The trend weight under acknowledged ignorance

Question. The construction tournament nominated this as its number-one next test: how much trend notional should the investor hold, when three instruments return three different answers and the disagreement is about a forward mean that no amount of resampling 1990–2026 can identify?

Decision it informs. The size of the stacked-fund line, and — more importantly — what has to be believed for any size to be right. It is not a recommendation on the repository’s behalf: decision 0004’s non-promotion and its zero-leverage default both stand, and decision 0009 clause 3 unblocks the measurement of the funding rule and nothing else.

Out of scope. Which wrapper to buy — the tournament shows the return evidence cannot separate RSST, MATE and JPFP. The exposure arithmetic, the financing stack and the two holdability routes, which are leverage and the notional budget’s. Whether trend has a premium at all, which is trend and managed futures’s, live managed futures’s and now the adversarial review §1’s; this page takes their answers as a weighted range on one stated basis and shows what the decision does across it.

as of 2026-08-22. Every figure regenerates from studies/trend_weight_regret.py via cd research && uv run python -m portfolio_edge.studies.trend_weight_regret; the closed forms and the minimax identity are pinned in research/tests/unit/test_studies_trend_weight_regret.py against independently computed fixtures. No experiment was registered and no ledger entry was written: this is a decision surface over quantities other pages measured.

Correction, and it moved the answer. The first version of this page entered the repository’s 1.80 pp/yr convention on a gross arithmetic axis. The adversarial review §1 traced that figure: it is AQR TSMOM’s own 2012–2025 geometric mean net of a 1.50% fee that this page’s cost term already charges. §1.1 reconstructs it from the pinned file and closes the arithmetic exactly. The prior below is rebuilt on one stated basis, two independent out-of-window constructions are added, and the recommendation moves from 20% to 25%. §8 records what changed and what did not.

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Conclusion

1. No weight is demonstrably right, and the reason is precise rather than vague. On the corrected prior, against the investor’s own unlevered portfolio, every decision rule this page can build — minimax regret, minimum expected regret, with and without the investor’s own capitulation priced inside the path, under every reweighting tried — returns 0.28 to 0.40. Against a leverage-matched control at this panel’s realised equity premium, every one of them returns 0.00 to 0.12. The entire disagreement is a choice of comparator, not a measurement, and at a 30% weight it would take 154 years of holding before this instrument could adjudicate it. §2, §3.

2. Minimax regret does not escape the prior. It relocates it, and the identity says exactly where. Regret is convex in the premium, so max regret sits at an endpoint of the stated range; equating the endpoints and applying the envelope theorem gives w_minimax = [G*(m_hi) − G*(m_lo)] / (m_hi − m_lo), the average of the weights that would have been optimal, under a uniform prior on the range. A minimax rule swaps a forecast of the premium’s mean for a forecast of its endpoints. The basis correction is the cleanest possible demonstration of this: it moved the prior’s median by 2.10 pp and its mean by 1.34 pp and left the full-support minimax weights exactly unchanged, because it moved no endpoint. §2, §8.

3. The defensible range for the forward premium is 0.00% to 10.98%/yr gross arithmetic per unit of trend notional at this panel’s 12.38% trend volatility — [−1.17%, +9.81%] net of the wrapper’s 116.5 bp — with a weighted median of +2.73% net and a mean of +3.35%. Eight scenarios, each traced to a page and a window, each carrying its gross/net and arithmetic/geometric status, three vendor-authored and labelled, two independent of the vendor and of the window. 15% of the prior sits at or below zero. §1.

4. The repository’s 1.80 pp/yr convention is the post-publication era, twice transformed, and it is not a separate scenario. 1.80 + 1.50 + ½ × 13.23²/100 = 4.17%/yr, against a measured 4.17% — the reconstruction closes to the last digit. Entering it raw compared a geometric figure with an arithmetic break-even and subtracted a fee the cost term already charges. The subsample’s own 95% interval is [−2.67, +11.00] and therefore contains the 10.98 it was being used to overturn. §1.1.

