Weight Precision in Index Construction: When the Hundredth of a Percent Matters

1. The precision question

The catalogue, at 84 indices as of July 2026, carries two different kinds of weight, and they have different precision semantics. Seventy-nine funds carry committee-set weights alone: whole percentage points — BTC 30, ETH 22, SOL 13 — that are statements of allocation policy, set at a design review and revisited on the governance calendar. Five funds additionally carry computed candidate targets beside their committee weights: OHRP12 (hierarchical risk parity, cross-asset, monthly), ORP6 (equal risk contribution, monthly), OLV8 (inverse volatility, quarterly), and OSHARP6 and OBAL6, where the hierarchical-risk-parity vectors currently serve as an evidence basis for scheme validation. Every production weight in the catalogue remains committee-set while the adoption reviews are pending (From Labels to Computation: HRP, ERC and Inverse-Volatility Weights in Practice). A computed target exists at full floating-point precision the moment the pipeline runs; rounding it is a publication step, not part of the estimate.

The two kinds are not perturbations of one another. OHRP12's committee vector reads BTC 18, ETH 14, SOL 9 — round numbers throughout. The July 23, 2026 recompute of its risk-parity target reads BTC 15.2, PAXG 23.0, SKY 9.9, with the largest single gap at 15.0 percentage points (PAXG, committee 8). The computed vector is a different object, produced by a different process, and the grid it is published on should be chosen on its own merits.

The question this paper answers: at which grid should computed targets be published? The pipeline today rounds to the tenth of a percent — one decimal — under an exact-sum largest-remainder scheme. The choice matters for three reasons: fidelity, meaning how far the published vector sits from the estimated one; the integrity of the published cost stack, meaning whether rounding artefacts share an order of magnitude with figures the desk actually reports; and convention, meaning what a professional reader infers from the grid itself.

There is also a housekeeping reason to decide now: the tenth grid is already broken in production, in both directions. OCI10 has carried committee-set weights of HBAR 5.25 and TRX 5.25 since the May 2026 weighting refresh — off-grid under the current convention. Meanwhile the trade surface already renders every weight at two decimals through a formatter quirk (a 9.5 target displays as "9.50%"), while the catalogue card truncates 5.25 to "5.3" — a live display defect — and the discovery surfaces round to whole percent by design. Three surfaces, three conventions. The grid question is also a coherence question.

The desk's answer is the hundredth. Sections 2 through 4 give the quantitative, conventional, and rule basis; Section 5 maps the implementation surface. Every decision cited in this paper is a desk recommendation pending ratification by the index committee.

2. Quantifying the rounding cost

Start with what the grid does not affect: the NAV level. Weights enter the index only through share counts fixed at each rebalance, and the divisor is recalibrated whenever the target vector changes, so a change of publication grid re-bases cleanly with zero NAV discontinuity. Precision is not a level question. What remains is fidelity — the tracking difference between a basket run on the rounded vector and one run on the full-precision vector.

The magnitude is straightforward to bound. On the tenth grid, each published weight sits within ±0.05 percentage points of the full-precision target, and largest-remainder allocation forces the errors to sum to zero across the basket. For an eleven-name risk block such as OHRP12's, the error vector carries an l2 norm of roughly 0.10 percentage points (about 0.029 points root-mean-square per name, times the square root of eleven). The daily tracking difference is approximately that norm multiplied by the cross-sectional dispersion of daily constituent returns — around 3% per day for a crypto basket — which gives roughly 0.3 basis points per day, or about 5 basis points a year annualised. A dispersion band of 2–4% per day brackets the figure at 3.5–7 basis points. Every term scales linearly with the grid, so the hundredth divides the artefact by ten.

The integer row is hypothetical — no computed target is published at whole percent — but it clarifies the logic: an integer grid is perfectly appropriate for a committee weight, because there is no underlying estimate to track, and it would be malpractice for a computed one.

