Four tilts the recommendation never priced

Question. The recommended portfolio was assembled by correcting the investor’s own list of eight tickers. It was never asked whether better tilts existed on the shelf. Four candidates were never scored against it: AVDV (developed ex-US small value), AVUV (US small value), MTUM (US momentum) and QVAL (Alpha Architect’s concentrated US value, which is not on the shelf at all). What does each add to the portfolio actually held, after everything it actually costs?

Decision it informs. Whether to change the construction as it stood when this page was written — RSST 25%, VTI 25%, VTV 15%, VXUS 25%, IDMO 5%, AVES 5% — and by how much. AVDV has since been adopted at 10% and the resulting portfolio has been tested as one object in the final construction test; every figure below is still measured against the pre-AVDV portfolio, which is what makes it a marginal figure. It also settles the question that decides whether international value re-enters the portfolio at all: two large-cap international value funds were dropped for delivering measurably negative returns, and AVDV is small-cap. Is that distinction real?

Out of scope. Whether any factor premium exists (factor persistence), what the trend sleeve is worth (trend), and the weights themselves (the recommendation, which this page does not edit).

as of 2026-08-23. exploratory. No specification was frozen before these numbers were seen and no experiment is registered for them. Reproduce with cd research && uv run python -m portfolio_edge.studies.untested_tilts; the arithmetic is in untested_tilts.py and the filing reads in _untested_tilts_tables.py.

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Conclusion

1. AVDV is worth adding, and it is the only one of the four that is. Funded out of VXUS at 5% of capital it changes expected portfolio return by about +0.16% a year, plausibly −0.06% to +0.38%; at 10%, +0.32% a year, −0.12% to +0.77%. That rests on exposure, cost and overlap, none of which involves its measured extra return — which is not distinguishable from zero and is not used here.
2. The small-versus-large distinction in international value is not established, and AVDV must not be recommended on it. On the 55 months DFIV and AVIV impose, all four large-cap international value funds read −2.3 to −2.9 with intervals excluding zero while AVDV reads +1.8. On the 78 months the two older large-cap funds also cover, the same two funds read −1.0 and −1.7 and neither excludes zero. The negative result is substantially a property of the window, not of the funds’ capitalisation. And over the months AVDV and DFIV both existed, their plain returns differed by −0.30 ± 5.16 pp/yr — AVDV did not out-return DFIV at all; it out-returned the model’s prediction for it.
3. AVUV is not worth adding to this portfolio. Against VTI it is worth about −0.01% a year once the US value line already held is accounted for: its active leg is +0.430 correlated with VTV’s own and +0.455 with the whole active position, and the exposure it adds beyond VTV is 87% size, on a premium of +0.33 pp/yr against a floor of 2.47. Replacing VTV with it outright is +0.09% a year at 15%, range −0.42% to +0.60% — a coin flip dressed as a decision.
4. MTUM is not worth adding, and turnover rather than overlap is what kills it. It delivers UMD +0.437 [+0.316, +0.559] over VTI, which is real. It also files 116%/yr of portfolio turnover against VTI’s 3%, costing 1.13 to 1.92 pp/yr — more than the entire gross exposure gain of +1.78 pp/yr on the US momentum premium, which is itself +4.19 against a detection floor of 7.27. Net: −0.03% a year at a 5% weight, range −0.18% to +0.13%. The overlap with IDMO is real but secondary: the two funds’ active legs correlate +0.554, so two momentum tickers are worth 1.29 independent bets out of 2.
5. QVAL is the clearest verdict on the page and it is negative. Its facts are established from its own filing: 28 bp, and 332%/yr of portfolio turnover. That is 3.29 to 5.59 pp/yr of trading cost against a gross factor gain of +1.1 pp/yr. At a 5% weight it is −0.30% a year, range −0.50% to −0.10% — the only one of the four whose portfolio effect the data can resolve, and it is resolved in the wrong direction.
6. The tax objection to momentum is false on the filed evidence, and it is the surprise of this page. MTUM’s own SEC-standardised after-tax table shows a distribution drag of 0.31 pp/yr against VTI’s 0.42 over the same five years — the momentum fund is 11 bp/yr more tax-efficient than the total-market fund despite turning over its whole portfolio each year, because the ETF in-kind redemption shield does the work. AVDV against VXUS is −0.01 pp/yr: parity. Tax does not decide any of these four.

