NZDCHF peak on US NFP-Friday (Fri 13:30/14:30 UTC), AUDCHF peaks on US-ISM Thursday (Thu 14:30 UTC). Cross-family generalization of the 2026-08-06 CADCHF and 2026-08-21 NZDCHF single-family posts.Statistics for Traders #22: Fisher's r-to-z on today's slot-1 US ISM Manufacturing × EURUSD sample — the 95% CI for r is [−0.42, −0.17] via Fisher, [−0.44, −0.17] naïve linear, 5% narrower and less symmetricThe Pearson correlation coefficient r isn't asymptotically normal — its distribution is skewed and bounded on (−1, +1). Fisher (1915) proposed z = arctanh(r) = 0.5·ln((1+r)/(1-r)), whose sampling distribution is approximately Normal with SE = 1/sqrt(n-3). Worked end-to-end on today's slot-1 US ISM Manufacturing × EURUSD 15m sample (n=198): overall r = −0.30, Fisher-CI [−0.425, −0.171], 5% narrower than the naïve linear CI. Within the big-beat bucket (n=21), both methods give CIs that cross zero — but Fisher's CI is asymmetric (lower endpoint further from zero than upper) reflecting r's bounded support. This installment closes the queue item flagged since Stats #11 introduced Pearson r 11 days ago.Paper Trail #22: A Five-Factor Asset Pricing Model (Fama & French, 2015) — the 22-years-later update to their own three-factor model, adds profitability (RMW) and investment (CMA), and finds HML redundant in U.S. data 1963-2013Fama and French returned to their 1993 three-factor model 22 years later, added Robust-minus-Weak (RMW, profitability) and Conservative-minus-Aggressive (CMA, investment) factors, and shipped the five-factor model that now anchors most academic asset-pricing work. The paper's most-cited finding is unexpected: in the presence of RMW and CMA, the value factor HML becomes redundant for describing average returns. The paper is also candid about the model's main failure — small stocks that invest heavily despite low profitability. Verified from the tevgeniou.github.io mirror of the JFE April 2015 publication.AUD Employment on AUDCHF: 0 of 9 big-miss prints since 2010 sent AUDCHF up (100% down at 15m), 22 of 26 big-beat prints sent it up (85%), and the pct-up walk is perfectly monotonic across all 5 buckets — first-ever AUDCHF News Impact anchor199 non-contaminated AUD Employment Change releases on AUDCHF, 15-minute window. Big-miss (n=9) is 9-for-9 down (100%). Big-beat (n=26) is 22-for-26 up (85%). The whole 5-bucket walk is perfectly monotonic on pct-up (0.0 / 12.8 / 54.5 / 75.0 / 84.6 percent) and monotonic-directional on median (−17.2 / −16.0 / +1.4 / +14.75 / +32.0 pips). First-ever AUD Employment × AUDCHF anchor in the ledger, and the AUD-family analog of the 2026-08-16 CAD Employment × CADCHF 23-of-23 finding. Same CHF-cross-strip mechanism, different commodity-currency family — and this variant carries clean unanimity on BOTH tails, not just one.New Zealand GDP q/q on NZDUSD: 0 of 18 miss prints since 2011 sent NZDUSD higher 15 minutes later, and every one of the 6 big-beat prints went up62 non-contaminated NZ GDP releases, 15-minute window on NZDUSD. Miss side (n=18): 0 up. Big-beat side (n=6): 6 up. Median walk −18.1 / −21.5 / +2.6 / +8.3 / +12.4 pips big_miss → big_beat, pct-up 0 / 0 / 52 / 67 / 100. The one 'noisy' feature is on the tail: the n=3 big-miss median (−18.1p) is smaller in magnitude than the n=15 small-miss median (−21.5p), a sample-size artifact rather than a signal. First-ever NZ GDP × NZDUSD post in the ledger, extending the 2026-08-06 NZ-CPI-tails unanimity pattern.NZDCHF is the quietest of the seven NZD-crosses — typical 30-minute range 7.80 pips, and its loudest weekday cell (12.00p) is smaller than every other NZD-cross's loudestAcross every 30-minute weekday cell of NZDCHF (excluding the Fri 21:00-23:30 UTC close artifact), the typical range is 7.80 pips — smaller than NZDUSD (8.10p), AUDNZD (8.60p), NZDCAD (8.90p), NZDJPY (9.90p), EURNZD (18.00p) or GBPNZD (22.00p). Its loudest cell of the entire week — Thursday 13:30 UTC on jobless-claims hour — prints only 12.00p, still 0.60p below AUDNZD's loudest and just under half GBPNZD's Fri 14:30 UTC peak. This is the NZD-family mirror of the 2026-08-06 CADCHF-quietest-CAD-cross post — same CHF-cross-of-a-commodity-currency mechanism.Statistics for Traders #21: Tukey-Hanning kernel n_eff = 106 on the same 196-release NFP × USDJPY sample — closes the six-method kernel-family arc, with the PSD-by-construction guarantee that doesn't quite holdSixth and final kernel-family installment on the same NFP × USDJPY 15m |move_pips| series. Andrews-1991 AR(1) plug-in for Tukey-Hanning: same a-value as QS and Parzen (0.9029), bandwidth constant 1.7462 gives M* = 4.92, τ_int = 1.8487, n_eff = 106.02. Sits between QS (108) and Parzen (101). The kernel-family arc now covers IID 196 → AR(1) 115 → Bartlett 113 → QS 108 → TH 106 → Parzen 101 → NW94 88 → block-boot 39. Tukey-Hanning is the one kernel Andrews flags as NOT PSD-by-construction — its spectral window can go slightly negative — but on well-behaved samples like this one, the compact-support cutoff at |u|=1 keeps τ_int positive.Paper Trail #21: The Sharpe Ratio (Sharpe, 1994) — the 28-year-later rebrand and generalization of Sharpe's own 1966 reward-to-variability ratio, and the paper that actually names itWilliam F. Sharpe returned to his 1966 reward-to-variability ratio 28 years later, renamed it the 'Sharpe Ratio' (he acknowledges bowing to popular usage) and generalized it from a fixed risk-free-rate benchmark to any zero-investment differential. The paper's canonical Fund XX vs Fund YY worked example shows why the higher-Sharpe fund wins for the same investor risk target — even when its nominal 'risk' looks bigger. Sharpe's own honest list of limitations reads like a preview of every subsequent paper that would refine the ratio: correlation-blind, distribution-shape-blind, time-period-dependent, and 'the use of unadjusted historic Sharpe ratios as surrogates for unbiased predictions of ex ante ratios is subject to serious question'. Verified from the author's own Stanford-hosted reprint at web.stanford.edu/~wfsharpe/art/sr/sr.htm.Canada GDP m/m on USDCAD: 24 of 24 big-miss and small-miss combined pct-up walks monotonically 87.5% → 72.7%, and the beat side saturates — small_beat median (−6.4p) is bigger than big_beat median (−4.5p)198 non-contaminated Canada GDP m/m releases on USDCAD, 15-minute window. Miss side is perfectly monotonic on both median (+16.6 / +8.0 pips at 15m) and pct-up (87.5% / 72.7% up-rate). Beat side saturates: the whole 5-bucket walk still descends through small_beat, but big_beat is smaller in magnitude AND flat on pct-up. Different shape from the 2026-08-15 cad-gdp-cadjpy-pct-up-monotonic sibling, which had perfectly monotonic pct-up across all five buckets on CADJPY. Same event, same 2020-05-29 COVID outlier — but USDCAD's smaller n=11 big-beat sample doesn't reproduce CADJPY's beat-side unanimity.UK Core CPI on EURGBP: 13 of 15 big-beat prints sent EURGBP down (86.7%), the 5-bucket median walk is monotonic through all five buckets, and by 4 hours the big-beat median has AMPLIFIED to −16.3 pips198 non-contaminated UK Core CPI y/y releases on EURGBP at 15 minutes: medians +10.7 / +7.4 / −0.5 / −1.6 / −6.3 pips, pct-up 73 / 79 / 47 / 34 / 13. Monotonic on medians across all five buckets. 11 of 15 big-miss prints (73.3%) sent EURGBP up; 13 of 15 big-beat prints (86.7%) sent it down. The mirror image of the 2026-08-12 GBPUSD sibling — and CLEANER on medians, because EURGBP strips out the parallel EURUSD flow that muddies GBPUSD. By 4 hours the big-beat median amplifies to −16.3 pips (2.6× the 15-minute magnitude).EURCHF and EURGBP hold all 20 of the quietest weekday half-hour cells across all 28 liquid pairs — and their 20th-quietest combined cell (3.20p) is quieter than every other pair's single quietest cell6440 weekday half-hour cells across 28 liquid pairs. Sorted by median range, EURCHF takes 9 of the top 20 quietest, EURGBP takes 11 — no other pair appears in the top 30. The 20th combined-quietest cell across the two pairs is 3.20 pips. Every other pair's SINGLE QUIETEST weekday cell is louder than that — CADCHF's quietest is 3.60p, EURUSD's is 3.90p, GBPNZD's is 14.00p. This is the mirror-inverse of the 2026-08-12 GBPNZD post: GBPNZD sweeps the loud extremes, EURCHF+EURGBP sweep the quiet extremes.Statistics for Traders #20: Parzen-kernel n_eff = 101 on the same 196-release NFP × USDJPY sample — Andrews-1991's cheap-to-compute q=2 kernel gives 6.5% more autocorrelation than QSThe fifth kernel-family installment on the same NFP × USDJPY 15m |move_pips| series. Parzen is the compact-support, PSD-by-construction q=2 kernel Andrews (1991) recommends as the computational substitute for QS. Same Andrews AR(1)-plug-in a(2) = 0.9029 as QS, different