5. The leverage-matched verdict is mostly a statement about the equity premium. At this panel’s realised 9.82%/yr the trend leg needs 7.68%/yr gross to beat levering the index at a 30% weight, and the minimax weight is 0.12. At decision 0004’s own 5.00% working figure it needs 2.86% and the minimax weight is 0.30. At the valuation-proxy mapping’s 1.50% it needs a negative net premium and the minimax weight is the grid ceiling. Haircutting the trend leg to a forward mean while holding the equity leg at its realised one is not a consistent comparison. §2a.

6. The two errors are asymmetric, they point in opposite directions, and the abandonment arm is now almost entirely conditional on the premium being gone. At the prior’s median, a 30% weight ends the position in 17.2% of thirty-year paths at a −20% relative-drawdown trigger; at the prior’s floor, in 66.7%. Holding 0% through the panel’s one flat-to-negative equity decade — 1999-03…2009-02, −2.55%/yr — forgoes +2.21 pp/yr at 30% and +1.49 at 20%, against +0.83 in every other decade. The position’s holdability and its return are a bet on the same parameter, which is not a diversification of the risk but the same risk twice. §4, §5.

7. The exchange-rate argument no longer identifies a cut-off below 30%, and that is the largest consequence of the correction. Priced per percentage point of abandonment probability, each step up the ladder now buys 174, 9.18, 3.49, 2.45, 1.81, 1.42 and 1.06 bp/yr. On the understated basis the same column fell below 1.0 by w = 0.20 and was read as an elbow; it no longer does. The 0.20 → 0.30 trade is now +31 bp/yr of expected growth for +15 points of abandonment probability — about 2.1 bp per point, against 0.86 before. §4b.

8. Sized answer: 25% of capital in the wrapper, robust over 20–30%, and 30% is no longer excluded. Nothing in the corrected growth-and-regret arithmetic argues below 0.28 on the investor’s own benchmark. What still argues lower is the premium-free holdability evidence in the notional budget — a tracking-error route and a CAPE-41 conditioned drawdown route landing at 15–25% — which the basis error never touched. 25% is the only weight both routes admit. §6. The published weight is 30%, which this page’s own robust range admits and none of its four routes selects; it is set in part A §2 on Experiment 016e’s one resolvable whole-portfolio comparison, and the recommendation records what that comparison does and does not isolate.

9. Cost is not what decides this. Every gap depends on the premium and the cost only through their difference, so the whole taxable-versus-sheltered question — RSST’s 32 bp/yr of distribution drag — is a 32 bp translation of the premium axis and moves no minimax weight by more than the grid spacing. §7.

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0. The panel, and why it is the tournament’s

US equity is Ken French Mkt-RF; the trend leg is AQR’s TSMOM; cash is French’s RF. The window is 1990-11…2026-05, 427 months, which is the tournament’s and was chosen by the data rather than by anyone. Using the same window on the same two series means this page’s disagreement with the tournament is a disagreement about a prior and never about a sample.

The 10.98% is the tournament’s own input. The decay, recomputed from the same pinned file rather than quoted:

These reproduce live managed futures §3 exactly. The adversarial review reproduces the same post-2008 decay on two constructions this vendor never touched — its own 4-asset book runs Sharpe 0.87 over 1990–2008 and 0.17 over 2009–2025, the JST book 0.55 then 0.19 — and also records a 1960s decade at Sharpe 0.07 followed by one at 0.80. The decay is real, it is not a vendor artefact, and a fifteen-year dry spell is inside this strategy’s historical range of behaviour. That is why premium gone carries 0.15 of the prior below rather than the 0.25 it carried before.

The one thing to keep in view. TSMOM is a vendor series, authored by a firm that sells the strategy, rebuilt in full on every update, stating no fee, transaction-cost, slippage or financing basis anywhere, and therefore gross of the vendor’s own trading costs by omission. Three of the eight scenarios below inherit that and are labelled.

