Leverage and the notional budget: what the candidate portfolio already carries, and what it should

Question. The investor says “I am okay with leverage but it absolutely must be with purpose and must understand market conditions.” Their candidate portfolio puts 30% of capital in a stacked ETF. What leverage is that, what leverage does the objective want, what does the leverage cost, and does any conditioning rule survive?

Decision it informs. How large the stacked-fund line should be, against which objective, and which constraint binds. It is not a recommendation on the repository’s behalf: decision 0004’s non-promotion and its zero-leverage default for recommended portfolios both stand, and decision 0009 clause 3 unblocks the measurement of the funding rule and nothing else. Everything below informs a recommendation that a person still has to make.

Out of scope. A forecast of any market. Whether trend has a premium — that question is capital efficiency’s and marginal sleeve value’s, and this page takes the answer as a range and shows the decision’s sensitivity to it. The equity/bond split, which is setting the equity share’s. The wrapper structure arithmetic delta = (1 − b) / d, which is capital efficiency’s.

as of 2026-08-22. Every measured figure regenerates from studies/notional_budget.py via cd research && uv run python -m portfolio_edge.studies.notional_budget, and every closed form in it is pinned in research/tests/unit/test_studies_notional_budget.py against an independently computed fixture. No experiment was registered and no ledger entry was written: this is a study, and it adjudicates nothing a frozen specification would have to.

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Conclusion

1. The investor is not taking equity leverage. They are taking 30 points of trend notional. 70% of capital in a core US equity fund plus 30% in RSST is 1.3216× gross notional, of which 1.0216 is equity beta and 0.3000 is trend. The financed part is +0.3216. The equity share is 2.16 points above a fully invested portfolio — a rounding detail. The whole decision is the 0.30. §1.

2. The binding constraint is holdability, in two forms, and neither of them is the unconditional drawdown. On this panel the overlay at 0.30 changes maximum drawdown by under one percentage point (−50.1% against the control’s −50.3%), and no unconditional drawdown tolerance tested binds the trend notional at all. What binds is (a) tracking error — 3.77%/yr against 100% equity, of which 3.74% is the overlay alone, with a central-case worst relative run of −21.3% over 320 months and a 5th percentile of −42.4% — and (b) the valuation-conditioned drawdown of conclusion 9, which cuts the equity notional and takes the overlay down with it. §3, §3.2, §6a.

3. The growth-optimal size is not identifiable, and 30% is not obviously wrong. 0.30 of trend notional is exactly growth-optimal at a gross forward trend excess of 1.50%/yr. The break-even, below which the optimum is negative, is 1.19%/yr — and moves between 0.98% and 2.31% across the whole plausible financing grid. The repository’s own post-publication estimate, roughly 1.80%/yr, sits inside that band. So the sign of the overlay’s contribution is not established, and the window in which 0.30 is sensible is narrow at both ends. §4, §4a.

4. The prize is small and the noise is enormous. At a 1.80% gross forward premium the entire trend overlay at 0.30 is worth 18.2 bp/yr of growth against 374 bp/yr of tracking error — an information ratio of 0.05 and 692 years to 90% confidence. Moving from 0.30 to 0.20 gives up 4.5 bp/yr and removes a third of the benchmark-relative risk. That asymmetry is the recommendation and it does not depend on the premium forecast. §4a.

5. The financing cost is the load-bearing estimate on this page, and nobody discloses it. RSST files 0.00% of interest expense and that figure is accurate and uninformative: a futures position borrows nothing, so financing lives in the basis and never reaches an expense ratio. The independent estimate here is 119.5 bp/yr all-in per dollar of RSST — 99 bp of fee plus 20.5 bp of equity-futures basis — which is 35.0 bp/yr of portfolio at a 30% weight and 116.5 bp per unit of trend notional obtained. The fee is the larger part in every cell of the sensitivity grid. §4.

6. Volatility targeting does not survive. Five windows, one declared target, costs and a 60 bp spread inside the path, tested against a volatility-matched constant-leverage control and deflated on the active series rather than on the arm’s own Sharpe. Four of five arms have a negative active return; the fifth is +0.13 pp/yr against an MDE₈₀ of 1.27. Deflated significance 0.284 at 2.70 effective trials and 0.048 at the 14.8 trials timing rules used. Nothing survives Benjamini–Hochberg or Holm. And short windows made the drawdown worse, not better. Verdict: unresolved, with the point estimates pointing the wrong way. §6.