bandwidth constant (2.6614 vs 1.3221), different kernel shape: n_eff = 100.75 at M* = 7.49. That's 6.5% below QS (108), 11% below Bartlett (113), 15% below NW94 (88 the other way), and 6.4× above the block-bootstrap (39). Full 5-method kernel-family arc is now complete: AR(1) 115 → Bartlett 113 → QS 108 → Parzen 101 → NW94 88.Paper Trail #20: An Improved HAC Covariance Matrix Estimator (Andrews & Monahan, 1992) — the paper that put a VAR(1) filter BEFORE the kernel, cutting kernel-HAC bias at the cost of estimator variance and closing the four-paper HAC-history arcAndrews came back to his 1991 kernel-HAC paper one year later with Christopher Monahan and a different angle on the same problem: PREWHITEN the residuals with a VAR(1) filter FIRST, then apply the kernel to the near-white residuals, then RECOLOR the estimate back via (I − A)⁻¹. Monte Carlo results show large gains in confidence-interval coverage and t-statistic size at the cost of higher estimator variance — the paper's honest bias-variance trade-off. Applied empirically to the same 196-release NFP × USDJPY sample the Stats arc has been using, an AR(1) prewhitening filter (β̂ = 0.27) collapses the raw lag-1 autocorrelation from +0.260 to −0.046 but leaves the ρ(2), ρ(4), ρ(11), ρ(15) higher-lag echoes intact — a compact demonstration of both what prewhitening fixes and what it doesn't.US GDP q/q on USDJPY: 7 of 8 big-miss prints (87.5%) sent USDJPY down at 15 minutes, the miss-side response amplifies 25% by 4 hours, and the one big-miss up-print is from February 202674 non-contaminated US GDP q/q (advance estimate) releases on USDJPY at 15 minutes: medians −14.7 / −7.4 / −4.3 / +10.5 / +8.5 pips, pct-up 12.5 / 45.5 / 46.9 / 71.4 / 66.7. Miss side is textbook: 7 of 8 big-miss prints sent USDJPY down (only exception: 2026-02-20 +17.2p). Beat side is messier — 3 of 9 big-beat prints went the wrong way (2018-03 and 2019-04 landed inside Fed tightening/pause regimes; 2020-07 was the COVID-collapse rebound artifact). By 4 hours the miss-side response AMPLIFIES 25% (big-miss median from −14.7p to −18.8p) while the beat side FADES back to +7.2p at big-beat and −1.6p at small-beat.US CPI m/m on EURUSD: 12 of 13 big-miss prints sent EURUSD up (92.3%), the whole 5-bucket walk is monotonic on both median AND pct-up, and the beat side lands twice on the same -8p median197 non-contaminated US CPI m/m releases on EURUSD at 15 minutes: medians +16.5 / +5.8 / +1.5 / −8.3 / −8.4 pips, pct-up 92 / 61 / 52 / 34 / 13. Monotonic through all five buckets. 12 of 13 big-miss prints — including the 2022-08 first-cool-off, the 2024-07 first-real-miss, and the 2026-07 −0.4% -4.6σ shock — sent EURUSD UP. The beat-side interesting quirk: small_beat median (−8.3p) and big_beat median (−8.4p) land almost exactly on top of each other, suggesting the m/m surprise-response saturates by the 'small_beat' bin.The Monday 22:30 UTC late-NY handoff isn't just a JPY-cross thing: it's the single quietest weekday half-hour for EURUSD, GBPUSD, and USDCAD too — three of the four G7 USD majors, plus CADJPY and EURJPYFor 5 of the 28 liquid FX pairs, Monday 22:30 UTC is the single quietest weekday half-hour of the week: CADJPY, EURJPY, EURUSD, GBPUSD, and USDCAD. Extend to bottom-3 and USDCHF, CHFJPY, GBPJPY join the list — 8 pairs total, split evenly between JPY-crosses and USD majors. The 2026-08-16 post found this window for the JPY-crosses only; this post shows the same multi-session handoff quiet zone extends to the four G7 USD majors too. London is closed, NY is 30 minutes from its own close, Tokyo hasn't opened yet.Statistics for Traders #19: Newey-West 1994's actual automatic Bartlett bandwidth on the same NFP × USDJPY sample is m = 8, n_eff = 88 — much wider than Andrews's 4.51, because the widely-cited [4·(T/100)^(2/9)] = 4 is the plug-in lag parameter, NOT the final bandwidthAlmost every online reference cites 'M = 4·(T/100)^(2/9)' as 'the Newey-West 1994 rule' for Bartlett-HAC bandwidth. Re-read the actual paper (NBER TWP #144, verified via OCR for today's Paper Trail #19) and that quantity is the plug-in LAG SELECTION PARAMETER n inside NW94's automatic procedure — used only to bound the sum over sample autocovariances that feeds the data-driven bandwidth γ̂·T^(1/3). On our 196-release NFP × USDJPY sample, n = 4 but the actual NW94 automatic bandwidth is m = 8, giving n_eff = 88 — significantly wider than Andrews-1991's M* = 4.51 (n_eff = 113) because NW94's procedure captures the empirical γ(4) = 299 lag-4 autocovariance that Andrews's AR(1) plug-in ignores. Which corrects yesterday's Stats #17 note claiming NW94 'essentially agrees' with Andrews.Paper Trail #19: Automatic Lag Selection in Covariance Matrix Estimation (Newey & West, 1994) — the sequel that gave NW87 the bandwidth rule Andrews-1991 had temporarily monopolised, and the paper whose actual proposed procedure is not what most textbooks call 'the Newey-West rule'Whitney Newey and Kenneth West came back to their 1987 HAC estimator with a data-driven automatic bandwidth rule seven years later. The paper's actual proposed procedure is a plug-in method: use a small number of empirical sample autocovariances (n = [4·(T/100)^(2/9)] of them for Bartlett) to estimate the spectral moments s(1) and s(0), then compute the final bandwidth as m = [1.1447·(s(1)/s(0))^(2/3)·T^(1/3)]. The commonly-cited 'M = 4·(T/100)^(2/9)' shortcut is the LAG SELECTION PARAMETER n inside that procedure — not the final bandwidth. Today's Stats #19 walks the full procedure on the NFP × USDJPY sample and finds the actual bandwidth is 8, not 4 as the shortcut would suggest, giving n_eff = 88 vs Andrews-1991's 113. The paper is also notable for actively DIS-recommending kernel choice as an important decision — where Andrews 1991 recommended QS, Newey-West 1994 conclude that if the bandwidth is chosen well, kernel choice is 'of secondary importance'.Canada CPI m/m on EURCAD: 196 releases with a perfectly monotonic 5-bucket walk on both median AND pct-up — 12 of 13 big-miss prints (92.3%) sent EURCAD up, and 14 of 20 big-beat prints sent it downFirst-ever EURCAD News Impact anchor. Canada CPI m/m at 15 minutes on EURCAD: medians +17.0 / +11.5 / +0.45 / −12.15 / −23.4 pips, pct-up 92 / 70 / 51 / 34 / 30 percent. Monotonic on both axes. Same event on CADJPY (2026-08-11) walked the mirror shape by CAD strength. EURCAD gets the cleaner miss-side unanimity (92% vs CADJPY's 69% at big_miss); CADJPY gets the cleaner beat-side (79% vs EURCAD's 70% at big_beat). Different pairs, same underlying rate-differential re-pricing, split by which tail your convention flatters.AUD Retail Sales on AUDJPY: 15 of 16 big-miss prints down at 15 minutes — and the one exception reverses by the 1-hour mark, making it 16 of 16188 non-contaminated AUD Retail Sales releases on AUDJPY since 2010. Big_miss n=16 median −20.0p at 15m with only one up print (2020-09-23, +2.5p). By the 1-hour mark that print is back below zero — 16 of 16 down. AUDJPY beats the AUDUSD sibling (2026-08-13, 14 of 16 down at 15m) on miss-side unanimity, and the JPY cross adds an 8% amplification of the median magnitude.The 28 pairs' quietest weekday half-hour: 26 of 28 land in ONE of TWO Monday-Asia handoff windows — Tokyo lunch (11 pairs) or late-NY / pre-Sydney (15 pairs)Fresh scan of all 28 liquid FX pairs on 2026-08-18. 27 of 28 pairs' single quietest weekday cell lands on Monday (a re-verification of the 2026-08-04 finding). And within Monday, 26 of the 27 split cleanly into two 90-minute Asia-timezone handoff clusters: Mon 04:00-04:30 UTC (Tokyo lunch, 11 pairs) or Mon 20:00-22:30 UTC (late-NY / pre-Sydney, 15 pairs). AUDNZD sits alone at Mon 17:30 UTC; EURCAD is the only non-Monday, at Wed 04:00 UTC.Statistics for Traders #18: Quadratic Spectral kernel n_eff = 108 on the same 196-release NFP × USDJPY sample — Andrews-1991's actually-preferred kernel gives 4% more correlation than BartlettYesterday's Stats #17 computed the Bartlett-kernel effective sample size (n_eff ≈ 112). Today's Stats #18 does the same computation with the Quadratic Spectral kernel — the one Andrews 1991 Section 10 explicitly recommended over Bartlett. Same sample, same autocorrelations, same Andrews AR(1)-plug-in bandwidth rule; different kernel: n_eff = 107.60 at S* = 3.72. QS gives ~4% more correlation-correction than Bartlett because its smoother spectral window picks up the ρ(2) and ρ(4) higher-lag mass that Bartlett's linear taper weights down.Paper Trail #18: A Simple, Positive Semi-Definite HAC Covariance Matrix (Newey & West, 1987) — the 6-page paper that made Bartlett-HAC the industry default, four years before Andrews proved QS was asymptotically betterThe paper that put the 'HAC' in Newey-West standard