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1. The prior, on one stated basis

Basis: gross arithmetic excess over cash, per unit of trend notional, at this panel’s 12.38% trend volatility. That is what the growth model consumes. Every row is on it and every row says so — the labels exist because the error §1.1 records was invisible without them.

One uncertain parameter. Every gap depends on the forward gross premium p and the retail cost c only through their difference, so the axis is m = p − c. c = 1.165%/yr — 99 bp of RSST fee plus 20.5 bp of equity-index-futures basis on the 0.331 of financed notional it carries, less VTI’s 3 bp, from the notional budget §4. §7 sweeps it.

Two rescalings, both explicit. A Sharpe measured at another volatility is multiplied by 12.38%, preserving the Sharpe — the right invariant when the volatility of the delivered exposure changes. A fund’s own fee is added back before the wrapper’s fee is charged, so no fee is counted twice.

Mean +3.35%, median +2.73%, support [−1.17%, +9.81%], P(m < 0) = 0.15.

Four things about this table matter more than its numbers.

The independent constructions are the strongest evidence in it and they were absent before. The 4-asset book runs Sharpe 0.58 over 1929–1990, 0.58 over 1990–2025 and 0.58 over the whole 96 years, at t = 5.48. That stability says the tournament’s 427-month window is representative — the window is not the problem for trend, and a premium is resolvable once the instrument is long enough. Neither book is a product: no trading cost is charged in the headline figure, there is no capacity constraint, four legs against a vendor’s fifty-eight understates by the breadth identity, and the JST book’s annual data with a one-year lookback is a coarser signal than monthly. They are weighted for what they are.

The fee add-back is not optimism, it is the avoidance of a double charge. The live index is already net of each fund’s fee, trading costs and slippage. An investor obtaining trend through RSST pays RSST’s fee, which is inside c, not DBMF’s. The two live scenarios are consequently the only ones in which implementation costs have actually been paid by anybody.

Three scenarios are gross of the vendor’s own trading costs by omission and the two independent books are gross of theirs. The only trading-cost estimate anywhere in the prior is the review’s 20 bp one-way charge on its own book, which moves that row from 7.18% to 6.19%.

The weights are a judgement. §2c sweeps them, including a weighting with every vendor-authored row removed. The support, not the weights, is what a minimax rule reads.

1.1 Where 1.80 pp/yr came from, reconstructed

Traced by the adversarial review §1 and reconstructed here from the pinned file. The only source in the repository is one sentence in decision 0004: “a post-publication trend excess return this repository measures at roughly 1.8 pp/yr” — no window, no estimator, no interval. It is:

Undoing both steps returns the era’s own arithmetic mean exactly: 1.80 + 1.50 + ½ × 13.23²/100 = 4.17%/yr, against the measured 4.17%. Sharpe-preserving rescale to this panel’s 12.38% volatility: 3.90%/yr.

Three errors followed from entering it raw on a gross arithmetic axis, and this page committed the third:

1. A geometric figure compared with an arithmetic break-even. The ½σ² term is 0.88 pp.
2. A 1.50% management fee subtracted twice — once inside the figure, once inside the wrapper’s 99 bp expense ratio that the cost term already charges.
3. A point estimate used with no error bar. The subsample’s own 95% interval is [−2.67, +11.00] and contains the 10.98 it was being used to overturn.

Consequently the tournament’s finding 11 — that at the repository’s forward premium the overlay subtracts — inverts. The like-for-like haircut is 6.91 pp/yr, not 9.18, against a break-even of 8.02, and the review §1 re-runs the frozen tournament to give proposal_rsst +0.34 rather than −0.35. The correct statement is not that the overlay subtracts at the repository’s own premium; it is that the sign is decided inside an interval nobody can narrow.

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2. The regret surface

Cells are annual after-cost log-growth gaps in basis points. Regret at (w, m) is the gap the best weight available on the same grid would have earned at that m, less the gap w earns. The action space is 0.00 to 0.40 in steps of 0.02; §2b reports how much of the answer that ceiling decides.

Benchmark A — the investor’s own unlevered portfolio. The question “should I put this in the wrapper instead of holding my index fund”.