7. The resampled drawdown cliff is real, is seed-stable, and is not a risk gradient. P(deeper) reproduces at 6.9% at w=0.30 and jumps 10.8% → 18.8% between w=0.58 and w=0.59 (not 0.60), on four independent seeds. But it vanishes entirely without the 60 bp financing charge (9.5% → 9.7%), and its mechanism is that the identity of the worst drawdown episode switches from the GFC — where trend paid — to 1937-38, where it did not. A “practical ceiling near 55%” read off it is a statement about which two episodes are nearly tied in one panel. §3a.

8. “How much trend” has three defensible answers because there are three objectives. Minimum variance says −0.015 on this panel and +0.216 in stacking and effective breadth; the two differ by nothing but one correlation estimate (+0.011 here against an implied −0.166 there). Maximum growth says +0.49 at a 1.80% premium and −0.67 at 0%. Drawdown tolerance does not bind. Pick the objective before the number. §8.

9. Under the valuation-conditioned drawdown assumption the defensible weight falls below the 30% proposed, and that is a headline rather than a sensitivity. Entries above CAPE 30 ran a median −51.8% real drawdown over the following fifteen years against −36.7% below CAPE 20, and US CAPE is 41.18 at 2026-08-01. Transferring only the ratio — 1.411×, because those figures are real and this page’s ladder is nominal — a stated −50% tolerance supports a base notional of 0.651 rather than 0.992, and at the candidate’s own overlay-to-equity ratio that is 19.1% of capital in the wrapper, not 30%. A −40% tolerance gives 14.9%. §3.2.

10. Today’s premium proxy sits where the growth objective wants less than a fully invested portfolio. The TIPS-based excess CAPE yield is at the 0th percentile of the entire 2003–2026 TIPS record (+0.02 to +0.08 pp) with the 10-year real yield at 2.35%. Mapped into this page’s units that lands near the 1–2%/yr arithmetic rows, where the frictionless growth-optimal exposure is below 1.0 at every volatility of 15.5% or more. It is not a timing signal — conditioning on it fails out of sample and after tax — but a leverage recommendation derived from a historical premium at a moment when the premium proxy is at a record low is exactly the failure this repository exists to prevent. §2.

11. Sized recommendation: 15% to 25% of capital in the stacked fund, centre 20%, which is 0.15–0.25 of trend notional and a gross notional of 1.16× to 1.27×. Two independent routes land on the same band — the tracking-error/holdability route in §6a and the valuation-conditioned drawdown route in §3.2 — and neither of them is the growth optimum. §9. The published weight is 30%, above this band, set in part A §2 on Experiment 016e’s growth comparison rather than on either holdability route; the trade between the two is stated on the recommendation.

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1. What the portfolio actually holds

Forecast-free. Every figure is a sum of filed notionals per dollar of capital; sources are canonical in src/content/shelf.ts and in capital efficiency.

Four readings the table does not make on its own.

The equity share barely moves. 1.0216 against a nominal 1.0000. Anyone comparing this portfolio with a 100%-equity one on equity exposure is comparing two portfolios that are the same on that axis. The 30 points of trend notional are the entire difference.

RSSB is two decisions, not one. Its base leg is global equity where this reader’s incumbent is US, so the row above changes the equity composition and adds an overlay, and no single number scores both. Read it beside the US/global question, not inside it.

MATE’s base leg is 1.1587, not 0.498. Reading the largest holding and stopping put it in the range where a wrapper is arithmetically worse than selling equity outright; the same filing carries a long E-mini future at 65.57% that takes the base leg to 115.87%. The trend leg above is the prospectus’s 100% target, because the E-mini line is not separable into base completion and the trend book’s own equity position. Full working in capital efficiency.

JPFP gets no number. It commenced 2026-05-27 and has filed no Form N-PORT; the first is due 2026-08-29 or 2026-09-29. A prospectus sentence is not a notional. not filed, with a date, is the finding — assigning it an assumed 1.0 + 1.0 would manufacture the exact quantity this page exists to compute.

1.1 A derivative book is not an exposure, and the two must never be summed

Every figure above is net economic exposure — the directional risk the holder carries. It is not the funds’ gross derivative book, which is much larger and counts contracts rather than risk:

A long/short trend book is long some contracts and short others, so the legs offset; a 120.3% FX-forward book is not 120.3% of directional risk. MATE’s book moved from 339% to 404.5% of net assets between two filings while its stated targets did not move at all, which is the cleanest available demonstration that the gross derivative number is an artefact of the volatility target rather than a quantity a portfolio can be sized on. Summing derivative notionals across the funds would put the candidate near 2.0× on RSST and 2.2× on MATE, and both numbers would be meaningless.

