0008 — Geometric growth decides; the certainty equivalent reports beside it

Date: 2026-08-12. Status: accepted.

Context

Three experiments in this repository judge a candidate by a CRRA certainty equivalent at gamma = 3, computed exactly over 35 non-overlapping calendar-year returns: Experiment 003, Experiment 004 and Experiment 010, the marginal sleeve valuation. The choice looked conservative. It is not: on that metric a candidate is paid for reducing risk, and the payment can exceed the materiality threshold on its own.

Experiment 010 measures the payment, because it carries a control designed to have no value at all. Its cash_control is cash added to a 100% equity core and funded pro rata from it, so it supplies zero alpha and zero diversification credit by construction. At the frozen 10% weight, on the net-pessimistic cost column, over 1991–2025:

A sleeve that supplies nothing is handed +0.809 pp/yr, 2.7 times the materiality threshold, purely for holding less equity — enough to carry a sleeve over the bar from a real growth contribution of −0.5 pp/yr. That is not a defect in the machinery: the growth reading comes out correctly negative, which is what the machine check was for. It is a property of the metric.

The mechanism, and how much of it no model predicted. The second-moment approximation the decomposition uses, (mu_i − mu_f) − gamma (sigma_ip − sigma_fp), does predict part of it: raising gamma from 1 to 3 triples the credit term and moves the control’s predicted marginal from −0.582 to −0.148 pp/yr at the reference weight, a de-risking allowance of +0.434. The realised allowance is +0.809. The extra +0.376 pp/yr is a left-tail reward that the second-moment model never sees: exact CRRA utility over only 35 observations weights the realised worst years far more heavily than a variance does, and cash is what was not in equities during them. Two further facts settle that this is measurement error rather than value:

• Even at gamma = 3, the model says the cash sleeve costs 0.148 pp/yr. The only thing that makes it look profitable is the exact utility over 35 points.
• Under cash funding — where the sleeve is the funding leg — the de-risking component collapses to −0.0005 pp/yr. The reward appears exactly when the sleeve removes equity and nowhere else.

The comparator decides how much this matters, and two experiments bracket it.

Experiment 004’s two arms carry 7.65% and 7.88% annualised volatility, so the de-risking is already removed from both sides before the difference is taken and only +0.030 pp/yr of its headline is de-risking. Experiment 010’s comparator is the portfolio the sleeve de-risks, so the whole of the gap survives into the answer — the gap is 487% of the certainty-equivalent figure itself. The metric is not the problem in isolation; the metric without a risk-matched comparator is.

The repository has, separately, already declared its objective to be net geometric growth, and decision 0003 already requires a risk-matched comparator whenever a candidate changes portfolio risk. This record closes the gap between those two commitments and the number the experiments actually read.

Decision

Geometric growth — the gamma = 1 certainty equivalent, which is the geometric mean of the calendar-year gross returns minus one — is the metric that decides every materiality threshold and every falsifier clause. The CRRA certainty equivalent is reported beside it, never alone and never as the deciding number.

The rationale is one sentence: the de-risking component is not an edge, because any investor obtains it free by holding less equity. A sleeve that clears a bar on it has been paid for something it did not supply, and the investor could have had the same thing for nothing.

Four constraints make this enforceable rather than rhetorical.

1. Every deciding figure names its basis. A marginal figure published without deciding_basis beside it is not reportable. Specifications carry parameters.decision_gamma; a specification frozen before this record and not naming one falls back to its crra_gamma, which is what it meant.
2. The pair travels together. Growth, the CRRA certainty equivalent, and the de-risking component that separates them are published as three numbers or as none. Publishing only the growth figure would hide how much risk a sleeve removes, which is the opposite error and equally bad. This is why the certainty equivalent is retained rather than deleted.
3. A certainty equivalent may be a primary metric only against a risk-matched comparator, in the sense decision 0003 clause 3 already requires: matched on an ex-ante risk budget with the same lagged estimator and the same exposure cap. Experiment 004 is the worked example of what that buys — 97.8% agreement between the two bases. Without it, the two bases are answering different questions and only the growth one is answering the asked one.
4. A control with no value by construction is the calibration, and every experiment whose metric could reward de-risking carries one. Experiment 010’s cash control is the model: it costs one cell of compute, it cannot promote anything because it is excluded from the multiple-testing family, and it is the only reason this error was found rather than published.

What this changes, concretely

Experiment 010’s family is now rejected, not unresolved. The metric change rewrites a frozen falsifier, so it is not a bug fix and could not be handled as a re-run of exp_010’s specification the way the convexity defect in exp_004 was. A new specification, exp_010b_growth_basis, was frozen: identical inputs, vintages, portfolios, sleeves, costs, window, eras and seed, differing only in decision_gamma. exp_010 keeps its own hash, its own runs and its recorded unresolved; exp_010b supersedes it on what the repository should believe, and adds zero trials to the search, because it re-judges data already spent.