Minimax-regret weight 0.36 (0.357 in closed form), max regret 41 bp/yr, robust over 0.36–0.40. Minimum-expected-regret weight 0.40. Break-even at w = 0.30 is m = −0.06%, a gross premium of 1.10%/yr — inside the notional budget §4.1’s independently derived 0.98%–2.31% break-even band, from a different code path.

Benchmark B — the cheap index levered to 1 + w, charged the same 62 bp financing basis, which decision 0009 clause 3 makes mandatory for a funding-rule result. Equity held at this panel’s realised 9.82%/yr.

Minimax-regret weight 0.12 (0.122), max regret 95 bp/yr, robust over 0.10–0.12. Minimum-expected-regret weight 0.00. Break-even at w = 0.30 is m = +6.51%, a gross premium of 7.68%/yr — a haircut of 3.30 pp/yr from TSMOM’s realised 10.98. Note that the independent 1929–2025 book’s 7.18% sits just below that break-even and the top of its own 95% interval, 9.75%, sits above it.

Two benchmarks, never added. The charter forbids combining results measured against different comparators. What the page shows is that the two answers — 0.36 and 0.12 — bracket the investor’s 30% from opposite sides, and that everything between them is decided by which question is being asked.

2a. The leverage-matched verdict is mostly a statement about equity

gap_matched = gap_index − w (a_e − f − sigma_e²) + w² sigma_e² / 2. The term separating the two benchmarks contains no property of the trend leg except its weight — pinned as a test — so the equity premium drives it entirely.

A forward view that cuts one leg by 84% and none of the other is not a forward view. Applied consistently, the leverage-matched control stops arguing for a small trend weight and starts arguing for a large one, because a low forward equity premium makes levering equity the expensive way to buy exposure. The tournament’s arms are basis-mapped constructions on a 65/35 global blend rather than on US Mkt-RF, so the two are not the same instrument, but the direction of the correction does not depend on that.

2b. What the endpoints and the ceiling decide

Minimax regret reads only the endpoints of the support, by the identity in conclusion 2. So the support is the assumption:

And the action space is the other assumption:

Against the investor’s own portfolio the minimax weight tracks the ceiling almost one for one: it is reporting the grid, not the data. That is the tournament’s finding 6 restated — with a correlation of −0.156 the marginal hurdle on the first unit of trend notional is −29 bp/yr, so growth wants more of it than any investor would hold and the constraint is always the cap. The row that matters most is “vendor evidence removed entirely”: at 0.334 it is barely below the full-support answer, so the conclusion no longer depends on the vendor at all.

2c. The prior’s weights, swept

The most pessimistic reweighting available now returns 0.28, where before the correction it returned 0.14. That is the single largest movement the basis fix produced, and it is not a movement in an endpoint — it is a movement in the top of the pessimistic support, which was being held down by the mis-stated 1.80.

Minimum expected regret is bang-bang under every weighting tried, because expected growth is linear in E[m] less a fixed variance drag. Neither classical decision rule produces an interior weight out of the growth arithmetic.

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3. Resolution: the verdict may not outrun the instrument

Decision 0010 requires this before any of the above may be read as evidence rather than as arithmetic.

Effective sample size: 427 months at a 24-month block is about 18 independent observations, and the decade tables below contain about 4 distinct decades. The correction cut the years to resolve by a factor of sixteen — 2,479 became 154 — and 154 years is still not a human investing horizon. Every number on this page is a decision aid, not a detection.

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4. The asymmetry, arm one: the position ends before the premium arrives

The rule: sell the sleeve the first month relative wealth sits a stated distance below its own running peak, then hold the control for good. 4,000 joint 24-month block resamples, 30-year horizon, both arms drawn on the same history. The trigger is an input, not an estimate — nothing in this repository measures a real investor’s capitulation threshold, and fitting one inside an optimiser would manufacture the quantity the design exists to expose. Read −20% against the notional budget §6a’s measured central-case worst relative run of −21.3%.