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2. Where the leverage recommendation changes sign

L* = (mu − r) / sigma**2 inverts to mu − r = L sigma**2. The exposure you hold is a premium forecast, whether or not you have written it down.

The middle column is the sign flip. At this panel’s 15.86% equity volatility the growth-optimal exposure is exactly 1.0 at a premium of 2.51%/yr. Below it, the growth objective wants less than a fully invested portfolio and any leverage at all is overbetting. This is the same quantity as capital efficiency’s funding-rule gap a_p − sigma_p**2, written as a break-even rather than as a difference — the gap changes sign at exactly the premium at which levering stops being growth-optimal.

The growth-optimal exposure on a premium × volatility grid, frictionless:

Across the plausible corner of that grid the answer runs from 0.31 to 3.55. An eleven-fold range, from “hold two thirds of a portfolio” to “hold three and a half”, produced entirely by moving two forecasts inside their honest bounds. Any leverage recommendation quoted without this surface is quoting one cell of it.

Where today’s premium proxy lands on that grid. The TIPS-based excess CAPE yield is at the 0th percentile of the entire 2003–2026 TIPS record, +0.02 to +0.08 pp, with the 10-year real yield at 2.35% — real rates at post-2008 highs have closed the premium proxy to roughly zero (valuation and the allocation). Two unit conversions are needed before that number can be read off the table above, and skipping them is how this kind of figure gets misused. An excess CAPE yield is a geometric real premium over long TIPS; the Kelly numerator wants an arithmetic excess over cash. Converting adds roughly sigma**2 / 2 — about 1.26 pp — and then subtracts whatever term premium sits between cash and the ten-year real yield. That lands somewhere around the 1.00% to 2.00% rows, where the frictionless growth-optimal exposure is 0.21 to 1.18 and is below 1.0 at every volatility of 15.5% or more. With §2.1’s kink and financing it is 0.42 to 1.00.

This is not a timing signal and must not be used as one — valuation and the allocation finds CAPE-level conditioning loses gross and net, loses out of sample at every horizon since 1990, and has 73.4% of its slope eaten by Stambaugh bias. It is an argument about where to centre the premium input, not about when to trade. And the direction it points is unambiguous: the grid’s low rows, not its high ones. The panel’s realised 8.54%/yr arithmetic excess, which produces L* = 3.40, is an illustration of the machinery and not a forecast anyone should size against today.

2.1 The kink, which is where most premium forecasts land

Borrowing costs more than lending, so the objective is piecewise quadratic with a kink at 1.0×. Charging a spread only on the financed part:

89.6 bp is not an assumption — it is the candidate’s own incremental wrapper fee (28.8 bp of portfolio) divided by the 0.3216 of financed notional it buys.

The bold cells are the kink, and it is a region rather than a point. A whole range of premium forecasts, exactly as wide as the spread in excess-return units, implies holding exactly what you already have. At a 15.5% volatility and an 89.6 bp spread that range runs from 2.40% to 3.30%/yr — a band that covers most defensible US equity premium forecasts. The frictionless answer’s precision is an illusion the friction removes.

2.2 Can the data identify it? Not at any horizon an investor plans over

SE(Lhat*) = 1 / (sigma sqrt(T)) contains no mu: precision comes from the calendar span of the sample alone, so sampling more finely inside a window buys nothing (Merton 1980).

On any sample under about twenty-five years the interval on the growth-optimal exposure includes 1.0 — the data cannot say whether to lever at all. The two rows that exclude 1.0 require believing that ninety years of US equity returns are one stationary regime, which setting the equity share §6 gives direct evidence against.

2.3 Fractional Kelly, and the bias claim done correctly

The commonly made claim is that estimation error biases the plug-in optimum upward. Run correctly it does not, and the correct version is worse news, not better. With sigma known, Lhat* is unbiased and noisy; what the noise damages is achieved growth, not the estimate. Estimating sigma too biases it upward by (n−1)/(n−3), which on 1,091 monthly observations is 1.0018 — a rounding error. The full derivation is setting the equity share §2.1 and is not repeated here.

The quantity that is large is the growth given up, 1/(2T), exact and free of every other parameter, together with the growth-maximising shrinkage f* = S**2 T / (S**2 T + 1) at this panel’s Sharpe of 0.5384:

Full Kelly is not the operating point, and the reason is variance under non-stationarity rather than bias. But the arithmetic supports a fraction near 0.9, not 0.5, and anyone using half Kelly here is asserting that ninety years of record are worth about seven years of stationary information. That may be right; it is a claim about regimes and has to be defended as one.