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1. The method, proved before it was used

Every published loading this page touches was first refitted on its own published window and checked against the shelf. This is what separates “a different answer” from “a different method”.

Largest gap across all twenty: 0.0020, and that one is RPV’s SMB, which the shelf publishes to one decimal place as +0.2 against a refit of +0.198. Every other loading reproduces to within 0.0005. SPMO is deliberately absent from this check: the shelf records its UMD loading with window: null, and a loading with no window cannot be reproduced or compared, so it is fitted from its own filings on a stated window instead. The fund return series is Form N-PORT Item B.5 — the fund’s own filed monthly total return, net of its own fees, with distributions reinvested — read by the same module Experiments 008, 009, 012 and 013 use. No price feed is involved, which is why decision 0002 does not reach it; see loading comparability §1 for the argument in full.

Two departures from the published numbers, both stated here rather than buried.

• A delivered exposure is fitted from the difference series. Rather than fitting fund and incumbent separately and subtracting two coefficients whose standard errors do not combine, the difference of the two funds’ filed returns is regressed on the panel directly. The coefficients are then the delivered exposures and the intercept is the extra return, each with an interval that means something.
• The shelf’s published alphas for DFIV and AVIV do not reproduce exactly. Every loading does, to 0.0005, on the identical window with the identical estimator; the alphas come back −3.88 and −2.88 against the published −4.11 and −3.13. The gap is 0.23 and 0.25 pp/yr, well inside both funds’ own detection floors, and nothing on this page turns on it — but it is unexplained and it is recorded.

One gap in the source, and it moves a window. QVAL has no Form N-PORT filing for the quarter ending 2021-09-30, so its history has a three-month hole. A Newey-West covariance laid across a hole treats two months a quarter apart as neighbours, so QVAL is fitted on its longest gapless run, 54 months, 2021-10…2026-03, and not on the 75-month span its first and last filings suggest.

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2. The crux: does large-cap international value’s negative result reach small-cap?

This is the question that decides AVDV, and the answer is no, but not for the reason it first appears.

On the window the young funds impose

DFIV and AVIV began filing in 2021, so any comparison including them is a comparison over 2021-10 onwards. Every fund below is fitted on those 55 months, on the developed-ex-US FF5+UMD panel, against the one-month bill.

Four large-cap funds from three different sponsors, all negative, all excluding zero. The one small-cap fund is positive. The difference regressions confirm it with much more power, because the common factor noise cancels:

On this window the distinction is real as arithmetic and comfortably resolvable.

On a longer window it evaporates

IVLU and EFV are old enough to be measured over 78 months. Refit them there and the result changes:

The two funds that can be measured on both windows lose their negative result on the longer one, and so does the small-minus-large difference. Add twenty-three months of 2019-10…2021-09 and nothing excludes zero any more. That is the same defect loading comparability §4 records for the US value shelf, appearing here in an alpha rather than a loading: the published verdict was a statement about which months each fund happened to exist for.

And even where it resolves, it is not a return difference

The most useful line on this page needs no factor model at all. Over the 55 months AVDV and DFIV both filed:

AVDV − DFIV: −0.30 ± 5.16 pp/yr. AVDV − AVIV: +1.70 ± 4.59 pp/yr.

AVDV did not out-return the large-cap funds. It out-returned the model’s prediction for it, because the model charges it for +0.56 of SMB and +0.38 of RMW that it holds and they do not. That is a statement about how well a six-factor model fits a small-cap international portfolio, not about money.

So the crux resolves as follows. Small-cap international value did not escape a fate that befell large-cap international value, because there was no resolvable fate: on the longest window available the large-cap funds’ negative returns are not distinguishable from zero, and on the shorter window the small-cap advantage is a model residual rather than a return. AVDV’s case must rest on something else, and it does.

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3. What each candidate actually delivers, and what it costs

Every exposure below is fund − incumbent, fitted on the difference series, on one window, with the interval and the smallest exposure the window could have detected.

Not one of the five extra-return figures is distinguishable from zero. Each smallest detectable effect is two to nine times the estimate beside it. No verdict on this page uses any of them, and that is deliberate: across dozens of funds the best-looking number is luck, and AVDV’s headline +2.47 on the shelf sits inside a ±3.96 band on a window chosen by nobody.