At a −20% trigger, P(the position is sold) over thirty years:

The correction changed this table more than any other on the page. At w = 0.30 and the prior’s median, abandonment fell from 42.3% to 17.2%. Median time to the sale at the median premium is now 18.1 years at w = 0.30 and 22.5 at w = 0.20.

Two readings survive it.

Quitting truncates both tails, and it truncates the good one hardest. At a negative premium abandonment saves money (−32 bp/yr held becomes −21 bp/yr after quitting at w = 0.30); at a positive one it costs (84 → 78). A growth-only surface cannot see this and neither can a Sharpe ratio.

Holdability and return are now a bet on the same parameter. Abandonment risk at 30% runs 66.7% if the premium is gone and 17.2% if it is the prior’s median. That is not a diversification of the risk; it is the same risk twice, and it is an argument for restraint that does not depend on the point estimate.

4a. The regret surface with capitulation inside the path

Pricing capitulation does not produce an interior optimum on the corrected axis. It flattens the top of the ladder — at the prior’s median, growth after abandonment runs 44, 57, 69, 78, 85, 87 bp/yr across w = 0.15 … 0.40, so the last twenty-five points of notional are worth 43 bp — but minimax reads endpoints, and the top endpoint is three and a half times the median.

4b. The marginal trade

Each step up the ladder, priced twice: the expected growth it buys under the prior with capitulation inside the path, and the abandonment probability it buys. Trigger −20%, benchmark A.

On the understated basis this column fell below 1.0 by w = 0.20 and was read as an elbow. It no longer does: every step from 0.15 to 0.40 still buys more than one basis point a year per percentage point of abandonment risk. The steep fall is now entirely inside 0.05–0.15. Stated as one move: 0.20 → 0.30 buys 31 bp/yr of expected growth and 15 percentage points of abandonment probability — about 2.1 bp per point, against 0.86 on the old axis. This is the largest single consequence of the correction for the recommendation, and it argues the weight up.

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5. The asymmetry, arm two: the decade the sleeve exists for

Every overlapping ten-year window, split on how the equity decade went. The windows overlap heavily, so these are not independent observations, no interval is offered, and the panel holds about four distinct decades.

At a 30% weight and the prior’s median the overlay turns the worst equity decade in the panel from −2.55%/yr into +0.05%/yr — it removes the lost decade rather than softening it. The overlay is worth roughly two and a half times as much in the worst equity decile as elsewhere, and it is worth something there even when the premium is zero (+0.71% at 20% and +1.04% at 30% at m = −1.17%), entirely from the correlation.

The named episodes, peak-to-trough drawdown over the frozen windows in the evidence base, trend restated to the prior’s median so the table prices the correlation rather than the realised mean:

1929-32, 1937-38 and 1973-74 are outside this window by construction — the panel starts 1990-11 — so the crisis-decade arm rests on one bad decade and two bad episodes. That limit cuts against arm two and is the single largest weakness on this page. The adversarial review’s 1929–2025 book reaches those years and finds the same Sharpe in both halves, which is reassurance about the premium and not about the crisis-conditional correlation, which nobody here has measured over that span.

The two arms answer the question directly and they do not agree. Being wrong by holding 30% when the premium is gone costs roughly 21–32 bp/yr and ends the position two thirds of the time. Being wrong by holding 0% when the premium is real costs 1.49–2.21 pp/yr in the decade the investor most needs it — an order of magnitude larger, in the state that decides whether the plan survives. What both arms agree on is that zero is the worse of the two extremes, and the correction widened that gap rather than narrowing it.

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6. The outcome distribution, and the sized answer

At the prior’s median premium, 4,000 joint 24-month block resamples:

Tracking error is w × 12.38%: 2.48%/yr at 0.20 and 3.71%/yr at 0.30, reproducing the notional budget §6a’s 3.74% from a different panel. Note that against a leverage-matched control the position still underperforms in four fifths of thirty-year histories at the prior’s median, and that comparison does not move with the weight.

The rule.

Hold 25% of capital in the stacked wrapper — 0.25 of trend notional, 1.25× gross — and understand that the binding constraint is holdability, not the premium.