Being at a fraction f of the optimum retains 1 − (1 − f)**2 of the peak excess growth — 0.75 at half, 1.00 at the optimum, 0.00 at twice it, and negative beyond. The parabola is symmetric in exposure, so the asymmetry is multiplicative: underbetting by a factor of two costs a quarter of the peak, overbetting by a factor of two costs all of it and carries four times the variance while doing so.

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3. What the record says, measured

Panel: 1934-07…2025-05, 1,091 months, imported from capital efficiency’s own instrument so the two pages cannot drift. Equity is Ken French Mkt-RF (excess 8.54%/yr at 15.86% volatility); the trend leg is the Moskowitz–Ooi–Pedersen construction on four instruments, volatility-targeted on a trailing 60-month window and charged 95 bp/yr (excess 7.40%/yr at 12.46%); cash is Goyal–Welch Rfree. Equity/trend correlation +0.0112. 1929-32 is absent by construction — the trend leg’s burn-in consumes the first 96 months — so every drawdown below is measured on a sample from which the deepest US equity fall on record is missing.

A. base held at 1.00, trend notional varied. 96 bp/yr charged on trend notional.

B. the same gross notional taken as levered equity, at a 60 bp financing spread.

Read A against B at matched gross and the whole case for a stacked fund is visible in one comparison. At 1.30× gross, the trend route drew down 49.3% and the levered-equity route 60.8%; the trend route’s Sharpe rose from 0.538 to 0.641, the levered route’s fell to 0.530. A gross-notional figure cannot tell them apart, which is why no wrapper may be scored from one. Note also that ladder B’s Sharpe declines monotonically — levering a single asset buys return with beta and nothing else, exactly as decision 0004 warns.

C. the candidate exactly as filed:

These are in-sample figures at the panel’s realised 7.40%/yr trend excess and must not be read as a forecast. §4a restates every one of them at premia the repository can defend.

3.1 Sizing by drawdown tolerance, which needs no forecast at all

The tolerances a reader is likely to state are below an unlevered equity portfolio’s own drawdown, so the base notional has to be varied downward for the question to have an answer.

The last column is the honest size of the overlay’s drawdown benefit, and it is tiny. At every tolerance the 0.30 overlay buys between one and three points of extra equity beta at the same drawdown. It is a real benefit and it is not what a 30% allocation is for.

The ladder a reader can pick a row from directly:

No drawdown tolerance in the tested range binds the trend notional. It binds the equity notional hard — that is what the “base alone” column is — and this asymmetry is the reason a drawdown-tolerance answer to “how much trend” does not exist in isolation. §3.2 shows how it reappears once the tolerance is applied to a valuation-conditioned drawdown and the overlay is held at a fixed share of the equity exposure.

3.2 The same ladder under the valuation-conditioned drawdown assumption

This is the section that most changes the answer. Entries above CAPE 30 ran a median −51.8% real drawdown over the following fifteen years, against −36.7% for entries below CAPE 20; the median buyer above CAPE 30 spent 59.7% of the next fifteen years below their real entry level against 5.0% for buyers below CAPE 20. US CAPE is 41.18 at 2026-08-01 — a level equalled or exceeded in 19 of the 1,748 months since 1881, 18 of them between March 1999 and September 2000. Measured in valuation and the allocation.

Those two drawdowns are real and this page’s ladder is nominal, so only their ratio transfers: 1.411×. Applying it is the same operation as asking for a tolerance that much tighter, which is the honest way to read a conditional drawdown against an unconditional ladder.

The equity notional is what moves, and it moves a lot. A −50% tolerance supports 0.992 of equity on the panel as measured and 0.651 once the ratio is applied — the same investor, the same stated tolerance, a third less equity.

Holding the overlay at a constant share of the equity exposure — the candidate’s own ratio of 0.294 — that converts directly into a weight in the wrapper, because a dollar of RSST delivers 1.000 of trend notional:

Every row is below the 30% proposed, and the −50% row — a tolerance most people who say they can hold through a bear market would give — lands at 19.1%. This is an independent route to the same answer §9 reaches from tracking error, and the two agreeing is worth more than either alone: one is a holdability-of-relative-performance argument, the other a holdability-of-absolute-loss argument, and they are not the same constraint.