errors. Six pages in Econometrica, one main theorem (positive semi-definiteness), one consistency proof, and one modified Bartlett weight function w(j, m) = 1 − j/(m+1). It shipped in 1987. Andrews (1991) — yesterday's Paper Trail #17 — proved four years later that the quadratic-spectral kernel was asymptotically superior and provided the missing data-driven bandwidth rule. By then, Bartlett-via-NW87 was already the default in every econometrics package. Path dependence, textbook example of.US ISM Services on XAUUSD: 9 of 12 big-miss prints sent gold higher at 15 minutes, and by the 1-hour mark the median +15.75p AMPLIFIES to +47.00p203 non-contaminated US ISM Services releases on XAUUSD since 2009. Big-miss n=12 median +15.75p at 15m with 9 of 12 up (75%); at the 1h mark the median swells to +47.00p and the up-rate lifts to 83.3%. Third leg of the ISM Services trilogy — dollar-strength on USDJPY (2026-08-07) and its EURUSD mirror (2026-08-14) established the beat-side story; XAUUSD's miss-side amplification is the fresh finding.US CPI m/m on XAUUSD: the 15-minute directional walk is monotonic — and the big-beat median FLIPS sign by 4 hours (from -16 pips to +52)Across 198 non-contaminated US CPI m/m releases, gold's 15-minute response to the surprise is clean and monotonic — big-miss +23p (83% up), big-beat -16p (43% up). Four hours later the big-beat median has flipped to +52p (67% up). Same event, two different macro narratives, different timescales.All 28 liquid FX pairs share their loudest weekday half-hour in a 25-hour Thu-Fri US-macro window — really just 5 half-hour cells, 2.1% of the trading weekFor every one of the 28 liquid FX pairs, the loudest weekday half-hour lands in one of five specific slots: Thu 13:30, Thu 14:30, Fri 13:30, Fri 14:00, or Fri 14:30 UTC. Twenty-eight peak cells, five containers, 2.5 hours total.Statistics for Traders #17: Bartlett-window effective sample size on the same 196 NFP × USDJPY moves — the AR(1) formula gave 115, the Andrews-1991 Bartlett gives 113, the block bootstrap gave 39, and the three numbers answer three different questionsStats #10 used the AR(1) formula for effective sample size and got n_eff ≈ 115 on the 196 NFP × USDJPY 15m moves. The Bartlett-window generalization with Andrews (1991) automatic bandwidth M* = 4.5 gives n_eff ≈ 113 — non-parametric and lag-1-dominated on this sample. Stats #16's block-bootstrap correction gave n_eff = 39. Three numbers, one series, three questions.Paper Trail #17: Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation (Andrews, 1991) — the paper that gave us Newey-West-standard-error automatic bandwidths, and quietly recommended a different kernel altogetherDonald Andrews's 1991 Econometrica paper is where the Newey-West-standard-error automatic bandwidth actually comes from. Rate O(T^(1/3)) for Bartlett with constant 1.1447, plug-in a = 4·ρ²/(1-ρ²)² — the same formula today's Stats #17 uses to get M* = 4.51 on the NFP × USDJPY series. Its finding: the Bartlett kernel is asymptotically inefficient. Its recommendation: use the Quadratic Spectral kernel instead. The industry mostly ignored the second half.AUD Employment on AUDNZD: 0 of 8 big-miss prints since 2010 sent the pair up, 23 of 26 big-beat prints did (88.5%), and the pct-up walk is perfectly monotonic across all 5 bucketsThe 8 big-miss AUD Employment prints since 2010 all pushed AUDNZD down at 15 minutes — an unblemished 0-of-8 down-rate on the tail. The 26 big-beat prints sent it up 23 times (88.5%). Every one of the 5 pct-up buckets falls in order: 0, 21, 64, 79, 89%.Canada Employment on CADCHF: all 23 big-beat prints sent the quietest CAD-cross higher 15 minutes later, and the miss side is 8-of-9 down199 non-contaminated Canada Employment Change releases on CADCHF at 15 minutes. Medians walk −20.8 / −5.7 / +5.1 / +21.8 / +34.0 pips across the five surprise buckets. Pct-up walks 11 / 32 / 62 / 84 / 100. Big-beat n=23 is unanimous. The single big-miss exception is the 2020-04-09 COVID collapse (−1 million jobs vs a −427,000 consensus, moved +10.4p in the pandemic chaos). Strip that outlier and both tails are 100%. Third clean 5-bucket monotonic Canada-Employment post in a row after USDCAD (2026-08-01) and CADJPY (2026-08-08); this one is on the quietest cross in the CAD complex, so the news-driven signal stands out even more against its usual noise floor.Every JPY-cross has its quietest weekday half-hour in the 20:00-22:30 UTC late-NY / pre-Tokyo handoff — and USDJPY's Mon 21:30 UTC cell at 5.3 pips is the quietest single cell in the whole setAll 7 liquid JPY-crosses have their median half-hour range 1.16× to 1.51× smaller in the 20:00-22:30 UTC window than across their overall weekday. Every one of them has its single-quietest weekday half-hour inside that window, mostly at Mon 20:00 or Mon 22:30 UTC. The mechanism is structural: London is closed, NY is winding toward its close, Tokyo hasn't opened yet, and Sydney handles the tape thinly on its own. The JPY-crosses have no active home-market for either leg of the pair.Statistics for Traders #16: Politis-White 2004 automatic block length b_opt = 4.98 on yesterday's NFP × USDJPY series — the data-driven optimum lands exactly where the E[L]=5 rule-of-thumb column was, confirming yesterday's leftmost column was already rightYesterday's stationary bootstrap ran three rule-of-thumb columns: E[L]=5 / 10 / 20. Today's Politis-White 2004 automatic block-length algorithm computes the OPTIMAL b_opt directly from the data's autocorrelation structure and returns b̂_opt = 4.98 (p_opt = 0.20). That's essentially yesterday's leftmost column exactly, meaning yesterday's rule-of-thumb was already well-tuned — but now we have the primary-source justification instead of a heuristic. Under-blocking (plain iid bootstrap) understates the CI by 32% relative to the optimal; over-blocking (yesterday's E[L]=10) widens it by 17% past the optimum. The correlogram flat-top cutoff picks the block size in one pass from ρ̂(3) through ρ̂(7) all lying inside the ±0.216 confidence band.Paper Trail #16: Currency Momentum Strategies (Menkhoff, Sarno, Schmeling & Schrimpf, 2012) — cross-sectional winners-minus-losers earns up to 10% p.a. on 48 currencies, but roughly HALF the pre-cost edge is eaten by full quoted bid-ask spreadsThe paper that documented FX cross-sectional momentum end-to-end. Menkhoff, Sarno, Schmeling & Schrimpf (2012), JFE 106(3):660-684, sample Jan-1976 to Jan-2010, up to 48 currencies. Rank each currency's monthly USD-excess return over a 1-to-12-month formation window; long the top quintile, short the bottom quintile, hold 1-12 months. Table 1 headline: MOM(f=1, h=1) earns 9.46% annualized (t=5.31, Sharpe 0.95); MOM(6,1) 8.54%; MOM(12,1) 6.16%. But applying the full quoted bid-ask spread drops MOM(1,1) from ~10% to ~4% (Table 7). The spread persists on cost-adjusted basis (~4%) but only because effective FX spreads are much smaller than quoted ones. The paper's other headline: currency momentum is largely uncorrelated with the carry trade and not explained by traditional risk factors — it's a genuine standalone anomaly, most likely explained by limits to arbitrage tied to idiosyncratic volatility.AUD Unemployment on AUDJPY: same 8 big-miss prints that took AUDUSD down, but on the JPY cross the median move is 46% bigger198 non-contaminated AUD Unemployment Rate releases on AUDJPY. 5-bucket median walk −35.3 / −17.6 / +1.1 / +19.1 / +22.9 pips; pct-up 0 / 25 / 51 / 72 / 72. Same 8 big-miss prints as the 2026-08-06 AUDUSD post — both pairs are 8-of-8 down on those releases. What the JPY cross adds is size: AUDJPY big-miss median is −35.3p versus AUDUSD's −24.1p, a 46% amplification. Same is not true on the beat side, where AUDUSD (+24.5p) and AUDJPY (+22.9p) move almost identically — a clean example of a JPY-cross behaving as a bigger-vol AUD-vol proxy specifically on the risk-off leg.UK CPI y/y on EURGBP: 12 of 13 big-miss prints sent the pair up (92.3%), the whole 5-bucket walk is monotonic on both median AND pct-up — and unlike its GBPUSD mirror, this edge doesn't fade196 non-contaminated UK CPI y/y releases on EURGBP at 15 minutes. Medians walk +15.20 / +10.50 / −0.75 / −3.40 / −5.30 pips across big_miss → big_beat — clean monotonic. Pct-up walks 92.3 / 87.2 / 45.6 / 26.9 / 18.8 percent — also clean monotonic. The GBPUSD leg (published 2026-08-02) shows the same shape on its miss side but with a small_miss > big_miss magnitude inversion, and the whole 15m edge fades by end of day. EURGBP holds direction all the way to 4h. Same release, two pair legs, one keeps the edge and the other doesn't.AUDNZD's top-2 loudest half-hour cells of the week are BOTH outside the London/NY overlap — Wed 21:00 UTC (12.60p) and Fri 