25% is not the minimax-regret weight on either benchmark and this page does not pretend it is. Benchmark A’s is 0.36 and benchmark B’s is 0.12; the charter forbids averaging results measured against different comparators. 25% is the weight at which the two surviving constraints overlap:

Robust over 20% to 30%, and 30% is no longer excluded. It sits inside benchmark A’s robust band, it is exactly the leverage-matched minimax weight at decision 0004’s own 5.00% equity premium, and its abandonment probability at the prior’s median is 17% rather than the 42% the old axis produced. Below 20% the investor gives up more than a percentage point a year in the decade the sleeve exists for, for a step whose exchange rate is the best on the ladder.

Not a repository recommendation. Decision 0004’s non-promotion and zero-leverage default are untouched.

6.1 What would change it

1. RSST’s measured loading on a trend benchmark. Never estimated anywhere here. Every premium above is per unit of exposure; if the fund delivers 0.7 of a unit per dollar, the same delivered exposure needs a larger capital weight and the same capital weight buys a smaller premium. The single largest unmeasured quantity in the decision, and it needs a licensed total-return series (decision 0002).
2. A trading-cost model for the independent constructions. They now carry 0.25 of the prior between them and only one cost sensitivity exists (20 bp one-way, moving 7.18% to 6.19%). A capacity and market-impact model would be the cheapest way to firm up the upper half of the range.
3. The live-fund panel, survivorship-corrected and extended. Two scenarios carrying 25% of the prior rest on 78 months with a hole that deletes funds from inside the window.
4. The fund-level financing spread, which the notional budget §4.1 shows decides the sign at the low end and which no filing discloses.
5. The forward equity premium, which moves the leverage-matched minimax weight from 0.12 to 0.40 across the three anchors this repository already holds (§2a).

6.2 The monitoring boundary

Monitor the evidence, on a calendar, not the price.

• Annually, refresh Experiment 012’s census and recompute the live-fund index’s excess net of fees, vol-matched to the trend leg. Halve the sleeve if it sits below the wrapper’s all-in cost per unit of trend notional for three consecutive annual refreshes. Three, not one: a single reading on 78 months cannot distinguish a drought from a death, and §3 says so quantitatively — as does the review’s 1960s decade at Sharpe 0.07 followed by one at 0.80.

• Remove the sleeve if RSST’s measured trend loading comes in below 0.7, or if the wrapper’s all-in cost per unit of trend notional exceeds 2.0%/yr — at which point the break-even passes the prior’s median.

  That loading has now been measured, and the rule as written does not resolve. From RSST’s own Form N-PORT returns it is +0.681 [+0.406, +0.955] over 31 months to 2026-04 (comparability). The point estimate is 0.019 below the trigger and the 95% interval contains both 0.7 and 1.0, on a window whose smallest detectable loading is 0.392. Firing a removal rule on a point estimate that its own instrument cannot separate from the bar would be the underpowered null read as evidence, which is the error this page exists to avoid; and moving the bar after seeing the number would be worse. The rule is recorded as not resolved by this measurement and stays as written. It becomes decidable when the interval clears 0.7 in one direction, which needs roughly two more years of filings — review when RSST’s filed history reaches 48 months, around 2027-09.

• Do not monitor on relative drawdown. A rule that cuts after a relative loss is the failure mode the notional budget §7 priced from the fund’s side: cutting the overlay after a loss costs 0.22–0.59 pp/yr and deepens the maximum drawdown by 1.3–2.9 pp, because the sleeve is removed for exactly the part of the path where it would have paid. §4 shows the same shape from the investor’s side.

• A performance review is not a monitoring rule either. At w = 0.30 and the prior’s median, the position underperforms the investor’s own portfolio in 25.3% of resampled ten-year histories, and at the prior’s floor in 70.8%. A ten-year review therefore reads the premium with about one bit of information, and setting one is a plan to sell after bad luck.