Three limits on it, stated because they cut both ways. The ratio transfer assumes the nominal-to-real conversion does not itself depend on the valuation regime, which it may. The CAPE-conditioned figures rest on a level conditioning whose forecasting content valuation and the allocation found to be nil out of sample — what survives is the constraint reading (what the buyer had to endure), not the forecast reading. And the whole calculation still terminates in a tolerable-drawdown number nobody has supplied, which is setting the equity share’s standing finding and this page does not fix it.

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3a. The resampled drawdown cliff, located and explained

Decision 0009 cites “a resampled P(deeper) that doubles between w=0.58 and w=0.60” as an argument about holdability that no funding-rule result touches. It reproduces exactly, and three things about it are new here.

Circular block bootstrap, 24-month blocks, 4,000 paired resamples, both arms drawn on the same history, at the published settings (95 bp fee on trend notional):

First, the jump is between 0.58 and 0.59, not 0.58 and 0.60, and it is seed-stable: across four independent seeds it sits in the same 0.01 of notional (10.8→18.8, 10.5→18.5, 10.7→18.4, 10.9→18.2).

Second, it disappears without the financing charge. The right-hand column ramps smoothly through the same region. The published §7 ladder charges no spread, so the ladder and the cliff are computed under different assumptions about the same portfolio.

Third, the mechanism is an episode switch, not a rising risk. On the actual path the overlay’s worst drawdown moves off 2007-10→2009-02 at w=0, where trend paid, and onto 1937-02→1938-03 at any overlay weight at all, where it did not — and the depths of the two are close enough that a large block of resampled histories crosses over at nearly the same weight. P(deeper) is therefore a step function of which of two episodes happens to be deeper in one panel. A “practical ceiling near 55%” read off it is a much weaker statement than it sounds, and it is well above anything this page recommends anyway.

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4. The financing cost, honestly

RSST files 0.00% of interest expense. That figure is accurate and uninformative. A futures position borrows nothing, so there is no interest-expense line to report; the financing is embedded in the futures basis over the rate the collateral earns and never appears in an expense ratio. MATE and JPFP are equally silent — unitary fees exclude interest expense, and MATE’s Other Expenses line is 0.00% and estimated. Every fee table on this shelf compares everything except the cost of the leverage, so the estimate below is load-bearing rather than supplementary.

Current rates, refreshed 2026-08-22 into research/cache: effective fed funds 3.63% (2026-08-20), 3-month constant-maturity Treasury 3.87% (2026-08-20), 3-month bill 3.73% (2026-07). The level nets out of a futures position — the holder forgoes the cash return on the notional and earns it on the collateral — so only the basis matters and the stack is a spread table.

All bp/yr. Legs of the central RSST row, with their sources — none of them measured here:

• E-mini equity futures, 0.331 of financed notional × 62 bp = 20.5 bp. The 62 bp is equity index futures over 3-month Term SOFR, ten rolls Dec-2022→Mar-2025, a genuine post-2022 regime change (structural and tax edges).
• Diversified trend book, 1.000 of financed notional × 0 bp = 0 bp. Hazelkorn, Moskowitz and Vasudevan (2023) measure the signed basis at −0.83 bp on average across 18 index futures, 2000–2017, against a mean absolute basis of 52–64 bp. A long/short book takes both sides by construction, so a systematic per-contract drag is not supported, and the absolute figure must never be applied as one.

The overlay hurdle is rho sigma_p sigma_d + cost per unit notional = 2.2 + 116.5 = 118.7 bp/yr of gross trend excess return before the first dollar of overlay adds any growth. The covariance term is essentially zero because the correlation is; the hurdle is almost entirely cost, and the fee is the larger part of the cost.

4.1 Sensitivity, because this is the estimate the answer turns on

Break-even gross trend excess return, %/yr:

The corresponding incremental portfolio cost runs from 28.8 to 68.7 bp/yr.

The whole grid spans 0.98% to 2.31%/yr, and the repository’s own post-publication trend estimate of roughly 1.80%/yr sits inside it. So the sign of the overlay’s contribution is decided by a financing spread nobody discloses and this repository has not measured. That is the single most valuable thing another measurement could resolve.

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4a. Every measured row restated at a forward premium

The panel’s realised gross trend excess is 7.40%/yr. Nothing in this repository signs a forward number anywhere near it. Every row below shifts the trend leg’s mean to a stated forward premium and leaves its volatility and its correlation with equity exactly unchanged.

Inverted: 0.30 of trend notional is exactly growth-optimal at a gross forward trend excess of 1.50%/yr (0.54% net). At 1.80% the optimum is 0.49, so 30% is about 61% of the growth optimum at the best forward number this repository has — a fractional-Kelly position arrived at by accident rather than by design.