21:30 UTC (12.50p), both Sydney/Wellington-morning cluster12 days ago I flagged AUDNZD as the only pair whose single loudest cell is outside the London/NY overlap window (Wed 21:00 UTC). Today's deepening: it isn't just the #1 cell. Ranking all 240 weekday half-hour cells by median 30-minute range, the #2 cell is ALSO in the Sydney/Wellington cluster — Fri 21:30 UTC at 12.50p. The overlap band contributes the #3, #4, #5 cells, but the top-2 belong to Asia. Half of AUDNZD's top-20 loudest cells are Asia-session, half are Overlap — a 50/50 split that no other liquid pair remotely approaches.Statistics for Traders #15: Stationary bootstrap on the 196-release NFP × USDJPY |move_pips| series — the plain iid bootstrap gives [33.03, 43.67] for the mean, the block-bootstrap correction (E[L]=10) widens it 74% to [28.99, 47.48]The plain percentile bootstrap from Stats #12 assumes iid observations. Stats #10 showed the NFP × USDJPY 15m |move_pips| series has lag-1 autocorrelation +0.26 — canonical volatility clustering, well outside the ±0.14 IID band. On that autocorrelated series the plain bootstrap under-covers. Today's worked example runs the Politis-Romano 1994 stationary bootstrap (yesterday's Paper Trail #14) end-to-end on the same 196-release series: draw blocks of geometric length, paste them together, compute the statistic on the pseudo-series. The result: 95% CIs 48-92% wider than the plain bootstrap, depending on the mean block length E[L].Paper Trail #15: An Empirical Evaluation of Accounting Income Numbers (Ball & Brown, 1968) — the paper that showed annual earnings correlate with stock returns AND that price starts moving on the news months before the releaseBall & Brown's 1968 JAR paper is the foundational finding that accounting income numbers do carry price-relevant information, that firms with positive earnings surprises see positive abnormal returns before and around the announcement, and that price continues to drift in the direction of the surprise for months AFTER the release. It's the paper Bernard & Thomas 1989 (Paper Trail #6) refined into what we now call post-earnings-announcement drift. The 1968 paper is behind JSTOR's paywall today; every claim below traces to open-access secondary sources — Ian Gow's open-source accounting textbook, Zach Williams's 2019 reexamination in JMI, and Wikipedia's PEAD article.Canada GDP m/m on CADJPY: pct-up walks a perfectly monotonic 26.1 → 27.3 → 50.0 → 70.8 → 90.9 across all 5 buckets — and the one big-beat 'down' print is a COVID-2020 math artifact196 non-contaminated Canada GDP m/m releases on CADJPY at 15 minutes. Big-beat: 10 of 11 prints sent the pair up (90.9%). Big-miss: 17 of 23 sent it down (26.1% up). The whole 5-bucket pct-up walk is monotonic. The median walk has a beat-side inversion (small_beat +7.20p is bigger than big_beat +3.10p) — but strip the one COVID-era outlier from big_beat and the direction rate becomes 10 of 10 = 100%. Sixth JPY-cross-beats-USD-pair post: the same event on USDCAD has 87.5% miss-side up-rate and a comparable beat-side inversion.Swiss CPI m/m on EURCHF: 199 releases with a monotonic median walk but a beat-side pct-up inversion — big_beat is up 36.4% of the time, small_beat only 20.9%199 non-contaminated Swiss CPI m/m releases on EURCHF at 15 minutes. Medians walk +12.50 / +2.95 / −0.10 / −2.10 / −2.90 pips big_miss → big_beat — monotonic across every bucket. Pct-up walks 83.3 / 71.7 / 47.8 / 20.9 / 36.4 percent — miss-side monotonic, but small_beat 20.9% is BELOW big_beat 36.4%. The same event on USDCHF (published 2026-08-05) has a clean monotonic pct-up walk. EURCHF's miss-side amplitude is roughly twice USDCHF's, but the beat side is where the two pairs part ways.Wed 14:30 UTC — the EIA petroleum-inventories slot — is a top-6 loudness cell for 14 of 28 liquid FX pairs, and a top-10 cell for 25 of 28The EIA Weekly Petroleum Status Report drops at 10:30 AM ET every Wednesday. That's 14:30 UTC in DST months. A prior post covered the 7 CAD-complex pairs that all rank the slot in their top-6; this one covers the other seven non-CAD-complex pairs that also do — GBPAUD (#3), AUDCHF, EURAUD, EURCHF, GBPCHF, GBPNZD (#6), NZDCHF (#6) — plus the surprising fact that only three of 28 pairs rank Wed 14:30 UTC outside their top-10.Statistics for Traders #14: BCa bootstrap — bias-corrected accelerated CI for the mean on today's slot-1 CHF CPI × EURCHF big_miss n=18 sample. Shifts both endpoints right vs plain percentile because z0=+0.04 and a=+0.044 for right-skewed dataThe BCa (bias-corrected accelerated) bootstrap of Efron 1987 is the refinement to yesterday's plain percentile bootstrap that adjusts both endpoints for finite-sample bias (z0) and for a skew-related acceleration term (a). Worked on today's slot-1 anchor CHF CPI × EURCHF big_miss n=18 sample. Plain percentile CI for the mean: [+9.97, +30.76]. BCa: [+11.01, +32.43] — both endpoints shifted right because sample skew is +1.22 and z0/a come out positive. Also demonstrates the median-specific edge case where jackknife perturbation is degenerate and a collapses to 0, so BCa reduces to a bias-only correction.Paper Trail #14: The Stationary Bootstrap (Politis & Romano, 1994) — the block-bootstrap variant that resamples random-length blocks with a geometric distribution so the pseudo-series is itself stationaryPolitis & Romano's 1994 JASA paper introduced the stationary bootstrap: a resampling scheme for autocorrelated time series where block lengths are drawn from a geometric distribution with mean 1/p, so each pseudo-sample has the same stationarity property as the original. It's the direct extension of Efron 1979 (Paper Trail #13) to serially dependent data and the primary source Stats #12 flagged as the upgrade required for the autocorrelated FX-move series Stats #10 first quantified. The 1994 paper itself is behind Taylor & Francis's paywall today; every claim below traces to Politis's own subsequent review (Politis & White 2004) and correction (Patton, Politis & White 2009).US ISM Services on EURUSD: 15 of 19 big-beat prints sent EURUSD down at 15 minutes, and the 5-bucket median walk mirrors the USDJPY version almost exactly (published 7 days ago)197 non-contaminated US ISM Services PMI releases on EURUSD at 15 minutes. Medians walk +14.50 / +8.00 / −2.30 / −10.00 / −10.80 pips big_miss → big_beat — monotonic across every bucket. Pct-up walks 72.7 / 73.2 / 45.7 / 17.8 / 21.1 percent — nearly monotonic. Big-beat n=19 with 15 down prints = 78.9% down-rate is the mirror image of the 2026-08-07 USDJPY post where 18 of 19 big-beat prints sent USDJPY up (94.7% up-rate). Same dollar-side flow, seen from both crosses.Canada Ivey PMI on CADJPY: 197 releases, both the median walk AND the pct-up walk monotonic across all five surprise buckets — and the first soft-survey release to do it on the JPY cross197 non-contaminated Canada Ivey PMI releases on CADJPY at 15 minutes. Medians walk −10.15 / −8.20 / +2.00 / +3.40 / +4.20 pips big_miss → big_beat, and pct-up walks 21.4 / 37.8 / 57.3 / 69.4 / 71.4 percent — both monotonic through every one of the five buckets. The same event on USDCAD is directionally right too, but its beat-side medians have a small_beat > big_beat magnitude inversion. Fifth JPY-cross-beats-USD-pair post in the ledger — and the first that's driven by a soft-survey release rather than a hard-data one, which is a genuine surprise given how noisy the Ivey response usually looks on the domestic USDCAD pair.Monday 12:30 UTC is the quietest half-hour of the entire London/NY overlap for ALL 28 liquid FX pairs — 1.4× to 1.7× quieter than that same pair's loudest overlap cellFor every one of 28 liquid FX pairs, the quietest half-hour cell inside the Mon-Fri 12:30-15:00 UTC London/NY overlap window is Monday's 12:30 UTC opening slot. Every pair. The ratio between each pair's Mon 12:30 median range and its loudest overlap half-hour ranges from 1.39× (GBPCHF) to 1.69× (USDJPY), median 1.51×. This isn't the same as the general Monday-is-quieter finding — it's the stricter claim that even inside the loudest three hours of the entire trading week, Monday is still the low. The mechanism is simple: Tue-Fri overlap includes Thursday jobless-claims at 13:30 UTC and Friday NFP + post-NFP at 13:30 and 14:30 UTC; Monday's overlap does not.Statistics for Traders #13: Information ratio via today's slot-1 CAD Ivey PMI × CADJPY sample — Sharpe against a real benchmark rather than cash, and how it becomes a Welch t-statistic for bucket-filter strategiesThe information ratio is Sharpe with the risk-free rate replaced by a real benchmark's return. For a bucket-filter strategy the calculation collapses to Welch's two-sample t-statistic. Worked on today's slot-1 CAD Ivey × CADJPY big-beat n=14 sample: per-trade Sharpe 0.488, IR vs all-events benchmark +1.84, IR vs non-tail-bucket benchmark +1.97 (both above the 1.5 rule-of-thumb for 'genuinely adding alpha'). The short-big_miss variant has an even higher IR of +2.81 because the non-tail-bucket baseline drifts slightly negative on CADJPY, which the short-side strategy diverges from usefully.Paper Trail #13: Bootstrap Methods — Another Look at the Jackknife (Efron, 1979) — the paper that gave us the percentile bootstrap yesterday's Stats #12 was built on, plus the enduring insight that 'the jackknife is a linear approximation to the bootstrap'Bradley Efron's 1977 Rietz Lecture, published in the Annals of Statistics 7(1) 1-26 (January 1979). The paper introduces the bootstrap as a general method for estimating sampling distributions from a single random sample by resampling with replacement, illustrates it on the sample-median variance problem where the jackknife is known to fail, and shows the bootstrap outperforming cross-validation for linear-discriminant-analysis error rates. Also names the three Methods (direct calculation, Monte Carlo approximation, Taylor-series expansion), showing that Method 3 IS the jackknife — hence the paper's subtitle. Verified via OCR of the image-only JSTOR/Project Euclid PDF; seventh Paper Trail post in a row with full primary-source access.AUD Retail Sales m/m on AUDUSD: 14 of 16 big-miss prints sent AUDUSD down (87.5%), the 5-bucket median walk is monotonic, but the beat side has a small_beat > big_beat magnitude AND up-rate inversion188 non-contaminated Australia Retail Sales m/m releases on AUDUSD at 15 minutes. Miss side: big_miss n=16 median −18.55p with only 2 of 16 up (12.5%); small_miss n=43 median −8.30p with 9 of 43 up (20.9%). Beat side: small_beat n=27 median +5.80p with 24 of 27 up (88.9%) but big_beat n=13 median +6.00p with only 9 of 13 up (69.2%). Both an up-rate inversion (small_beat 88.9% > big_beat 69.2%) and a magnitude near-tie on the beat side. Clears the 2026-08-12 considered-but-not-used ledger item that flagged this exact combo — first published post on Australia Retail Sales.Canada Retail Sales m/m on USDCAD: every column of the 5-bucket table walks monotonically — median, mean, AND up-rate — across all 194 releases194 non-contaminated Canada Retail Sales m/m releases on USDCAD at 15 minutes. Medians walk +16.7 / +12.7 / +2.3 / −6.0 / −17.25 pips big_miss → big_beat, means walk +23.6 / +17.5 / +5.9 / −10.3 / −20.0, and pct-up walks 80 / 84.6 / 62.4 / 31.1 / 10 percent — every single column monotonic across every single bucket. Nine of 10 big-beat prints sent USDCAD down; 12 of 15 big-miss prints sent it up. The fourth Canadian macro release to show a clean 5-bucket walk on USDCAD, after Employment, Trimmed CPI, and Unemployment.GBPNZD holds 19 of the 20 loudest weekday half-hour cells across all 28 liquid pairs — and its 20th-loudest cell beats 25 of the other 27 pairs' single loudest cell6636 weekday half-hour cells across 28 liquid pairs. Sorted by median range, GBPNZD takes 19 of the top 20 slots. The one interloper is GBPAUD Fri 14:30 UTC at #20. GBPNZD's own 20th-loudest cell (Tue 15:00 UTC = 29.80p) is louder than the single loudest cell of every pair except GBPAUD and GBPCAD. This is a deeper claim than the 2026-08-05 post which framed GBPNZD as 'the loudest pair' — GBPNZD isn't just loud in its peak hour, it's louder EVERYWHERE across the week than any of the 25 lower-volatility pairs are in their single loudest hour.Statistics for Traders #12: Percentile bootstrap 95% CI for today's big-miss n=15 CAD Retail median is [+11.1, +50.5] — narrower than the order-stat CI, wider than the t-CI for the mean, and the right choice for asymmetric tail-bucket samplesThe plain (i.i.d.) percentile bootstrap resamples with replacement 20,000 times and takes the 2.5% and 97.5% percentiles of the resampled medians. On today's slot-1 anchor — CAD Retail m/m × USDCAD big_miss n=15 — that gives 95% CI [+11.10, +50.50], width 39.4p. Contrast: the distribution-free order-stat CI from Stats #3 is [−5.30, +52.30] (wider, safer), and the t-CI for the MEAN from Stats #7 is [+8.23, +39.01] (narrower, assumes normality). Bootstrap is the middle ground — data-shape-aware, no distributional assumptions, but requires block bootstrap when observations are autocorrelated as Stats #10 flagged for the NFP volatility series.Paper Trail #12: Conditional Heteroskedasticity in Asset Returns — A New Approach (Nelson, 1991) — the paper that added the leverage effect to GARCH and gave us EGARCHTwo days after covering Bollerslev's 1986 GARCH, the natural follow-up: Daniel B. Nelson's 1991 EGARCH paper (Econometrica 59(2):347-370) that fixed the three biggest problems with GARCH. Nelson modeled ln(σ²) instead of σ², removing the need for nonnegativity constraints. He added the g(z_t) = θ·z_t + γ·(|z_t| − E|z_t|) function so negative and positive return shocks affect volatility asymmetrically. On CRSP daily returns 1962-1987 (n=6408), his estimated θ = -0.118 (SE 0.008) says negative shocks have 7.2× the volatility-impact of positive shocks of the same magnitude — the 'leverage effect' Fischer Black identified in 1976 that vanilla GARCH couldn't capture.UK Core CPI on GBPUSD: 13 of 15 big-beat prints sent GBPUSD up (86.7%), and the pct-up walk is monotonic — but the small-miss median is BIGGER than the big-miss median, which tells you something specific about noise198 non-contaminated UK Core CPI y/y releases on GBPUSD at 15 minutes. Pct-up walks 26.7 / 18.9 / 54.8 / 62.3 / 86.7 percent — cleanly monotonic across every one of the 5 surprise buckets. Big-beat n=15 with 13 up prints. But the median walk isn't monotonic on the miss side: big_miss median is -13.70p while small_miss median is -16.00p — the small-miss cluster produces LARGER absolute moves than the big-miss cluster. That's the signature of mean-reversion in the event's noise floor, not a random inversion. Explains why: the small-miss population is dominated by publisher-error / algo-reversal outliers that the big-miss samples don't see.Canada CPI m/m on CADJPY: 15 of 19 big-beat prints sent the pair up, and the 5-bucket median walk is monotonic — the JPY cross beats USDCAD once again194 non-contaminated Canada CPI m/m releases on CADJPY at 15 minutes. Medians walk −11.1 / −4.8 / +1.1 / +10.4 / +18.7 pips across big_miss → big_beat, and pct-up walks 15.4 / 35.4 / 55.6 / 63.6 / 78.9 percent — both monotonic through all five buckets. The same event on USDCAD is directionally right too, but its miss-side medians are non-monotonic (big_miss +12.8p is smaller than small_miss +12.95p). Third instance of the JPY-cross-beats-USD-pair pattern in the ledger — UK CPI on GBPJPY (2026-08-08) and CAD Employment on CADJPY (2026-08-08) did the same trick.Wednesday 14:30 UTC is a top-6 weekday half-hour for every single CAD-cross — the closest thing to a Canadian NFP hour comes from a US oil-inventory releaseThe EIA Weekly Petroleum Status Report drops at 10:30 AM Eastern every Wednesday. In UTC (during DST months) that's 14:30. For all seven liquid CAD-crosses — USDCAD, CADJPY, CADCHF, AUDCAD, EURCAD, GBPCAD, NZDCAD — that half-hour ranks in the top 6 of the weekly grid of 237 half-hour cells. GBPCAD ranks it #2 (behind only Fri 14:30 UTC post-NFP). The only cells that consistently rank higher across the CAD complex are Fri 12:30-14:30 UTC (NFP hour and its neighbors) and the Thursday ECB/BoE-decision window (12:30-14:30 UTC). No non-oil release comes close.Statistics for Traders #11: Pearson r across the whole CAD CPI × CADJPY sample is +0.44 — but within the big-beat bucket alone it's −0.15, and the bucket labels carry the signalThe 5-bucket monotonic walk we see across the tool is what a positive Pearson correlation of +0.44 looks like when you discretize a continuous relationship. But when you drop back into each of the five buckets and ask 'does knowing the exact surprise-z inside this bucket help me forecast the move?', four of five bucket-level r values have 95% CIs that straddle zero. The bucket boundary IS the signal — trying to squeeze extra edge from the exact z within a big_beat print doesn't work.Paper Trail #11: On Persistence in Mutual Fund Performance (Carhart, 1997) — the paper that added momentum to Fama-French and killed most of the 'hot hands' persistence storyMark Carhart's 1997 Journal of Finance paper extends Fama-French's 1993 3-factor model with a fourth factor: PR1YR, a zero-investment portfolio long last year's top 30% return firms and short last year's bottom 30%. On a survivor-bias-free sample of 1,892 diversified equity funds from 1962-1993, the 4-factor model plus investment costs explain 6.3 of the 8 percentage points