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7. Cost, which is a translation and not a decision

Because every gap depends on p and c only through m = p − c, the entire taxable-versus-sheltered question is a 32 basis point translation of the premium axis, and it moves no minimax weight by more than the grid spacing.

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8. What the basis correction changed, and what it did not

The two rows in bold that did not move are the page’s own thesis, demonstrated rather than asserted. The correction moved the prior’s median by 2.10 pp and left both minimax weights untouched, because minimax regret reads only the endpoints and the correction moved no endpoint. That is exactly what conclusion 2 says a minimax rule does.

What was wrong and is retracted. The first version reached 20% partly on an exchange-rate elbow that only existed on the understated axis, and it stated the abandonment probability at w = 0.30 as 42.3% when the corrected figure is 17.2%. The “20% over 30%” trade as I originally quantified it does not survive the correction. What does survive is the framing — two benchmarks that bracket the answer, minimax as an endpoint rule, the two-armed asymmetry — and the premium-free holdability evidence on the sibling page, which is now doing the whole job of holding the recommendation below the regret surface’s own answer.

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Verified, assumed, open

Verified here. The panel’s moments and all three era rows, recomputed from the pinned AQR and Ken French files and matching live managed futures §3 and the tournament’s 10.98 exactly. The 1.80 pp/yr reconstruction, which closes to the last published digit (§1.1). The leverage-matched closed form, rebuilt in a test from the definition of log growth — two portfolios’ mean − variance/2, differenced — sharing no algebra with the implementation. The break-even as the exact inverse of the gap at five weights on both benchmarks. The minimax identity, against a brute-force minimax over a 1,001-point action space and against a 20,001-point numerical average of the optimal weight over the support. That the term separating the two benchmarks contains no property of the trend leg. That the capitulation probability rises with the weight, that a trigger which cannot fire reproduces the held gap exactly, and that a constant-return pair annualises to 12 log(1+c) − 12 log(1+k) to 1e-12.

Assumed.

1. The trend leg is TSMOM, not RSST. No loading has ever been measured for the fund, so every figure is about the exposure.
2. Three of eight scenarios are vendor-authored and gross of the vendor’s own trading costs by omission; the two independent books are gross of theirs, with one 20 bp sensitivity.
3. The two independent constructions are taken from the adversarial review §1 rather than recomputed here, rescaled Sharpe-preserving to this panel’s trend volatility. They are constructed rules, not investable products.
4. The prior’s weights are a judgement. §2c sweeps them; the support, not the weights, is what the minimax answer reads.
5. The action-space ceiling of 0.40 decides most of the benchmark-A answer. §2b.
6. The capitulation trigger is stated, not estimated.
7. A block-stationary null at 24 months, so a 30-year row is an extrapolation of that null.
8. The correlation is the full-sample −0.156. The charter’s rule applies with force: a low average correlation is incomplete evidence about crisis dependence. §5 is the direct evidence; the notional budget’s 1934–2025 panel measures +0.011 on a differently constructed trend leg, and this page cannot adjudicate between them.
9. US equity only, nominal, and pre-tax except in §7.
10. Log growth is the loss function. Regret prices terminal wealth and, in §4, the sale of the position. It prices no utility over drawdown.

Open.

1. RSST’s loading on a trend benchmark, §6.1 item 1 — the largest unmeasured quantity here.
2. Trading costs and capacity for the independent constructions, now 0.25 of the prior.
3. The pre-2019 live-fund gap, where a survivorship haircut would actually do its work.
4. Which correlation is right, −0.156 here or +0.011 on the longer panel, and what the crisis-conditional one is over the 1929–2025 span the review reaches.
5. A capitulation threshold estimated from anything. §4’s whole arm is a sensitivity to an input.

Reproducibility. cd research && uv run python -m portfolio_edge.studies.trend_weight_regret. Closed forms and decision rules in studies/trend_weight_regret.py; the cache-touching report in studies/_trend_weight_regret_tables.py; tests in research/tests/unit/test_studies_trend_weight_regret.py. Seed 20260822, 4,000 resamples, 24-month circular blocks.