4a.1 The size of the prize, which is what the whole decision turns on

Peak excess growth from the trend leg alone is a_net**2 / (2 sigma_d**2) at notional a_net / sigma_d**2; growth at any other notional is that peak times 1 − (1 − f)**2. Tracking error against 100% equity is w sigma_d.

bp/yr of the portfolio’s growth rate, from the trend leg alone, on the lognormal model rather than on the realised path. The 1.80% row is the decision. The entire overlay is worth at most 22.7 bp/yr of growth, 18.2 bp of it captured at 0.30 — against 374 bp/yr of tracking error, an information ratio of 0.05, and 692 years to 90% confidence.

Moving from 0.30 to 0.20 gives up 4.5 bp/yr and removes a third of the benchmark-relative risk. That trade holds at every premium in the defensible range, and at a 0% premium it also removes 13.5 bp/yr of loss.

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5. The outcome distribution

4,000 joint 24-month block resamples; both arms drawn on the same history so each draw is one investor’s two portfolios. Drawdown percentiles are reported rather than the worst resample, which is an extreme order statistic that moves several points with the seed.

Trend at the repository’s 1.80% forward premium, against 100% equity:

At a 0.00% forward premium the sign flips: P(underperform) 60.6% / 62.1% / 64.2% and a median relative wealth of 0.933 at thirty years. At the realised 7.40% it is 3.0% / 0.3% / 0.1% — which is the number a backtest would report and which nothing here supports as a forecast.

Against levered equity at 1.3216× the candidate underperforms in 75.5% / 80.6% / 85.0% of resamples at the 1.80% premium. That comparison is real and it is not the one to size on: the levered-equity arm carries a −61.5% drawdown against the candidate’s −51.1%, so it wins terminal wealth by taking a risk the drawdown table already says the investor should not. These two benchmarks answer different questions and their answers do not add.

The limitation that cuts against every row. Block resampling preserves dependence to 24 months and destroys it beyond, so a 30-year row is an extrapolation of that null rather than a measurement of a 30-year holding period.

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6. “Understand market conditions”: vol-targeting does not survive

The investor’s second requirement is the better-evidenced one — volatility really is far more forecastable than return, which is why this is tested rather than dismissed. The rule: leverage_t = clip(15% / trailing vol(t−w … t−1), 0, 2) applied to the candidate portfolio’s excess return, with a 60 bp spread on the financed part and 10 bp of round-trip cost per unit of notional traded, all inside the path. Five arms, one declared target, windows 3/6/12/24/36 months.

“Active” is the volatility-matched difference against a constant-leverage arm at the same mean exposure, which is the only comparator that makes this a timing test rather than a leverage test.

The deflation is run on the active series and never on an arm’s own Sharpe. Every arm here is long the candidate portfolio all of the time, so its raw Sharpe contains the equity premium and deflating it returns a pass by construction — the same mis-specification timing rules on the equity sleeve identified. The best arm’s raw Sharpe is 0.622 and that is not the number deflated.

Benjamini–Hochberg and Holm across the five arms reject nothing: BH-adjusted p-values run 0.133 to 0.788, Holm 0.133 to 1.000. The one arm with a nominally significant raw p (6-month, p = 0.027) is significant in the wrong direction and does not survive correction.

Verdict: unresolved, with the point estimates pointing the wrong way. Four of five arms have a negative active return; the one positive arm is +0.13 pp/yr against an MDE₈₀ of 1.27, a tenth of the smallest effect the design could see. And two facts make the practical case worse than the statistical one:

• Short windows made the drawdown deeper, not shallower — −72.3% at a 3-month window against the unconditional −50.1%. The cap binds in calm periods, so the rule is levered going into the spike, which is precisely the failure mode §7 exists to price.
• Turnover is 0.25 to 4.14 whole portfolios of notional a year, and the tax is not priced in any row above. In a taxable account each leverage change is a realisation; at the investor’s marginal rate a short-term realisation of that size is the largest single term in the rule and dwarfs the 2.5 bp of trading cost the best arm actually charges.

Trading cost is not what kills it. At the best arm, moving the round-trip assumption from 5 to 20 bp moves the geometric return from 12.78% to 12.74%. The rule fails because there is no timing effect to capture at this frequency on this portfolio, not because it is expensive.

6a. What the tracking error means for the stretch to sit through

The overlay is essentially the entire benchmark-relative risk budget. This reproduces stacking and effective breadth’s ~400 bp total and 372 bp from the overlay, from a different code path.