of annual spread between decile-1 and decile-10 past-return funds — leaving the residual 'hot hands' story with almost nothing left. Verified against the JSTOR-hosted PDF, OCR-recovered because the reprint is image-only.Every major central-bank rate decision buckets 82-98% 'in_line' — 845 of 897 decisions across the Fed, BoE, ECB, BoJ, BoC, RBA, RBNZ, SNBAcross eight major central banks over 10-30 years of data, 845 of 897 rate decisions on the tool land in the 'in_line' bucket. The BoE is the most predictable at 98.1% in-line; the SNB the least at 82.1%. That's not because rate decisions don't matter — it's because OIS (overnight index swap) markets price the decision to the actual outcome by the morning of the meeting. The 5-15% of surprises that DO happen move HUGE: median move-pips per surprise range from ±25 to ±227 across the eight CBs. Practical implication: rate decisions are pre-priced by construction, not tradeable via the standard bucket-response framework the tool was built for.Australia Employment Change on AUDJPY: 21 of 26 big-beat prints sent the pair up 35.6 pips at 15m, with a cleaner beat-side walk than on AUDUSD198 non-contaminated Australia Employment Change releases on AUDJPY at 15 minutes. Medians walk −18.2 / −21.9 / +1.7 / +19.5 / +35.6 pips big_miss → big_beat, monotonic across all five buckets. Pct-up on the beat side walks 53 → 75 → 81 percent. Compared with the same event on AUDUSD (covered in the 2026-08-02 two-employment-reports post), the JPY-cross wins on beat-side pip magnitude and the USD-pair wins on miss-side unanimity (0-of-8 big-miss prints went up on AUDUSD versus 2-of-8 on AUDJPY).Tokyo takes lunch at 03:00 UTC — and every liquid JPY-cross gets 14-18% quieter for the next 90 minutesAll seven liquid JPY-crosses have a local minimum in typical half-hour range between 03:00 and 04:30 UTC. That window is Tokyo's lunch break (12:00-13:30 JST), and it dips 14-18% below the bracketing 02:00 UTC and 05:00 UTC half-hours. Japan doesn't observe DST, so the dip is stable year-round.Statistics for Traders #10: autocorrelation and why 196 NFP releases behave like 115 independent samples once you look at the volatility clusteringThe 196-release NFP history on USDJPY shows near-zero autocorrelation in signed move direction (as efficient-markets weak-form predicts) but a striking +0.26 lag-1 autocorrelation in absolute move size. Volatility clusters. Treat that 196-sample history as if it were 115 independent observations for confidence-interval purposes — otherwise your CIs will be systematically too narrow by about 30 percent.Paper Trail #10: Generalized Autoregressive Conditional Heteroskedasticity (Bollerslev, 1986) — the paper that gave us GARCH(1,1)Tim Bollerslev's 1986 Journal of Econometrics paper generalizes Engle's ARCH by letting past conditional variances enter the variance equation. The GARCH(1,1) form — h_t = α_0 + α_1·ε²_(t−1) + β_1·h_(t−1) — became the workhorse volatility model for the next 40 years. Verified against the full 21-page PDF Bollerslev hosts on his Duke faculty page.NFP on USDJPY: 14 of 14 big-beat prints sent USDJPY up at 15 minutes, and the small-miss bucket falls harder than big-miss196 non-contaminated NFP releases on USDJPY at the 15-minute window. Medians walk −16.2 / −26.0 / +1.8 / +24.5 / +30.2 pips big_miss → big_beat, monotonic. Big_beat n=14 lands 100% of prints on the up side. The small_miss bucket actually falls further than big_miss (−26 vs −16 pips) — a small-sample-on-tail artifact that shows up on several employment-print pairs.CAD Unemployment on USDCAD: 22 of 26 big-beat prints sent USDCAD down, and the whole 5-bucket walk is monotonic across every window from 1 minute to 4 hours196 non-contaminated Canada Unemployment Rate releases on USDCAD at 15 minutes. Medians walk +15.1 / +19.5 / +4.5 / -10.9 / -39.3 pips across the five surprise buckets. Pct-up walks 70 / 79 / 54 / 36 / 15 percent. This is the third Canadian labour post in the batch — completing the trilogy after CAD Employment Change on USDCAD (2026-08-01) and CAD Employment Change on CADJPY (2026-08-08). Both Canadian labour prints trade the same way: a Canadian jobs improvement pushes CAD stronger against the US dollar.Thursday 13:30 UTC — jobless-claims hour — is the loudest half-hour of the week for 9 pairs, more than Friday's NFP hour is for 7Across the 28 liquid FX pairs, the single loudest half-hour of the week lands on Thursday 13:30 UTC for 9 pairs, on Friday 14:30 UTC (the post-NFP echo) for 8, and on Friday 13:30 UTC (NFP itself) for 7. NFP-hour is not the modal peak. Weekly US Initial Jobless Claims plus the rotating monthly cluster of Retail Sales, GDP, Philly Fed, and PPI at the same 08:30-US-Eastern slot turn Thursday 13:30 UTC into a structurally loud cell for USD-, EUR-, and CHF-based pairs.Statistics for Traders #9: Sortino ratio via the CAD Unemployment × USDCAD big-beat bucket — a Sortino of 4.79 vs a Sharpe of 0.98, and why the gap tells you the loss distribution is asymmetricThe 26 big-beat CAD Unemployment prints on USDCAD produce a per-trade Sharpe of 0.98 for a short-USDCAD strategy — respectable but not extraordinary. The Sortino ratio on the same 26 trades is 4.79. That's not a computational quirk; it's the loss distribution telling you something concrete: 22 of the 26 trades won, and 3 of the 4 losers were small (-3.2, -3.5, -9.0 pips). Only one trade (2017-08-04 at -35.1p) was a meaningful loss. Sortino divides mean return by the RMS of downside returns, ignoring the upside variance that Sharpe's denominator sums over. When the ratio Sortino/Sharpe is well above the sqrt(2) that a symmetric distribution would predict, the loss side is genuinely rarer or smaller than the win side. This is the follow-up to Stats #8 (Sharpe ratio) and grounds today's slot-1 anchor in a distributional-asymmetry lens.Paper Trail #9: Mutual Fund Performance (Sharpe, 1966) — the paper that introduced what we now call the Sharpe ratio, applied to 34 mutual funds over 1954-1963William F. Sharpe's 1966 Journal of Business paper introduced the reward-to-variability ratio (R/V) as a single-number risk-adjusted performance metric, applied it to 34 open-end mutual funds over 1954-1963, and found the best fund's R/V of 0.78 was only 1.8× the worst fund's 0.43. Same-period rank correlation of R/V vs Treynor Index across the 34 funds: +0.974 — they rank the same funds almost identically. Cross-decade predictive rank correlation (1944-53 → 1954-63): +0.360 — modest, but a full standard error above zero. The paper also observed that median 'percentage of variance due to comovement with the Dow-Jones Industrial Average' was 90.33% across the 34 funds — most mutual funds were, at that point, well-diversified market proxies. Full primary-source verification against a JSTOR-sourced PDF.UK Unemployment on GBPUSD: 18 of 23 big-beat prints sent GBPUSD up, with the pct-up walk cleanly monotonic across all 5 buckets198 non-contaminated UK Unemployment Rate releases on GBPUSD at 15 minutes. Pct-up walks 25 / 47 / 57 / 60 / 78 percent across the five surprise buckets — monotonic. Tail medians walk -21.7 / +2.3 / +16.7 pips. Contrarian: a print that BEATS (comes in lower than consensus, fewer unemployed) pushes sterling UP against the dollar. Second unemployment-prints-are-contrarian post in the batch after CAD Unemployment on USDCAD (today's slot 1). The G10 pattern holds: labour-market improvements strengthen the home currency, and 15-minute FX prices reflect the surprise-direction almost immediately.UK CPI on GBPJPY: 42 of 47 small-miss prints sent GBPJPY down, and the whole 5-bucket walk is cleaner than on GBPUSD196 non-contaminated UK CPI (y/y) releases on GBPJPY at 15 minutes: medians walk −20.90 / −22.20 / +2.60 / +9.75 / +11.45 pips across the five surprise buckets. Pct-up walks 31 / 11 / 54 / 69 / 81 percent. The small-miss bucket is unusually clean — 42 of 47 prints sent GBPJPY down. The sterling leg dominates both crosses at the print (176 of 196 GBPJPY and GBPUSD moves share a sign), but the JPY-cross magnitudes are ~35% bigger at the tails and the small-miss unanimity is a touch stronger.The half-hour AFTER NFP is louder than NFP itself for 17 of 28 liquid FX pairsFor 17 of 28 liquid FX pairs, the Friday 14:30 UTC half-hour — the second half of the NFP hour, after the release-time bar closes — has a larger typical 30-minute range than the Friday 13:30 UTC release cell itself. Four pairs (EURUSD, AUDUSD, NZDUSD, GBPUSD) peak at Friday 14:00 UTC instead. Only 10 pairs (mostly JPY-crosses) have Fri 13:30 as their loudest of the NFP hour. If you're trading NFP with a hold-through-the-hour plan, the follow-through cell is where more of the risk actually shows up.Statistics