Cost, from each fund’s own filing

Fees and turnover are from each fund’s own Form 497K: iShares 2025-11-28 for MTUM (fiscal year to 2025-07-31), Avantis 2025-12-31 for AVDV and AVUV, Alpha Architect 2026-02-01 for QVAL, Vanguard 2026-04-28 for VTI and VTV and 2026-02-27 for VXUS. The cost range carries two widths at once: the trading-cost coefficient’s own 1.0-to-1.7 calibration, and the fee against the net cost.

Net cost has since been read, and it moved nothing. Form N-CEN securities-lending income is now on the shelf for AVDV (5.97 bp, so 30.03 bp net), AVUV (0.46, so 24.54), VTV (0.30, so 2.70) and four other tilt funds, beside VTI’s 1.84 and VXUS’s 3.57. No fund on this shelf has negative net cost and no verdict on this page changes, because every centre figure below is quoted at the worse end of its cost bracket and that end is the gross fee. The gain shows up only in the better end — AVDV’s incremental cost bracket widens downward from 0.31 to 0.25 — and the arithmetic is in the final construction test §2. MTUM’s and QVAL’s lending remains unread; both are rejected on turnover, which lending cannot reach. The code (FundCost.net_cost_bp) still raises rather than letting a fee be quoted where a net cost belongs.

Tax, and the assumption it overturns

The investor’s money will be spent in retirement, so there is no §1014 step-up to forgive a turnover-heavy fund’s realised gains, and roughly a third of the portfolio is taxable. The natural worry is that MTUM’s 116% turnover is a tax disaster.

It is not. From each fund’s own Form N-1A standardised after-tax table, all over the same five years to 2024-12, at the highest historical individual federal rates:

A momentum fund that rotates its whole portfolio each year distributes less taxable income than a total-market index fund, because an ETF’s in-kind redemption mechanism removes appreciated lots without a sale and momentum names carry low dividend yields. Structural and tax edges already records that “the ETF in-kind shield does not survive its turnover” for a high-turnover momentum fund at a 5% weight; on the distribution measure, for this fund, the filed evidence says it does. The two are compatible — that finding is about ranking the shelter queue, and this is about what the fund distributes — but the tax objection to MTUM in a taxable account is not supported by MTUM’s own filing.

Three limits. The table measures distributions, not the tax on eventually selling. It assumes the top federal bracket throughout. And no after-tax table was read for QVAL, whose 332% turnover decides it without one.

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4. The sleeve edge, and what survives what is already owned

The line is the repository’s: sum_k (h_fund,k − h_incumbent,k) × premium_k − cost, with no capture fraction anywhere in it — the code refuses the argument. Four premium scenarios, none of them a forecast, all carried from stacking §2.

Per dollar of sleeve, pp/yr, the range spanning the cost bracket:

Which premia can be signed matters more than which fund is picked. AVDV’s edge is mostly developed-ex-US HML, +5.07 pp/yr against a 3.67 floor — one of the two premia this repository can sign on its own panel. MTUM’s is entirely US UMD, +4.19 against a 7.27 floor — the premium is smaller than the smallest effect its own test could see. AVUV’s marginal exposure over VTV is 87% SMB, +0.33 against a 2.47 floor. Two of the three candidates are buying an exposure to something the evidence cannot establish exists.

Conditioning on what is already held

The held active position is 0.25(RSST − VTI) + 0.15(VTV − VTI) + 0.05(IDMO − VXUS) + 0.05(AVES − VXUS), built from the funds’ own filed returns. Correlations are measured, not modelled. marginal edge = candidate edge − beta × held edge, delegating to the same alpha_k / omega_k stacking §3 defines.

54 months, 2021-10…2026-03, own-panel premia at the worse end of each cost bracket. On the 30 months that include the trend wrapper the ordering is unchanged.

Pairwise, each candidate’s active leg against each held one, on the longest run of months each pair shares:

AVDV keeps about nine tenths of its standalone case. It is +0.333 correlated with the US value line and negatively correlated with both international positions already held. It is not the same bet as anything in the portfolio.

AVUV loses its whole case to VTV. Its active leg is +0.455 correlated with the held position, most of that with VTV’s own +0.430, and once that is netted off its marginal edge is negative. This is the investor’s own objection made exact: a sleeve that looks acceptable alone can add nothing in a portfolio. Replacing VTV instead of sitting beside it is a different and slightly better proposition, and it is still small.

QVAL is worse conditioned than standalone, because it is +0.505 correlated with what is already owned and its standalone edge is already negative.