Against basket volatilities of 40–70%, all of these figures are invisible in return terms. The materiality argument is about the published cost stack, not P&L. The rebalancing ledger reports implementation-cost estimates of 1.1 to 15.3 basis points a year at a 10-basis-point execution assumption. A 5-basis-point rounding artefact sits inside the range of numbers the desk publishes; a half-basis-point artefact sits below every figure on every surface. The desk's view is that a publication grid should keep its own rounding noise below the resolution of everything else it prints.

Turnover is unaffected, and the claim is quantified rather than asserted. No new rebalance events: triggers are calendar-based or drift-based at a 25-percentage-point threshold, the largest drift observed anywhere in the book is 10.1 points, and a grid step of 0.01 points is more than three orders of magnitude below the threshold. In steady state, moving from the tenth to the hundredth shifts each target by at most 0.05 points per name; across an eleven-name event this induces one-way turnover noise on the order of ±0.15 percentage points, against observed per-event one-way turnover of 1.39% to 17.28% across the tradable book. The expected incremental cost drag at 10 basis points is at most 0.004% a year — below the two-decimal resolution at which the ledger itself reports. For the indices on the adoption path, the one-off transition is absorbed inside the adoption event itself (23.1%, 5.0%, and 20.6% one-way for OHRP12, ORP6, and OLV8 respectively, per the July 23 recompute), of which the grid component is at most 0.15 points.

A final execution note. A 0.01-point order is one dollar per ten thousand dollars of NAV. If live execution ever wants a floor under trade sizes, that belongs on the execution side as a de-minimis band — for instance, ignoring legs below 0.05% of NAV — which is orthogonal to the precision of the published target. The target should not be degraded to simulate an execution constraint that does not exist.

3. Institutional convention

The reference practice is settled. S&P Dow Jones Indices and MSCI publish constituent weights to the hundredth of a percent in their index factsheets. The holdings files of the major ETF issuers — iShares, State Street — carry two decimals. On the crypto side, the monthly holdings disclosures of the Bitwise 10 do the same. The convention underneath all of these is identical: computation at full precision, publication at 0.01%. The published grid is a reporting resolution, not a confidence interval — a market-capitalisation weight is every bit as much an estimate as a risk-parity weight, and the industry publishes both to two decimals.

The divisor method is what makes the finer grid free. Because index level is maintained through a calibrated divisor, and because share counts are recomputed from the target vector only at rebalance, the precision of the published weight never reaches the NAV arithmetic: a finer grid moves share counts by parts in ten thousand and the divisor absorbs the re-basing exactly. This is precisely why the institutional providers can afford the hundredth — the index mechanics are indifferent to it — and OLTA runs the same mechanics.

That is also the credibility point. OLTA already wears the rest of the costume: the divisor method follows the S&P convention (methodology paper, Section 2), and the rebalance calendar follows the standard quarterly-with-off-cycle pattern. Publishing computed targets at the tenth is the one piece of the outfit that does not match. Under the hundredth, it matches — and OCI10's committee-set 5.25s stop being an off-grid anomaly and become ordinary residents of the published grid.

4. The recommended rounding rule

The desk submits the following four-clause rule to the index committee for ratification.

R1 — Publication grid. Computed targets are published to the nearest 0.01%. Internal computation remains at full precision end to end; rounding is applied exactly once, at publication. Nothing downstream re-rounds.

R2 — Exact sum. Rounding uses largest-remainder allocation in an integer domain of hundredths: floor each weight at the grid, distribute the remaining hundredths by largest fractional remainder, break ties deterministically by constituent order. Published vectors sum to exactly 100.00 — or to the risk-block total where a stable sleeve exists: OHRP12 publishes a 92.00 risk block beside an 8.00 USDC sleeve. This is the current pipeline's behaviour transposed from tenths; today's one-decimal vectors already sum exactly (ORP6's July 23 target: BTC 20.5, ETH 15.5, BNB 20.8, LINK 16.1, SOL 15.1, AAVE 12.0 — precisely 100.0).

R3 — Cap-aware. Names bound at a cap or floor receive residual hundredths only when no unbound name can absorb them. The bounds themselves remain policy integers. OBAL6's July 23 vector publishes SPYon at exactly 40 (cap-bound) and ETH at exactly 2 (floor-bound), and would continue to on the finer grid: caps and floors are rules, not estimates, and their precision should say so.