But an annualised standard deviation is not what anybody experiences. The experienced quantity is the worst run of relative underperformance and how long it lasts:

At the repository’s own forward premium the investor should expect, as a central case, to be 21% behind a simple 100%-equity portfolio at some point, and to spend twenty-six years below a previous relative high. The realised-premium row understates this by a factor of two because it embeds a trend premium nobody will underwrite. This is the number that decides whether the position is holdable, and it is why the recommendation in §9 is smaller than 30%.

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7. The specific danger: leverage, a volatility spike, forced deleveraging

Peak-to-trough inside each named episode from the evidence base:

The overlay helped in the slow crises and did not help in the fast ones. It took 3 to 5 points off the dotcom bust, the GFC and 1973-74, and it was worse than the control in 1987, 1937-38 and 2022. That is the signature of a trend book: it needs a trend to form.

1929-32 is missing by construction and its absence is not a detail — it is the deepest equity drawdown in the record, removed from the sample by the trend leg’s own burn-in.

Forced deleveraging, priced as the wrapper’s own risk control cutting the overlay after a loss and restoring it only at a new high-water mark:

Cutting the overlay after a loss costs return and deepens the drawdown, because the sleeve is removed for exactly the part of the path where it would have paid. A return-stacked ETF cannot margin-call its holders, so this is the fund’s own risk control seen from inside — and the investor’s version of the same mechanism, selling the wrapper after a bad stretch, is larger and is not estimable from any series held here. §6a’s 320 months of relative underperformance is the input to that failure mode.

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8. Three answers to “how much trend”, each optimising something else

These are not competing estimates of one quantity.

The two variance-minimising numbers do not disagree about method. With the base at b, portfolio variance is minimised at w* = −b rho sigma_e / sigma_d — an identity. On this panel the measured equity/trend correlation over 1,091 months is +0.0112, statistically indistinguishable from zero, so w* is −0.015. Inverting the identity, 0.216 requires rho = −0.166. The entire gap between the two answers is one correlation, measured on different instruments over different windows:

Neither measurement is resolvable against the other from anything held here, and the charter’s rule applies with force: a low average correlation is incomplete evidence about crisis dependence, and this identity uses the average one. §7’s episode table is the direct evidence — the correlation that matters is the one in 1937-38 and 2022, not the one in the full sample.

8.1 If the objective is drawdown control, rank the ways to buy it

Read the first row against the second. Holding 0.90 of equity and nothing else buys a drawdown 3.9 points shallower than 1.00 of equity, for nothing, in one trade, with no wrapper, no financing, no Cayman subsidiary and no forecast. On this panel the 0.30 overlay’s own drawdown reduction is under one percentage point. The overlay is not a drawdown instrument at this size. It is a return bet and it must be argued as one.

That does not make it a bad bet — its geometric return is 2.9 pp/yr higher than the 0.90-equity row’s, at the panel’s realised premium — but it relocates the argument. The overlay’s case is that it raises growth at unchanged drawdown, which requires a forward trend premium above the break-even in §4.1, and that is exactly the quantity nobody here can sign.

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9. The sized recommendation

Not a recommendation on the repository’s behalf. Decision 0004’s non-promotion stands, no sleeve is promoted, and the zero-leverage default for what this repository recommends is unchanged. What follows informs a decision the investor makes.

Size: 15% to 25% of capital in the stacked fund, centre 20%. That is 0.15 to 0.25 of trend notional and a gross notional of 1.16× to 1.27×, against the proposed 1.32×.

The objective it is optimal for: expected after-cost log growth subject to holdability — both kinds. It is not the growth optimum (that is 0.49 at a 1.80% premium) and it is not the variance minimum (−0.015 here, +0.216 elsewhere).

Two constraints bind, from opposite directions, and they agree.

What does not bind. Drawdown as measured on the unconditioned panel — §3.1 shows no tolerance in range binds the trend notional. The resampled cliff — §3a puts it at 0.58–0.59, nearly three times anything considered here, and shows it to be an episode-identity artefact of one panel. The growth optimum — §2.2 shows its 95% interval spans 1.0 on any sample under about twenty-five years.

Both binding routes land inside 15–25% and neither of them is a forecast of trend returns. That is the strongest thing this page can say, because the trend forecast is the one input it cannot supply.

Why 20% and not 30%, in one line: the move gives up 4.5 bp/yr of expected growth at the repository’s own forward premium and removes a third of the benchmark-relative risk that would break the position. Being at 0.20 against the model’s own 0.54 optimum retains 60% of a peak that is itself only 22.7 bp/yr; the left branch of the growth parabola is nearly flat here and the holdability cost is not.