for Traders #8: Sharpe ratio via the UK CPI × GBPJPY big-beat bucket — a +16-pip mean move looks great until you divide by 23 pips of noiseThe 16 big-beat UK CPI prints on GBPJPY had a mean 15-minute move of +16.06 pips and a standard deviation of 23.39 pips. Divide the mean by the standard deviation and you get a per-trade Sharpe ratio of 0.687 — well below the ‘decent’ threshold of 1. Sharpe is the trader's answer to “how much edge per unit of noise?” — a bigger number means the edge is bigger relative to the round-trip variability you'll actually experience. Worked here on today's slot-1 anchor, with an explicit comparison to the same-event GBPUSD version, an annualization illustration, and the four assumptions Sharpe quietly makes about your data.Paper Trail #8: Common Risk Factors in the Returns on Stocks and Bonds (Fama & French, 1993)The paper that supplanted CAPM in the industry's default asset-pricing toolkit. Fama and French argued that the single-factor market beta of CAPM misses two systematic sources of return variation — the size premium (small stocks beat big stocks over long horizons) and the value premium (high book-to-market stocks beat low book-to-market stocks). Adding SMB (small-minus-big) and HML (high-minus-low) as factors alongside the market takes the R² on their 25 test portfolios from CAPM's 2-of-25 above 0.9 to the three-factor model's 21-of-25 above 0.9. Every quantitative claim in this post is traced to the fetched PDF at bauer.uh.edu.Canada Employment on CADJPY: all 23 big-beat prints had CADJPY higher 15 minutes later, and the whole 5-bucket walk is stronger than USDCAD197 non-contaminated Canada Employment Change releases on CADJPY at 15 minutes. Medians walk −19.3 / −13.4 / +5.2 / +27.9 / +42.9 pips across the five surprise buckets. Pct-up walks 22 / 32 / 61 / 81 / 100 percent. The big-beat bucket has never sent CADJPY down — 23 for 23 up prints, the largest unanimous-up-rate sample in my published set. The USD cross I posted on 2026-08-01 showed the same directional shape but the JPY cross amplifies it: two same-sign pushes (CAD stronger + JPY weaker on the commodity-friendly print) versus one on USDCAD.US ISM Services PMI on USDJPY: 18 of 19 big-beat prints saw USDJPY higher, and the whole 5-bucket walk mirrors ISM Manufacturing on USDJPY almost exactly197 non-contaminated ISM Services releases on USDJPY at 15 minutes: median moves −25.9 / −9.35 / +1.2 / +11.55 / +12.4 pips across the five surprise buckets, pct-up walk 9 / 20 / 57 / 83 / 95 percent. Compare that with ISM Manufacturing on USDJPY, published four days ago — same walk, same signs, beat-side tail-unanimity is actually a touch stronger for Services. The two ISM releases print two days apart every month and move USDJPY the same way.Every liquid FX pair's loudest weekday half-hour is at least 2× its quietest — and EURUSD's is nearly 5×For each of the 28 liquid FX pairs, divide the median range of its loudest weekday half-hour by the median range of its quietest. Every one of the 28 lands above 2×. 13 land above 3×. Six land above 4×. EURUSD tops the list at 4.97× — its Thursday 13:30 UTC cell is nearly five times louder than its Monday 22:30 UTC cell. If your default risk model uses a session-average range, you're systematically over-sizing your quiet-window trades and under-sizing your loud-window ones.Statistics for Traders #7: the t-distribution 95% CI for the mean, worked on the 11 ISM-Services big_miss USDJPY moves — and why the answer is narrower than the median CI, but you should trust it lessThe 11 big-miss USDJPY moves following ISM Services PMI: mean −38.69 pips, standard deviation 39.81 pips, standard error 12.00 pips. Applying the t-distribution formula, the 95% CI for the true mean move is [−65.43, −11.95] pips — a 53.5-pip window. That's narrower than the distribution-free CI for the same sample's median (Stats #3 method: [−87.60, −6.00], width 81.6p). But the t-CI's tightness depends on assuming the data are normally distributed, and Stats #6 already showed that FX bucket distributions are fat-tailed. The narrower CI comes from an assumption the data violates.Paper Trail #7: Trading Is Hazardous to Your Wealth (Barber & Odean, 2000)78,000 households, six years of discount-brokerage trades, and one of the most cited findings in retail-investor research: the households that traded most earned an annualised 11.4% net-of-costs, while the market returned 17.9%. Buy-and-hold households earned 18.5%. The gross-return spread was ~3-4 percentage points; the rest of the seven-point gap was pure transaction cost. What the paper actually says, in the paper's own numbers.US CPI on EURUSD: 196 releases walking a clean 5-bucket monotonic response — and the mirror image of UK CPI on GBPUSD once you correct for pair convention196 non-contaminated US CPI y/y releases on EURUSD at 15 minutes: median moves +11.8 / +8.6 / +3.0 / −6.35 / −16.2 pips across the five surprise buckets. 11 of 13 big-beat prints — including the entire summer-2022 inflation panic — pushed EURUSD down. Compare that with UK CPI on GBPUSD (published 2026-08-02): same shape, flipped sign, because base-currency convention flips too. Both are the same underlying rate-differential re-pricing.AUD Unemployment Rate on AUDUSD: all 8 big-miss prints pushed the pair down, monotonic across all 5 buckets198 releases of Australia's Unemployment Rate on AUDUSD since 2010. Median 15-minute moves: −24.10 / −15.30 / −0.10 / +16.45 / +24.50 pips (big_miss → big_beat). Up-rate column: 0 / 28 / 49 / 70 / 72. All 8 big-miss prints moved AUDUSD down. Cleanest 5-bucket monotonic labour-print I've pulled from the tool.CADCHF is the quietest of the seven CAD-crosses — typical 30-minute range 7.25 pips, and its loudest cell of the whole week barely beats USDCAD's medianAcross every 30-minute weekday cell of CADCHF, the typical range is 7.25 pips — smaller than USDCAD (9.1p), CADJPY (9.9p), EURCAD (11.85p) or GBPCAD (15.0p). Its loudest cell of the entire week — Friday 13:30 UTC, on NFP — prints just 14.2p. Which is smaller than GBPCAD's median. If you want a CAD cross without a peak, this is the one.Statistics for Traders #6: fat tails, kurtosis, and why NFP's 'in-line' bucket contains the biggest outlier moves in the datasetKurtosis is tail-thickness — how far the min-to-p25 and p75-to-max whiskers reach relative to the IQR. On NFP × EURUSD 15m, the in_line bucket has BOTH whiskers over 2.3× IQR (Tukey's outlier threshold is 1.5×). The 'quiet' bucket contains the largest observed candles in the dataset: −104.8p from a 165k print in 2013, +86.0p from a 162k print later that same year. Fat tails are what happens when 'in-line' meets tape you didn't schedule for.Paper Trail #6: Post-Earnings-Announcement Drift (Bernard & Thomas, 1989)The paper that turned a curious 1968 observation into a durable anomaly with a name. Bernard and Thomas took the drift that Ball & Brown had found — stock prices continue moving in the direction of an earnings surprise for weeks after the announcement — and showed that no risk-based story could explain it. Fama would later call PEAD 'the granddaddy of underreaction events'. It's the equity-market cousin of everything the News Impact Explorer measures on FX.NZ CPI on NZDUSD: 0-of-3 big-miss prints went up, 6-of-6 big-beat prints went up — the cleanest tail unanimity across every G10 inflation print I've published this week63 quarterly NZ CPI prints on NZDUSD at 15 minutes: median moves −54.9 / −29.0 / +2.1 / +12.45 / +13.45 pips across the five surprise buckets. Every one of the 3 big-miss prints pushed NZDUSD down; every one of the 6 big-beat prints pushed it up. Small samples on the tails but strong pattern — and it's the fourth 'inflation-print monotonically moves the domestic USD pair' finding in a row, after Switzerland, Canada, and Australia.Swiss CPI on USDCHF: clean 5-bucket directional response with 198 releases behind itAcross 198 monthly Swiss CPI prints since 2010, USDCHF's 15-minute median move climbs monotonically from −4.5 pips on a big beat to +6.6 pips on a big miss, and the pct-up rate walks from 36% up through 78%. Beats and misses each get 11+ tail-bucket observations — enough sample to say the shape is real.GBPNZD is the loudest liquid FX pair — its typical 30-minute range beats USDCHF's loudestAcross every 30-minute weekday cell of GBPNZD, the typical range is 21.9 pips — bigger than USDCHF's single loudest cell of the entire week (16.0p). The single loudest cell across all 28 major pairs is GBPNZD Friday 14:30 UTC at 34.55p. The pair is flat, hot, and gives you nowhere to hide.Statistics for Traders #5: how to read skew off the tool's p25/median/p75 columnsSkew is distributional asymmetry, and the tool