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5. Momentum in two regions

Factor persistence measures one factor across three regions as worth 1.35 to 1.55 independent bets out of 3, from the research factors. The same question can be asked of the two funds, from their filed returns:

MTUM over VTI against IDMO over VXUS: ρ = +0.554 ± 0.219 over 80 months (2019-08… 2026-03). Two momentum tickers are worth 1.29 independent bets out of 2.

Beside it, for scale: AVDV’s active leg against IDMO’s is −0.124, and AVUV’s is −0.305. Adding a second region of momentum buys about a quarter of a bet; adding a different style buys more than a whole one. That is stacking’s “geography is nearly free breadth, style is real breadth” reproduced on live funds rather than on research factors.

But overlap is not what decides MTUM. At a 5% weight the portfolio-level cost of the +0.554 correlation is small — the marginal edge falls from −0.28 to −0.53 pp/yr per dollar of sleeve. The turnover charge alone is 1.13 to 1.92 pp/yr. MTUM would fail on cost even if IDMO were not held.

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6. The recommendation, in plain percentages

Centre is the marginal edge on the own-panel premia at the worse end of the cost bracket. The range carries the premia’s own standard error at 95%. The null column is what the candidate costs if every premium turns out to be zero.

AVDV: add it

Take 5% of capital out of VXUS and put it in AVDV. Ten percent is defensible and is not what this page recommends, for two reasons stated below.

• Why it earns its place. It delivers HML +0.464, SMB +0.639 and RMW +0.703 over VXUS, all three with intervals excluding zero on 78 months, and its HML sits on the developed-ex-US premium that clears its own floor. It files 4%/yr of turnover, the lowest of any factor product in either audit, so essentially none of its cost is trading. Its distribution tax drag is a hair below VXUS’s. And it is uncorrelated with — slightly negatively correlated with — both international positions already held.
• Which account. A sheltered one: the Roth, or the rollover IRA. Structural and tax edges finds that every international fund outranks every US equity fund in the shelter queue for an investor of this shape, and AVDV’s 0.78 pp/yr distribution drag is the highest of any candidate here. It is not disqualifying in taxable — it is at parity with the VXUS it replaces — but shelter is strictly better, and a 5% line fits inside a third of the portfolio easily. If the employer plan is part of the tax-deferred third, AVDV will not be on its menu; that is the captive-menu problem the recommendation records, and the answer is the Roth or the rollover.
• Why not 10%. Two reasons and neither is a measurement. Nearly half of AVDV’s gross edge is the RMW and SMB legs, whose premia are +1.68 against a 2.62 floor and +0.49 against a 2.83 floor — unsignable. And its +0.703 RMW over VXUS is partly an artefact of VXUS’s own −0.275 RMW on a developed-ex-US panel, which is emerging markets read through a developed lens; priced against VEA instead, the RMW delta is +0.416 and the sleeve edge falls from +3.60 to +2.99 pp/yr. Five percent is the size at which the unsignable half of the case does not matter.

AVUV: do not add it

Not because it is a bad fund — its delivered exposure is the largest on the US shelf — but because this portfolio already holds VTV at 15% and 87% of what AVUV adds beyond VTV is size, on a premium of +0.33 pp/yr against a 2.47 floor. Its active leg is +0.455 correlated with what is held, and conditioning on that turns +0.82 into −0.20. Replacing VTV outright is worth about +0.09% a year on a range from −0.42% to +0.60%, at 11.9 pp/yr of tracking error against 7.6 for VTV. That is more risk for a number the data cannot resolve. If the investor wants US small value on non-evidential grounds, replacing VTV is the right way to buy it and 15% is the right size; it is not an improvement this page can demonstrate.

MTUM: do not add it

116%/yr of turnover against VTI’s 3% costs 1.13 to 1.92 pp/yr, and the exposure it buys is worth +1.78 pp/yr gross on a premium of +4.19 against a 7.27 detection floor. The turnover charge alone can exceed the entire gain. Add the +0.554 correlation with IDMO and the case is −0.03% a year at a 5% weight. The tax objection turns out to be wrong — MTUM is the most tax-efficient fund on this page — and it does not rescue the trading cost.