Why not zero: at a 1.80% gross premium the overlay’s contribution is positive, the wrapper keeps 100% of the funding-rule gap (delta = −0.07), the structure and cost are verified from filings, and §7 shows a real 4-to-10-point drawdown benefit in the slow crises (5.4 points in the GFC, 4.2 in the dotcom bust, 10.5 in 1973-74). Why not 30%: the break-even is 1.19% and moves to 2.31% across the financing grid, so the sign is not established, and 30% sits at 61% of an optimum computed from a premium the repository will not underwrite.

Confidence. Low on the number, moderate on the direction, high on the framing.

• High confidence (arithmetic, or filed): the exposure table in §1, the sign-flip premium, the kink, the 1 − (1 − f)**2 retention, the financing identity, and the fact that the overlay is the whole tracking-error budget.
• Moderate confidence (one panel, exploratory): the drawdown ladders, the crisis table, the cliff’s location and mechanism, the vol-targeting null.
• Low confidence (a forecast this repository refuses to make): everything that depends on the forward trend premium — which is to say the sign of the whole overlay contribution. §4.1’s grid is the honest statement of that, and 1.80% sits inside it.

The single measurement that would change this answer is a fund-level financing spread. It is no longer a measured RSST trend loading: that has been estimated from the fund’s own Form N-PORT returns at +0.681 [+0.406, +0.955] over 31 months to 2026-04, against an equity beta of +0.979 (comparability). Every trend figure on this page is still a figure about the exposure, and the correction is now sized rather than unknown: the fund delivers about seven tenths of a dollar of index per dollar of filed notional, on an interval wide enough that a full dollar is not excluded.

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Verified, assumed, open

Verified here. The exposure arithmetic against the filings. The kinked growth optimum against a 500,001-point grid search on the objective itself. The two-asset optimum against a 1,201² grid search. premium_for_leverage as the exact inverse of kelly_leverage at twelve parameter pairs. The trailing-volatility rule’s absence of look-ahead, by perturbing one future observation and checking that no earlier leverage moves. Joint resampling, by confirming that a constant-ratio pair has zero spread in relative terminal wealth. The published P(deeper) figures of 6.9% and 10.8%→18.9%, reproduced exactly and then localised and explained.

Assumed on this page.

1. The trend leg is a construction, not RSST. No loading has ever been measured for the fund. Every trend figure is about the exposure.
2. The financing spreads are borrowed, not measured: 62 bp for equity index futures over 3-month Term SOFR, 15 bp for Treasury futures over OIS, ≈0 signed for a long/short book. §4.1 varies all of them.
3. The panel excludes 1929-32 by the trend leg’s burn-in, so every drawdown is measured on a sample missing the deepest US equity fall on record.
4. §3.2 transfers a ratio, not a level. The −51.8% and −36.7% are real fifteen-year drawdowns from valuation and the allocation; this page’s ladder is nominal and full-sample. Only 1.411× is carried across, on the assumption that the nominal-to-real conversion does not itself depend on the valuation regime.
5. A block-stationary null in §5 and §6a, which destroys dependence beyond 24 months.
6. Nominal, US, pre-tax throughout. No tax is charged anywhere on this page; §6’s turnover is the place where that omission is largest and it is named there.
7. MATE’s trend leg is a prospectus target, not a filed number; JPFP has no profile at all.

Open.

1. The fund-level financing spread. It decides the sign. Nothing on the shelf discloses it and no fee table can.
2. RSST’s loading on a trend benchmark. Needs a licensed total-return series.
3. Which correlation is right — this panel’s +0.011 or the +0.216-implying −0.166. §8’s sensitivity is the honest interim answer, and the crisis-conditional dependence in §7 is what would actually settle it.
4. A tax-aware version of §6. The vol-targeting null is robust enough that tax cannot rescue it, but the same machinery applied to a rule that did survive would need it.
5. The 2.0 pp/yr materiality threshold and the 0.30 pp/yr sleeve bar remain undefended (decision 0009 clause 7). This page uses neither.

Reproducibility. cd research && uv run python -m portfolio_edge.studies.notional_budget. Panel imported from studies/_overlay_stress_tables.py; closed forms in studies/notional_budget.py; tests in research/tests/unit/test_studies_notional_budget.py. Seeds 20260817 (+1, +3, +5), 12345, 999983, 20260822; 4,000 resamples; 24-month circular blocks. Cash rates refreshed from FRED on 2026-08-22.