exposes it two ways: is the median centered inside the IQR (or does it tilt toward one edge?), and are the whiskers the same length (or is one much longer)? On NFP big_miss XAUUSD, the IQR is centered but the right whisker is 2.56× the left — 'inside-symmetric, outside-right-tailed'. Read both signals; sometimes they agree, sometimes only one signals.Paper Trail #5: ARCH (Engle, 1982)The paper that formalised what every trader already knew: volatility clusters. Big-move days sit next to other big-move days; calm days sit next to other calm days. Nobody assumes a stock's variance is 'a constant' anymore, and the reason nobody does is this paper.Canada's Trimmed CPI is the second BoC-preferred inflation metric to move its USD pair monotonically — and 5 of 5 big-miss prints pushed USDCAD up82 releases of Canada's Trimmed-Mean CPI y/y on USDCAD, split into five surprise buckets. Medians climb monotonically from −9.0p on small_beat to +15.8p on big_miss, and 5 of 5 big-miss prints went positive. Same shape as yesterday's AUD Trimmed Mean CPI post on AUDUSD — different currency, same rate-differential mechanism.AUDUSD trades Australia's Trimmed Mean CPI like a rate decision — cleanly and monotonicallyAcross 67 Trimmed Mean CPI releases, AUDUSD's median 15-minute response climbs monotonically from −36 pips on a big miss to +21 pips on a small beat, with 0% and 17% up-rates on the miss buckets. It's the cleanest directional shape any AUD data point produces on the pair.27 of 28 liquid FX pairs' quietest half-hour of the week is on MondaySweep every pair in the Calm Zones catalogue for its minimum-range weekday cell and Monday wins 27 times out of 28. The one exception (EURCAD, Wed 04:00 UTC) is in the same pre-London Asia sleep window as the Monday holdouts. The finding is more consistent than any single pair's loudest-cell story.Statistics for Traders #4: what the tool's p25 and p75 columns actually tell you (and why they're not the same as ±1σ)The median tells you the center. The IQR (p75 − p25) tells you the width. On NFP big_beat n=14, half of all outcomes landed between −52 and −16 pips, but the outer half stretched from −124 to +9. Position-sizing depends on which of those windows you're planning against.Paper Trail #4: Efficient Capital Markets (Fama, 1970)The paper that put 'you can't beat the market' on formal footing. Fama's three forms of efficiency, plus the empirical work he cites — including Jensen's 1968 study where 89 of 115 mutual funds underperformed a comparable-risk market portfolio by an average of 14.6% over ten years, net of fees.US GDP surprises move gold in the textbook direction — miss up, beat down, monotonic across all five bucketsAcross 72 US GDP releases on XAUUSD, the median 15-minute move climbs monotonically from −25 pips on a big beat to +56 pips on a big miss, with 88% up-rates on miss-side prints. Same directional mechanism as NFP-on-gold, on a different macro event class.US ISM Manufacturing PMI on USDJPY: 0 of 12 big-miss prints had the dollar higher an hour laterAcross 196 ISM Manufacturing PMI releases since 2010, USDJPY responds monotonically to the surprise: -23 pips on a big miss, +14 on a big beat, and only 1 of the intermediate buckets breaks the pattern. The direction holds cleanly through end of day.AUDNZD is the only major pair whose loudest hour of the week isn't in the London/NY overlapAcross all 28 pairs in the Calm Zones catalogue, 27 have their loudest half-hour cell fall in the London/NY overlap window on a Thursday or Friday. AUDNZD is the exception. Its loudest cell is Wednesday 21:00 UTC — the Sydney/Wellington open.Statistics for Traders #3: why the big_miss bucket's +12 pip median could actually be +105 or −24Sample size is the difference between a tool that shows you a signal and a tool that shows you noise pretending to be one. Here's what a small-n bucket median actually tells you — and why the tool marks small buckets faint on the chart.Paper Trail #3: The Disposition Effect (Odean, 1998)Ten thousand discount-brokerage accounts, seven years of trades, and one uncomfortable finding: retail investors realized 50% more of their winners than their losers — and the winners they sold went on to outperform the losers they kept by 3.4% over the following year.NFP moves gold in the exact opposite direction it moves the dollar — and the mirror is remarkably cleanThe typical NFP big-beat prints XAUUSD 108 pips lower in the first 15 minutes and 92% of big-miss prints send it higher. That's a cleaner directional signal than NFP produces on any USD pair, and it makes physical sense.UK CPI on GBPUSD: the clean directional edge is gone by end of day196 clean releases show a textbook first-hour reaction — miss and pound falls 20 pips, beat and it rises 8. By end of day, the big-beat bucket has flipped sign. The move is real; the drift is not.EURGBP is the quietest liquid major, and its loudest cell isn't close to anyone else'sAcross 237 weekday half-hour cells since 2010, EURGBP's typical median 30-min range is 5.8 pips and its single loudest cell is 11.4. Both numbers are smaller than the equivalent numbers on every other G10 major.Statistics for Traders #2: what "±35 pips of noise" actually means for your stopThe typical NFP small_beat moves EURUSD -28 pips at 15 minutes. The standard deviation of that same distribution is 35 pips — almost as large as the median move itself. Here's what that number really tells you.Paper Trail #2: Momentum (Jegadeesh & Titman, 1993)The paper that turned 'buy what's going up' from folk wisdom into a documented anomaly. 1.31% per month on a winners-minus-losers zero-cost portfolio, 1965–1989 US stocks, with half the return giving back over the following 24 months.Two employment reports, both textbook at 15 minutes. Only one is still textbook by end of day.AUD Employment on AUDUSD and CAD Employment on USDCAD look nearly identical in the first fifteen minutes. By the New York close their miss sides have gone in opposite directions.CAD Employment on USDCAD is the textbook surprise-response event196 clean releases show a symmetric five-bucket distribution: big miss +40 pips, big beat -41 pips, in-line does nothing. No mean-reversion at EOD. Reproducible in the tool.GBPJPY's loudest half-hour of the week is Friday 13:30 UTCAcross 802 Fridays of GBPJPY data, the median 30-minute range in the 13:30 UTC slot is 28.3 pips — 2.5x the Asia-session median. The full Wed–Fri overlap band dominates every other slot in the week.Statistics for Traders #1: what "z-score" actually tells you about an economic surpriseA 14k NFP beat and a 113k NFP beat can bucket into completely different surprise sizes. Z-scoring against the release's own history is why. Worked through the last three months of NFP prints.Paper Trail #1: Prospect Theory (Kahneman & Tversky, 1979)The paper that reframed how economists model risk. Losses feel bigger than equivalent gains, people flip from risk-averse to risk-seeking when framed differently, and the S-shaped value function that describes both is still the reference decades later.156 out of 174 RBA meetings didn't move AUDUSD. The 18 that did, moved it in one direction.Since 2010, 90% of RBA cash-rate decisions have printed exactly on consensus and moved AUDUSD by a median 3 pips. The other 10% were 9 misses (100% AUDUSD down, median -64p at 15m) and 9 beats (100% AUDUSD up, median +46p). RBA meetings are all about the surprise.EURUSD Thu 12:30 is quiet 15% of the time. Here's why.127 of 832 Thursdays at 12:30 UTC were calm on EURUSD. Why the number isn't zero, and why the tool marks this cell DST-ambiguous.Four XAUUSD reaction records fell in four weeksFed, GDP, NFP, CPI: four US macro events between June 17 and July 14 each broke the largest 15-minute XAUUSD reaction on record, by 1.74x to 2.33x. What the data shows, and what it doesn't.How to check what a release does to your pairEvery scheduled release has a track record. Here is how to read it in News Impact Explorer, panel by panel, using NFP on gold as the worked example.What actually happens to EURUSD in the 15 minutes after NFP (and the next five days)195 releases, sorted by surprise, measured from 15 minutes out to 5 days. The story isn't drift. It's asymmetric: beats mean-revert, misses hold, in-line does nothing.Why your backtested win rate doesn't survive contact with real news eventsSome of your backtested wins and losses came from news flow that had nothing to do with your setup. Here's how much, and how to filter it out.The Bloomberg terminal problem: why institutional edge on macro events was never available to retailThe pros really do have data you don't. Here's exactly what it is, why the gap stayed open for so long, and why it's finally closing.