Seven sleeves cleared the 0.30 bar on the certainty equivalent. Six fail it on growth: trend 1.172 → 0.258, the US momentum overlay 0.734 → −0.299, the developed-ex-US overlay 0.886 → 0.007, the emerging overlay 0.924 → 0.202, long-only US momentum 0.321 → 0.269, and the modelled long-duration Treasury proxy 0.492 → −0.385. Only US small value survives the bar, 0.590 → 0.392, and it is rejected anyway on the negative-credit and Holm clauses. The proxy was exp_010’s sole non-rejected sleeve, reaching unresolved only because no rejection clause fired; on growth, clause (a) fires and clause (c) with it, and nothing is left unresolved.

The change is not uniformly hostile clause by clause, and the exception is recorded rather than suppressed: emerging small value goes 0.248 → 0.543 and clears the bar on growth having failed it on the certainty equivalent, because its de-risking component is negative — it adds risk, and the CRRA metric was charging it for that. It stays rejected on Holm alone.

Experiments 003 and 004 do not move, which was checked from their own published artifacts rather than assumed. Every exp_003 policy is negative against buy-and-hold on both bases at every cost basis, and its largest de-risking component anywhere is 0.111 pp/yr; the best policy’s identity changes (annual calendar → 25% relative threshold) and both remain far below the 0.25 threshold, so the rejected status and every clause are unmoved. exp_004’s headline is 97.8% growth, as above.

Alternatives considered

Keep the certainty equivalent and raise the threshold to cover the de-risking. Rejected. The de-risking component is not a constant: it ranges from −0.295 to +1.033 pp/yr across exp_010’s own sleeves and depends on the funding leg, so no single threshold covers it. A threshold that absorbed the worst case would be 1.03 pp/yr and would reject genuine value along with the artefact.

Lower gamma to 2 rather than to 1. Rejected. It shrinks the artefact without removing it and buys an argument about the right value in exchange. gamma = 1 is not a milder preference — it is the absence of a preference term, and it is the objective the repository already declared. Any gamma > 1 reintroduces a term that pays for risk reduction, and there is no principled stopping point between 1 and 3.

Delete the certainty equivalent. Rejected, and this is the constraint most likely to be violated later by someone tidying up. Growth alone cannot say how much risk a sleeve removes, which is a real thing an investor is entitled to know and to want. The error was never computing it; it was letting it decide. Reporting it beside growth, with the difference named, makes the de-risking visible instead of both hidden and decisive.

Edit exp_010’s frozen specification in place. Rejected, firmly. The committed YAML is evidence precisely because it was written before the result was read; editing its falsifier after reading the result destroys that, whatever the edit says. Git would hold the history but no reader of the file would see a pre-registration. A superseding specification costs one file and preserves the property.

Treat the change as suspect because it was made after the results were seen. Not rejected — recorded, because it is the honest objection and it is right about the direction of danger. Two things bound it. The change was calibrated on a control that carries no hypothesis and whose correct answer was known before any data was seen. And it is strictly hostile: it removes a reward, raises the effective bar for every sleeve that was clearing it on de-risking, and moves a family’s status to a worse one. A metric changed after the fact that made everything look better would be worthless; this one makes everything look worse, which is the only direction in which such a change is cheap to trust.

Consequences

• Every future specification names decision_gamma. Omitting it is not a neutral default; it silently inherits the pre-0008 meaning, which is why the fallback is documented at the point it applies rather than left implicit.
• Any experiment reporting a certainty equivalent as a primary must build a risk-matched comparator first, which costs a volatility estimator and an exposure cap. Experiment 004 already pays that cost. Nothing else in the repository does, so nothing else may quote a certainty equivalent as its deciding number.
• A “de-risking component” field is now part of a reportable marginal figure, on the same footing as an interval and a cost basis. A figure quoted without it is incomplete in the same way a tilt quoted without its tracking error is (decision 0006 constraint 3).
• Downstream pages that quote a certainty equivalent as a verdict now carry a superseded framing, and each has to be re-read against this record before it is cited again. That coupling is the cost of having let one metric decide three experiments.
• Nothing is promoted or demoted by this record except exp_010’s family. No sleeve moves; decision 0004 stands in full, and the change makes the case for promotion strictly harder rather than easier.
• Supersede this record, do not amend it, if a risk-matched comparator is ever built for the portfolio-marginal question: the third constraint would then permit a certainty-equivalent primary in a place it currently forbids one.