R4 — The signature convention. Committee weights are never force-converted: 40 stays 40, not 40.00. The committee continues to express policy in round numbers, and decimal precision becomes the signature of a computed weight — a reader who sees 15.21 knows an algorithm produced it, and a reader who sees 40 knows a committee did. Where a committee split genuinely requires finer granularity, as with OCI10's paired 5.25 sleeves, the grid accommodates it; but the committee default remains whole numbers precisely so that a decimal stays informative.

The serious objection to the finer grid deserves a direct answer. Publishing 15.21% could be read as claiming an estimation confidence that a 180-day covariance window does not possess — OHRP12's walk-forward targets move 9 to 11 percentage points month to month, an annualised churn near 120%. The desk's response is that publication precision is not a confidence statement, and the industry it borrows from does not treat it as one: S&P and MSCI publish equally-estimated market-cap weights at the hundredth. The honest instrument for estimation uncertainty is churn disclosure in the methodology card, not a coarser grid — the tenth makes the same implicit claim as the hundredth while carrying ten times the tracking noise. R4 is the structural guard against decimal cosmetics: precision appears exactly where a computation stands behind it, and nowhere else.

5. Implementation notes

The change is small because it was designed to be. The engine consumes floating-point weights at any precision, so the NAV computation, the backtest engine, the drift monitor, and the cap-and-floor logic are all untouched. The implementation surface is confined to the last mile:

• Rounding routine. The pipeline's largest-remainder function generalises from a fixed tenths domain to a parameterised grid, operating in integer hundredths. Same algorithm, same cap-aware residual handling, same deterministic tie-break; roughly ten lines of change plus test cases for exact sums at two decimals.
• Compute script. Two delta-rounding call-sites move from one decimal to two. The research export serialises the finer values natively.
• Display. One adaptive weight formatter replaces the three inconsistent conventions: whole numbers render bare ("40"), tenth-grid values render one decimal ("9.5"), hundredth-grid values render two ("5.25"). This fixes both live defects at once — the forced "9.50" on the trade surface and the "5.3" truncation on the catalogue card. Discovery surfaces keep whole-percent bars by design. The worst case gains one character in tabular numerals; the mobile allocation donut already renders two-decimal labels without overflow.
• Methodology copy. One sentence, recommended verbatim: "Constituent weights are computed at full precision and published to the nearest 0.01%; published weights sum to exactly 100.00% (largest-remainder)."

Conversion across the catalogue is mechanical, and for most of it the mechanism is identity:

Only the five computed indices change anything material, and "material" means fidelity and convention, not P&L. The 79 committee-weighted funds convert by identity: no edits, no trades, no divisor events. Nothing in this recommendation rewrites a committee weight.

Two sequencing points accompany the recommendation. First, a single wave rather than per-family phasing: phasing would leave two publication grids coexisting for months, which is strictly worse than the current mixed state the rule is meant to repair. Second, order of operations: the pipeline rule should land before the adoption validation gates run, so that the gates evaluate the vectors that would actually ship — a grid applied after gating would mean certifying one set of numbers and publishing another. If ratification or the gates delay adoption, the grid rule stands on its own; it is a pipeline and display change, and the committee funds have nothing to migrate. On the first regeneration under the new rule, walk-forward histories recompute wholesale onto the finer grid, so the research export never carries mixed-grid history.

The hundredth-grid vectors themselves are deliberately not printed in this paper: they will be produced by the first pipeline run under the ratified rule, and by construction each name moves at most 0.05 percentage points from the one-decimal vectors quoted here.

Status: desk recommendation, pending index-committee ratification. Vectors quoted are the July 23, 2026 recompute (180-day lookback). Tracking-noise figures are derivation-based bounds under the stated dispersion assumptions. Turnover, drift, and cost figures are backtest reconstructions — no live trades were executed — and follow the published cost convention at a 10-basis-point execution assumption (Reconstructed Rebalancing Ledgers: A Transparency Standard for Simulated Index Products).