If US momentum is wanted anyway, SPMO is the fund and it is also not worth adding. Its facts have since been read: 13 bp, 44%/yr of turnover against MTUM’s 116%, 12.93 bp of net cost, a distribution tax drag below VTI’s, and UMD +0.395 [+0.281, +0.508] delivered over VTI on 78 months — fitted on a stated window, because the shelf’s published +0.414 carries none and therefore cannot be compared with anything. At a 5% weight it is +0.02% a year, plausibly −0.14% to +0.18%. It beats MTUM on every knowable dimension and still cannot be told from zero, because the premium it buys is +4.19 pp/yr against a 7.27 pp/yr floor and its active leg is +0.626 correlated with IDMO’s — a tighter overlap than MTUM’s. See the final construction test §4.

QVAL: do not add it, and the facts are established

QVAL is Alpha Architect’s U.S. Quantitative Value ETF, CIK 1592900, series S000046016, inception 2014-10-21, benchmarked to the Solactive GBS United States 1000 Index. From its summary prospectus dated 2026-02-01: total annual fund operating expenses 0.28% (management fee restated to current), and portfolio turnover 332% of average portfolio value in the most recent fiscal year. On its longest gapless run of filings it delivers HML +0.503, SMB +0.409, RMW +0.396 over VTI — a genuinely deep value tilt — for a gross factor gain of about +1.1 pp/yr on the own-panel premia against 3.29 to 5.59 pp/yr of trading cost. At a 5% weight that is −0.30% a year on the whole portfolio, and it is the only figure on this page whose sign the data can resolve. It also duplicates what is held: +0.505 correlated with the existing active position, +0.754 with AVUV’s active leg.

It should be added to the shelf as rejected, which is done.

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Verified, assumed, open

Verified here. Eighteen published loadings reproduced on their own windows to within 0.0005 across two panels. Every delivered exposure, extra return, interval and smallest detectable effect above, from Form N-PORT Item B.5 and Ken French’s factor files. Every correlation, from the funds’ own filed returns. Fee, turnover and standardised after-tax returns for AVDV, AVUV, MTUM, QVAL, VTI, VTV and VXUS from their own Form 497K filings, each dated above. QVAL’s missing 2021-Q3 filing.

Since closed. A 10% AVDV line has been through the construction tournament, at the final construction test §1: two whole portfolios at identical gross notional differing only in AVDV give +0.28 pp/yr [+0.05, +0.56] against a 0.29 floor, and the unlevered tilt-only pair gives +0.29. Two independent routes to the same number as this page’s +0.32% at a 10% weight.

Assumed.

• Every premium is an input, carried across four scenarios; nothing here estimates one.
• Trading cost is k × turnover basis points at k from 1.0 to 1.7. On MTUM and QVAL the choice between the two ends is larger than the whole edge, and both are reported. The coefficient is the repository’s, calibrated in portfolio_edge.core.costs, and it has never been validated on a mega-cap US momentum universe where the real figure is probably nearer the low end.
• Securities lending is now read for five of the seven funds and each candidate is still charged its gross fee at the centre, which is unfavourable to every candidate. MTUM and QVAL remain unread.
• The premium standard errors are backed out of published MDE80 figures and summed rather than added in quadrature, which is the perfectly-correlated bound and the wider of the two defensible readings.
• AVES’s edge (+1.408) and the trend leg’s (+1.0) are carried from stacking rather than refitted here.
• The held position’s tracking error is measured over 54 months without the trend wrapper and 30 with it. Both are reported; neither changes an ordering.

Open.

1. Why the shelf’s DFIV and AVIV alphas differ from a refit by 0.23 and 0.25 pp/yr.
2. Whether AVDV’s +0.703 RMW over VXUS is exposure or panel mismatch. Against VEA it is +0.416. The gap is VXUS’s emerging sleeve read through a developed-ex-US panel, and the clean fix is an emerging-inclusive panel that this repository does not have.
3. Everything here rests on 54 to 78 months. That is shorter than one value cycle, and the crux of §2 is precisely a demonstration of what twenty-three extra months can do to a conclusion.

What this does not establish

• Not that AVDV’s measured extra return is positive. It is +0.68 [−1.88, +3.25] on 78 months and is not used anywhere in the recommendation.
• Not that international value “works”. §2 establishes the opposite of a clean story: the negative result for large-cap international value is a window effect, and the small-cap advantage over it is a model residual.
• Not that AVUV, MTUM or QVAL are bad funds. Each is scored against this portfolio at this moment; AVUV against a portfolio with no US value line would read differently.
• Not a promotion. Nothing here is production-eligible, no specification was frozen, and no experiment is registered.